Amazing Round of "Split or Steal"

In Liars and Outliers, I use the metaphor of the Prisoner's Dilemma to exemplify the conflict between group interest and self-interest. There are a gazillion academic papers on the Prisoner's Dilemma from a good dozen different academic disciplines, but the weirdest dataset on real people playing the game is from a British game show called Golden Balls.

In the final round of the game, called "Split or Steal," two contestants play a one-shot Prisoner's Dilemma -- technically, it's a variant -- choosing to either cooperate (and split a jackpot) or defect (and try to steal it). If one steals and the other splits, the stealer gets the whole jackpot. And, of course, if both contestants steal then both end up with nothing. There are lots of videos from the show on YouTube. (There are even two papers that analyze data from the game.) The videos are interesting to watch, not just to see how players cooperate and defect, but to watch their conversation beforehand and their reactions afterwards. I wrote a few paragraphs about this game for Liars and Outliers, but I ended up deleting them.

This is the weirdest, most surreal round of "Split or Steal" I have ever seen. The more I think about the psychology of it, the more interesting it is. I'll save my comments for the comments, because I want you to watch it before I say more. Really.

For consistency's sake in the comments, here are their names. The man on the left is Ibrahim, and the man on the right is Nick.

EDITED TO ADD (5/14): Economic analysis of the episode.

Posted on April 24, 2012 at 6:43 AM • 162 Comments

Comments

fracaiApril 24, 2012 7:38 AM

There's another factor here as well. If Abraham feels slighted by Nick's proclamation of stealing, and doesn't trust that Nick will indeed split the winnings afterwards, he may choose to Steal. Nick may be going into the choice with the thinking that they both came in with nothing, so in the worst case they both leave with nothing. By stating that he will Steal, but actually choosing Split, he guarantees that either they both receive money or at least the other walks away with a prize.

Bruce SchneierApril 24, 2012 7:38 AM

Think about Nick's strategy. He can't trust that Abraham will split. More importantly, he can't trust that Abraham will do what he said, because it's in Abraham's best interest to say one thing and do another. So he changes the game. He offers to split the pot outside the game -- set up a meta-game of sorts -- and removes Abraham's incentive to lie.

In effect, Nick turns the Prisoner's Dilemma, where both players make their decisions simultaneously, into a sort of Trust game: where one player makes a decision, and then the other does. In a classic Trust game, Player A gets a pot of money. He gives some percentage of it to Player B. It is then multiplied by some amount, and Player B gives some percentage of it back to Player A. In a classic rational self-interest model, it makes no sense for Player B to give any of the money back to Player A. Given that, it makes no sense for Player A to give any of the money to Player B in the first place. But if Player A gives player B 100%, and Player B gives Player A back 50% of the increased pot, they both end up the happiest.

Nick sets himself up as Player B, promising to give Abraham 50% of the jackpot outside of the game. Abraham is now Player A, deciding whether to give Nick the money in the first place. But unlike a classic Trust game, Abraham can't keep the money if he doesn't give it to Nick. So he might as well give the money to Nick. The game is turned on its head; trusting Nick now means letting him have all the money. Not trusting Nick means...well, it doesn't mean anything anymore. All that's left is not letting Nick have the money out of spite -- and that emotion seems out of place in the conversation. Abraham decides to trust Nick, because it's the only option that makes any sense. (Although the process is funny to watch. Abraham can't figure out what's going on. He tries to steer the conversation back to mutual trust -- how important his word is -- but it's no longer relevant. And, at the end, he first picks up the "Steal" ball before saying "okay, I'll tell you what, I'm going to go with you" and changing his mind. That bit of honesty demonstrates how effectively subterfuge was removed from Abraham's game.)

Nick, for his part, having removed the subterfuge from the game, can safely choose "Split." Although notice that he does so before Abraham chooses, so he's sure his psychological manipulation worked. I wouldn't have been so cocky.

wasylApril 24, 2012 7:51 AM

This endgame would be even more interesting if you had three choices: Split, Steal and Catch.

If both players split, they get 50% each. Steal beats split (the stealer gets 100%), catch beats steal (the "caught" player goes away with nothing), but split beats catch. If both choose to steal or catch, they both get nothing.

You couldn't do the same trick in this game, as there is always a strategy to beat the other player completely, independent of what he chooses.

MichaelApril 24, 2012 7:53 AM

Well, he's already proclaimed that he's definitely choosing "Steal", if he hesitates that might make Abraham suspect that he is being played somehow.

Simon ProctorApril 24, 2012 7:53 AM

The thing is Bruce he HAD to be confident about his ball selection. If he'd waited on Abraham picking before going for his ball Abraham might have changed his mind.
By confidently picking a ball, which could well have been the Steal ball he said he was going to take he showed that he had made his decision and was sticking to it, reinforcing the choice for Abraham.

BrettApril 24, 2012 7:58 AM

I actually think that Nick's choosing before Abraham is an important part of his strategy. It signals to Abraham (perhaps consciously, perhaps not) that Nick really has already made up his mind like he claims to have done.

AdrianApril 24, 2012 7:59 AM

I disagree Bruce, I think that confidence at the end was what finally convinced Abraham to go along with Nick's plan. Abraham originally picked up his steal ball, but quickly switched it at the last moment, probably because Nick's quick choice and continued insistence that he would steal made him believe that Nick would be true to his word.

Rob van SteeApril 24, 2012 8:01 AM

What are the last few words of the video? "With the money I've won, I'll go..."? I want to know because the other player looks so shocked at this!

JakobApril 24, 2012 8:02 AM

I remember watching that episode when I was at the gym. I'd watched a few episodes and tried to work out a way to do what Nick did, in an idle way, and it was pretty awesome to watch someone actually do it. I differ in my reading of Nick's actions at the end though - I think he chose Split because he believed his own logic, not because he was cocky.

Firstly, his confident choice of ball let's Abraham know he is confident. If he let's Abraham choose first, that implies he's not as set on Stealing as he stated, and that might influence Abraham's choice.

Secondly, in a very real way it's irrelevant which ball he picks. If Abraham believes him, and chooses to Split, then he get's the money either way (assuming he's not planning on going back on his promise). If Abraham chooses Steal, all Nick's choice can do is deny Abraham the money, which doesn't benefit Nick, so why would Nick choose Steal?

Marc Moisan April 24, 2012 8:19 AM

Bruce, He might as well choose his ball before Abraham because he has nothing to lose and everything to gain. Either his psychological manipulation worked and Abraham will choose "split" or it failed and Abraham will choose "steal" out of spite. In the latter case, Nick lose anyway and may as well give it to Abraham.

ChelloveckApril 24, 2012 8:21 AM

Because iocaine comes from Australia, as everyone knows, and Australia is entirely peopled with criminals, and criminals are used to having people not trust them, as you are not trusted by me, so I can clearly not choose the ball in front of you.

John HApril 24, 2012 8:36 AM

Yes, unless Nick intends to renege on his promise to split the money after the game, there is no situation in which 'steal' is the right choice.

The best outcome in either case is that he gets half the money. The worst outcome if he steals, is that nobody wins. The worst outcome if he splits is that Abraham gets all the money -- which in my world is a better result.

If you want to take a selfish view, Abraham getting everything is still a better result than nobody getting anything, because you'd have a chance to guilt-trip him into giving you some of it after the game.

JonadabApril 24, 2012 8:43 AM

Nick has effectively said, "I don't trust you, but you can still get something if you trust me."

The choice from Abraham's perspective (assuming he believes that Nick is indeed going to take the "steal" ball as he says -- I suspected that he might not, but I don't think Abraham saw that coming) is much simpler than in the usual case: it's a choice between guaranteed nothing and the possibility of something. The only reason to take the guaranteed nothing of the steal ball would be, as others have pointed out, spite. Given that they were strangers before the show, spite is not a particularly potent motivator; consequently, the optimistic desire to believe that he might indeed still be able to get half the money is able to overpower it.

It would NOT work (for most people) if they'd known one another for a long time, because in that case the feelings of betrayal (at not being trusted) would run deep enough to overcome the promise of a few thousand pounds (between $10 and $11 thousand at the current exchange rate). But Nick is a stranger, so the fact that he doesn't trust Abraham doesn't hurt so badly. We're somewhat accustomed to the idea that strangers don't necessarily always trust us. It still stings a little (if nothing else, the explicit, stated nature of Nick's distrust comes across as more blunt than is usually socially acceptable), but the feelings of betrayal and spite have to do battle with the desire to believe that it might still be possible to salvage half the money -- if Nick is honest, which seems like his only obvious motivation for saying he's going to take the steal ball.

Note Abraham's comment that choosing the split ball was actually rather hard work for the money. He wasn't *comfortable* trusting Nick, and it was difficult for him to do so. He only did because he felt that he had no other way to get any of the money.

robmanduApril 24, 2012 8:56 AM

Future players that have seen this episode will now be wise to this tactic.

The next guy who promises 100% that he'll "steal" and share the winnings after - and then actually chooses "split" - will find the other player has chosen "steal" knowing the ploy at hand.

The end-game's premise of Prisoner's Dilemma is kept intact. Addressing Bruce's point in his comment above, there is no meta-game now (nor was there ever really, just the idea that there might be).

McGroartyApril 24, 2012 8:56 AM

Nick's compelled Abraham to play to the audience, with Abraham placing his character above Nick's. Abraham made various indignant moral declarations about the right thing to do, and enjoyed placing himself as something of a victim. Nick's responses were abrupt and uncompromising, yielding Abraham as much time as possible to respond by escalating his statements about himself.

Had Abraham chosen Steal in retaliation, his public declarations still stand. He would have to offer the same after-the-show split, or he would face being a very public hypocrite. The public would not be kind to the man who monologued about his character and victimhood, then victimized a man who gave better than he promised.

I'm not sure that this was about forcing a choice. I believe Nick bettered the odds that an opponent's "Steal" ends up shared as a split.

AnonApril 24, 2012 9:01 AM

@Rob van Stee
"spray my yacht" were the last words spoken, he was indicating he was already rich/well to do and or just jabbing Nick via braggadocio. I'm going to get my yacht repainted and then sink it, it's only money, muahahah. It's british humor, what can you do.

RandyApril 24, 2012 9:06 AM

My first instinct would be to turn Nick's suggestion around on him and tell Nick to trust *me*.

PJ's example with the man and woman is probably the more common outcome.

Does anyone know the split/steal ratios for the end game?

For me, my internal emotions and giving nature might prevent me from stealing. I wouldn't want to be known as the man who stole...even if it was a game. However, being known as the sucker might be just as bad. I like Nick's strategy.

Randy -- trustme

Bruce SchneierApril 24, 2012 9:09 AM

Interesting point from several of you about Nick's confidence and his picking first. I think you're right.

hohumApril 24, 2012 9:13 AM

A more powerful variation would be to offer the same deal but without looking at the balls at the beginning, stating that you will pick one at random.

The other player is then forced to split or risk walking away with nothing.

mooApril 24, 2012 9:15 AM

Oh come on, it wasn't *that* amazing. As soon as the guy said "I'm going to steal" it was obvious what the outcome would be.

If his opponent thought that he was going to pick "split", then the opponent would have an incentive to pick "steal". He bluffed to remove that incentive--to convince his opponent that the options were "split and maybe get something" or "steal and definitely get nothing".

mooApril 24, 2012 9:30 AM

I have a better strategy you can use, if you trust your opponent. It's basically the dual of Nick's strategy.

Say to your opponent "You pick steal, and I'm going to pick split. You get all of the money, and we'll split it 50/50 after the game." Get him to say something that indicates agreement. Then be true to your word and pick split. (You can pick first, with confidence, but it doesn't actually matter).

Your opponent now has no incentive to pick split: at best they will end up with the same amount of money. At worst they will lose it all if you were bluffing and actually chose steal... but they can probably assume you wouldn't choose steal because that would be the "spite" action and would cause BOTH of you to get nothing.

If your opponent does what you suggested and picks steal, then he wins all of the money, and then you ask him for half after the game. If he won't give it to you, you sue him in court for breach of (verbal) contract!

aynonymousApril 24, 2012 9:41 AM

> the conflict between
> group interest and self-interest

This was definitively settled by a Hollywood-screenwriter-turned-New-York-author who despised "flyover country".

If everyone acts in a purely selfish manner, a perfect equilibrium will be achieved.

BebrehemApril 24, 2012 9:44 AM

I think that Nick has split the game into two phases where there is only one optimal strategy. With Nick declaring that he will definitely steal, Abraham has no choice but to split, because that's the only way for him to get some money. But once Abraham is going to split, the best strategy for Nick is to take split, because then at least one of them will get something and maybe they can work it out afterwards.

Put differently: by making the offer, Nick isn't playing to get everything, he's merely playing to avoid the steal-steal outcome. He's ok with getting only half the money.

The point is probably that Nick's announcement determines Abraham's optimal strategy.

Chris WApril 24, 2012 9:55 AM

@wasyl

Your suggestion changes the game to a simple game of rock, paper, scissor and turns it away from a confidence/trust game into a chance game.

The most interesting part about that episode is that Nick basically cheats the game. He defeats it by changing the dilemma of 'Greed vs Trust' into a 'Greed vs Revenge'. He kept repeating 'Trust me' over and over, just to give more weight to Greed than Revenge, but his intent was to remove the Trust factor entirely. A very slick social game.

Note that Nick's choice to actual choose Split (despite saying he would take Steal) indicates he didn't want to risk losing everything due to a double Steal. Meaning he was probably trustworthy, and would've split out-of-game.

Abraham's initial choice of Steal might be Revenge driven if he believed Nick, or Greed driven if he thought Nick would choose Split anyway and wanted all of it for himself, either reason would be a good indication he is untrustworthy.
I believe it's the later, Abraham only changed his mind because he saw Nick pick up the ball without hesitation realizing he would lose everything.
Nick's uncompromising stance was vital, absolutely vital, otherwise Abraham would've picked Steal... definitely.

I'm not sure what to think of this 'game' though. There is a 3 in 4 chance one player gets away depressed. Still, excellent 'research'.

John David GaltApril 24, 2012 10:02 AM

I would be surprised if such an outside-the-game deal is even allowed by the players' contract with the TV show. Other game shows, such as The Weakest Link, specifically forbid such things, and I would expect the rule to be upheld if it ever gets to court (not to mention that if a dispute does go to court, then the lawyers are going to end up with most of the money anyway).

@Marc Moisan: I think you have it backwards. If my opponent has in fact chosen Steal, then he's made it impossible for me to get anything, so to hell with him: I'm going to choose Steal in return. That way, if he's telling the truth, he gets his just deserts, and if he isn't, it serves him right for lying.

DoubleDownApril 24, 2012 10:04 AM

@PJ

I have never heard of Liv Boree and I watch and play a lot of poker (though I've been out of the scene the last couple of years). But I will guarantee Tom "Durrr" Dwan would roll her heads up. ;)

Speaking of interesting game show intellectual exercises, I assume most of you are familiar with the Monty Hall Problem. This problem was made famous by "Let's Make a Deal." The problem is essentially as follows:

Suppose there are 3 doors. Behind one of the doors is a car and behind the other two doors are goats. The host knows what is behind all the doors. At any rate, you select a door #1. Instead of opening your door, the host opens door #3 to reveal a goat. He then asks you "Do you want to open door #1 as you originally selected or do you want to switch to door #2?" What should you do? Stay with door #1 or switch to door #2?

This question was posed to Marilyn Vos Savant in her Parade Magazine column back in 1990. Marilyn is famous because she at one time had the highest IQ on record (Guiness Book). A psychologist estimated her at 220 when she was a child. But to be fair, one can't use childhood IQ scores and make them scale to adulthood (I am really digressing here, but basically modern psychometrics makes a distinction between ratio IQ scores and the more modern method of deviation scores. If Marilyn were measured as an adult she would probably be in the 185 range -- or about 1 in 20 million rarity assuming a S.D. of 15).

As I said, Marilyn got the Monty Hall problem posed by a reader in her column. Her answer was that you *should* indeed switch your pick and go with door #2. She said going with door #2 gives you a 2/3 chance of getting the car, while staying with door #1 is a coin flip.

She got lots of reader mail from PhD mathematicians and other academics saying she was wrong. They claimed it was 50/50 no matter which door was selected. However, it turned out the academics were wrong and Marilyn with no college degree or formal math training (which is incidentally why the academics love to pick on her) bested them all. Do you know why?

Don't cheat and Google it. ;)

BenApril 24, 2012 10:13 AM

It's not a situation where you can trust the other person's word. Whatever they say, you're aware that getting you to pick split is what they're trying to do.

You might be able to make better or worse gambles - after all if they lie they've put an upper bounds on the value of their word. And if I know your word is only worth a few thousand pounds I'll never give you a job as long as you live. But even then they might gamble no-one's liable to remember in a few years....

Nick could, after saying he was going to steal, pick split and /still/ have got outdone by the other guy.

#

The obvious solution would be to show the other guy your balls. But I suspect that's against the rules.

It's not immediately clear that agreeing to split the money after the game doesn't constitute a verbal contract, either. In which case that would be a very good strategy.

AnotherAnonApril 24, 2012 10:16 AM

Nick doesn't win Abraham's trust at all in this game. Appropriately so, because Nick's choice solidly shows he lied. Promising to steal, Nick changes Abraham's decision from, "Do I take a chance by stealing (or sharing)?" to, "Do I give Nick the money or not."

Nick uses the outrageous surprise of telling Abraham that he'll 'steal' and builds a level of credibility. Had he pushed for mutual sharing, no one should believe his intent was sincere. While its outcome is uncomfortable, this choice has enough shock value to force Abraham to rethink his strategy. Now he's doing damage control instead of persuasive negotiation. Furthermore, if Nick is bluffing, the outcome can only benefit Abraham.

Promising to share the winnings after the show is mostly a distraction. Abraham does not appear convinced that Nick plans to follow through on the offer. Perhaps some might mistake Nick's steadfastness with trustworthiness. Still, this strategy does little to control his opponent's choice. It merely depends on how generous Abraham cares to be.

I think this would have been an equally interesting round had Abraham stayed with 'steal' instead!

anonApril 24, 2012 10:29 AM

Reminds me of how the mafia solved the prisoner's delimma; kill the rats. In both cases they're taking control outside the game, and removing the incentive to defect.

But in the real world (multi-round), you need to follow through. You need to steal, and maybe hand over some of the money. By announcing he would steal, he's laying down the law. It's important for the other guy to know that the money is coming from Nick's hand, and not someone else. When you play this strategy you can never let anybody believe they can cheat you. If someone challenges you, you need to deny them, even if it means hurting yourself.

Nick was smart, but played too soft. He'll get taken when playing against a tougher opponent.

JoeNotCharlesApril 24, 2012 10:32 AM

@hohum: You're right, that's a great strategy. Don't even look at your balls, and tell the other person you're going to pick at random, and that if you end up with all the money you'll split with them after the show.

Then if they pick split, they're guaranteed half the money (if they trust you) or have a 50% chance at half, and 50% chance at nothing (if they don't). If they pick steal, it's a 50% chance to get all of it and a 50% chance of nothing, whether they trust you or not. Hmm, maybe not so great but it does change their calculation. Depends on how risk-averse they are.

David ScrimshawApril 24, 2012 10:33 AM

I wonder about how this will affect Nick in the rest of his life.

He has demonstrated that he will share with others, but he's also shown that he's not exactly honest or at least that his threats might not be honest.

I hope for his sake that he's not in a profession where this will hurt him.

JJoensuuApril 24, 2012 10:35 AM

@DoubleDown
A question about what you write:
However, it turned out the academics were wrong and Marilyn ... bested them all.

The question is about that I am not able to find information showing that this has been empirically tested. I thought that would be the case in order to conclusively determine who was correct (Marilyn or the academics with contrary view).

Do you know if any proof exists?

Additionally in my opinion the idea of a probability RATIO can be ignored in the particular problem stated in Marilyn's column. Instead the game contestant should keep 2 questions in mind AFTER door #3 has been opened:
A. my choice is now ONLY between door #1 and door #2, what is the probability to choose the right door when it is one of two (the answer is: 50%)?
B. next to these two doors is an open door #3. Does this open door somehow affect the probability of the car being behind either #1 or #2? (the answer is: an open door next to #1 or #2 does not have any effect)

If you replace door #3 with a window with a goat standing behind it, would you believe that somehow affects which one of the doors #1 or #2 has the car?

Part of the problem was that Marilyn was thinking in terms of A CHANGE in probability which whould change when one of the doors can be removed. The contestants original probability to choose the correct door was 1/3. After being displayed one door that can be ignored, the probability of the contestant having chosen the correct door increases to 1/2.

However this change in probability is only because one door can be removed from consideration. Doors #1 and #2 can (and should) after that be viewed in isolation.

Another part of the problem was that Marilyn was adamant that she is correct even when she was shown she was wrong. But refusing to admit defeat does not necessarily make her viewpoint correct.

John David GaltApril 24, 2012 10:47 AM

@JJoensuu: The proof is obvious. (You may want to verify this by playing out a few rounds of the Monty Hall scenario, with cards or something).

The key fact is that if your first pick was not the winning door (which is true 2/3 of the time, and is NOT CHANGED by what Monty shows you afterward) -- then by switching, you will always wind up with the winning door.

whidbyApril 24, 2012 10:52 AM

I think that "trust" played less of a role into Nick's success than the potential for public humiliation.

From what I understand, the game usually centers on each contestant trying to convinc the other that they will pick share. So trust is essential. Here Nick announced to the world - and perhaps more importantly to the studio audience - his intention to steal.

So if Ibraham stole, he would look like a fool in the face of Nick's clearly announced intentions.

In the usual scenario, everyone knows that there is bluffing and people trying to create trust so a "wrong" decision isn't really subject to public ridicule.

hash1babyApril 24, 2012 10:58 AM

@hohum That would decrease Nick's expected pay-off.

Abraham expects pay-off for selecting "split" as (1 + t) / 2 where t is the probability that Nick would honour his promise to split post-match. But for the case of selecting "steal", his pay-off is (0 + 2) / 2. So unless Abraham has absolute trust in Nick, he should choose to steal. He doesn't even suffer the opprobrium of breaking a deal.

Matthew WeigelApril 24, 2012 11:05 AM

@JJoensuu: You can write a simple simulation in any programming language you like to verify it. Run it a thousand times and see what happens.

IsaacApril 24, 2012 11:05 AM

If your opponent does what you suggested and picks steal, then he wins all of the money, and then you ask him for half after the game. If he won't give it to you, you sue him in court for breach of (verbal) contract!
Absurd. It's within the context of a game where you agreed that lying was possible. Nothing binds you legally to be truthful.

It's like claiming you're going to sue someone after lying at Poker.

Bruce SchneierApril 24, 2012 11:09 AM

"Oh come on, it wasn't *that* amazing. As soon as the guy said 'I'm going to steal' it was obvious what the outcome would be."

But that's exactly why it was amazing.

DoubleDownApril 24, 2012 11:10 AM

@JJoensuu

Yes a proof exists, and Marilyn was right. She provided proofs for it and others have since provided others. The proofs are quite simple really.

Part of the problem is that the original question is like a riddle in some ways. However, even when the question was made more clear (and revised by mathematicians later for clarity), one study consisting of 228 participants showed that only 13% decided to switch doors.

I will not repeat a lot more here since the Wikipedia article on "the Monty Hall Problem" covers all of this in detail.

However, I did find this quote from the Wiki article quite telling, as it gives an interesting insight into human psychology:

In her book "The Power of Logical Thinking", vos Savant quotes cognitive psychologist Massimo Piattelli-Palmarini as saying "... no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer."

So apparently even a Nobel Prize winning physicist got it wrong.

And this:

"This "equal probability" assumption is a deeply rooted intuition (Falk 1992:202). People strongly tend to think probability is evenly distributed across as many unknowns as are present, whether it is or not (Fox and Levav, 2004:637)"

And finally:

"The problem continues to attract the attention of cognitive psychologists. The typical behaviour of the majority, i.e., not switching, may be explained by phenomena known in the psychological literature as: the endowment effect (Kahneman et al., 1991); people tend to overvalue the winning probability of the already chosen—already "owned"—door; 2) "

Anyway, I thought this problem fit in well with the topic of the thread. Sorry if I sidetracked anyone. ;)

Bruce SchneierApril 24, 2012 11:13 AM

"A more powerful variation would be to offer the same deal but without looking at the balls at the beginning, stating that you will pick one at random. The other player is then forced to split or risk walking away with nothing."

That's a really good idea, but it works less well in the context of the game show. The host has the contestants peek, and then converse. Nick would have to declare "I'm not looking" By talking out of turn.

Also, I think, it's a little harder to explain to the other contestant.

Fred PApril 24, 2012 11:30 AM

@DoubleDown - I recall that.

The simplest way of describing the proof is that originally, you had a 1/3 chance of selecting the correct door. Opening an incorrect door after that does nothing to change the fact that you had (and still have) a 1/3 chance of being correct (given that the host will always open an incorrect door - apparently, that wasn't always done on the show this problem was based off of).

The rest of the probability of being correct is now in the door you didn't select, which is 2/3.

Ben FApril 24, 2012 12:18 PM

I've come across this method of "breaking" the prisoner's dilemma before. I guessed what the method in the video was before watching it (I seem to recall another television show which presented the same problem, only maybe the person removing the incentive to lie was only willing to give 40% instead of 50%), though I wasn't too sure if Nick would choose Split anyway.

I thought it could be more interesting if both parties had thought of this solution already. In which case, why trust Nick will bother picking Steal, maybe he'll just pick Split? That is not altogether rational, but in Nick's position, Split would be my choice, because the idea of trying give away a large sum of money makes me think of tax ramifications and other headaches. So now, in Abraham's shoes, I have an incentive to Steal anyway. Because Nick still actually has an incentive to lie. At least, he lied anyway.

But this kind of thinking can go on forever. I just don't think trust is no longer necessary, because you can't even be sure a party won't lie about their intention to defect. It just potentially lowers the consequences of trust... rationally, anyway. It seems like there should be a better way of saying that last sentence, but I'm not thinking of it.

J.D.April 24, 2012 12:32 PM

Quoth hohum: "A more powerful variation would be to offer the same deal but without looking at the balls at the beginning, stating that you will pick one at random.

The other player is then forced to split or risk walking away with nothing"

That actually seems like a much worse strategy. The non-random player (NRP) can choose either to split or steal. If he splits, and the random player (RP) indeed chooses his ball at random, then there is a 50% chance of a split-steal combination (NRP gets 0) and a 50% chance of a split-split combination (NRP gets half the prize). But if the NRP chooses steal, there is a 50% chance of a steal-steal combination (NRP gets 0), and a 50% chance of a steal-split combination (NRP gets whole prize). So, instead of being "forced to pick split", in purely expected value terms the only rational choice for the NRP is to choose steal.

Dave PageApril 24, 2012 12:36 PM

moo, I think you'll find that a verbal contract isn't worth the paper it's printed on here...

Nyhm, the presenter is standup comedian Jasper Carrot, not Baldrick actor Tony Robinson.

MichaelApril 24, 2012 12:42 PM

By offering the possibility of a payout in the case that Abraham ends up on the losing end of a Split-Steal aren't they changing this from a case of Prisoner's Dilemma to one of Chicken (i.e. the double defection is strictly the worst outcome for either party)?

NyhmApril 24, 2012 12:44 PM

@Dave Page: Nuts, I was so sure it was Tony Robinson, I didn't even bother to look it up. I retract my former comment.

Timm MurrayApril 24, 2012 12:46 PM

Another wrinkle: taxes. I'm not sure if UK taxes work this way, and I'm not even sure how US taxes apply in this case, but I think the ramifications are potentially interesting.

Assume Nick takes all the cash at the table and makes good on his split offer afterwords. To make the math easy, let's say he gets 10k and taxes are 10%.

Nick takes the cash and the government takes 10%, leaving 9k. If Nick splits it before taxes, then Abraham gets 5k and then the government gets 0.5k from him. The government took 1.5k total. Abraham has 4.5k and Nick has 4k.

If Nick splits after taxes, then Abraham gets 4.5k and then the government takes 0.45k. Government takes 1.45k total. Abraham is left with 4.05k and Nick with 4.5k.

mooApril 24, 2012 1:02 PM

@Fred P: It sure is an interesting problem...

A good way to see how it works is to increase the number of doors, say to 1000.

You have a 1/1000 chance of picking the correct door at the beginning, and a 999/1000 chance of NOT picking the correct door at the beginning. Those probabilities don't change, even while the host opens 998 incorrect doors. But the entire 999/1000 probability ends up being concentrated in the 1 door he didn't open.

In effect, if you picked the correct door at the beginning, then the host's choices are random and meaningless, because all 999 of the other doors were incorrect doors. But there's only a 1/1000 chance that you picked correctly. The far more likely outcome, is that you picked an incorrect door, and the host now has to "randomly" open ALL of the 998 other incorrect doors, while avoiding opening the winning door. If you switch, its like choosing all 999 of the other doors simultaneously! Because you only need to find the 1 winning door, and the host ruled out 998 non-winning doors for you, which has the effect of concentrating all of their chances of being the correct door behind that single remaining door.

DavidApril 24, 2012 1:05 PM

Semi-OT but I was appalled at what Liv Boeree did. Poker players will and should bluff at the table. But outright lying is over the line.

Did she consider this a poker game? I don't, and I play in plenty of them.

Ben RosengartApril 24, 2012 1:23 PM

@JJoensuu: I suggest you play the Monty Hall game with a paper and pen and a friend. I did this with my brother, and it did not take many rounds before we had convincing empirical proof.

John David GaltApril 24, 2012 1:25 PM

@Timm: I'm a tax professional. The IRS does not tax gifts unless they're in the range where the gift might otherwise evade estate tax ($2M+). Thus in the US, you would split the sum after taxes (simple to do if the winner knows which bracket he's in) and the recipient would not be taxed further.

Not sure what the UK would do, though.

Paul JohnsonApril 24, 2012 1:53 PM

This reminds me of a PD game I played on a management training course for beer money. We were split into two teams, and as it happened both teams had someone on them who had read The Evolution of Cooperation and knew about "tit for tat". I happened to be that person on my team. So we played T4T, and so did the other side, until the last round, where they defected.

Then we met up and headed for the bar. At this point the other team wanted to split their "ill-gotten" winnings with us, but everyone on my team refused this offer. It was at this point that I got a fundamental truth about finite iterated PD: there is no such thing in the real world. The formal game was over, but the real game continued.

Robert ThilleApril 24, 2012 1:59 PM

The nice thing is that even if Abraham took steal, then Nick could say, "See, I was just trying to make sure one of us got the money so we could split it. Now give me 1/2."

keithApril 24, 2012 2:53 PM

Very cool. I don't understand why Nick chose split though. Surely that ruins it for anyone in the future?

I've played poker with Liv Boeree and she's a better actor than that, or maybe you get distracted more in person, she's very flirty. I was sure the other guy was lying too though.

It's Ibrahim not Abraham, btw.

FigureitoutApril 24, 2012 3:23 PM

Just from the examples given, did anyone notice how the females seemed to be less trustworthy..? My decision to steal or split might be affected if my opponent is of the opposite sex...

The decision is also affected by the publicity of the t.v. show and the audience. This goes back to the societal/reputational pressures Bruce talks about that are more likely to coerce people to act truthfully.

If this was played in a basement somewhere I think people's underlying greed might shine a little more freely...and it may devolve into a scene from "Fight Club"...

BasilApril 24, 2012 3:38 PM

This is no different than convincing someone else to split some other way. If Abraham could have instead said "Cool idea, but instead of me trusting you to trade me half after the game, I promise you I will steal and you have to trust me to split it with you after the game", and we'd be back to a the initial situation, essentially.

One potential strategy in terms of bargaining about who would steal could be to offer more than half: "I'm asking you to trust me and you're asking me to trust you. If you choose to trust me, I'll actually give you 75%" or something.

DavidApril 24, 2012 3:39 PM

Some have commented that the strategy won't work in the future. Maybe not if the split is 50/50. Suppose the future Nick character offers a different split, say 60% to future Abraham. Playing the meta-game changes everything.

Mike ScottApril 24, 2012 3:39 PM

@Timm, there are generally no taxes payable on prize winnings in the UK.

tddApril 24, 2012 3:51 PM

One thing that jumps out at me that hasn't been mentioned by you or the other commentators is this: While the presenter is explaining the rules, at around 1:25 in the video Nick becomes absolutely fixed on Abraham's eyes, as if to size him up.

MsasApril 24, 2012 3:57 PM

Maybe by having the possibility to split the money “out of band”, beyond the game, it stops being a prisoner’s dilemma.

Say if they don’t know each other, don’t have ways to communicate after the show and their word is not binding in any way. For instance, one is Australian and the other is American and the money is deposited in their respective bank account in 30 days. Then Nick’s offer does not make sense.

Andy CunninghamApril 24, 2012 4:10 PM

Just one point - this is a UK gameshow and winnings are non-taxable, but gifts can be. So the complexity is that given the money after the show, the recipient could then have to declare it as income, but the show winner pays nothing.

Good bit of social engineering, though.

BCRApril 24, 2012 4:12 PM

What happens if you agree to choose each other's balls?

I choose one and give it to you.
You choose one and give it to me.

There's no incentive to give the other person a steal as far as I can tell. Job done. No trust required.

DavidApril 24, 2012 4:28 PM

@tdd I noticed in the Liv Boree video, she was DEFINITELY "reading" her mark.

MApril 24, 2012 4:46 PM

@BCR Wow, that's really clever! But I guess it would not be allowed on the show.

Cosmo WenmanApril 24, 2012 5:26 PM

In normal gameplay of this type, a liar steals: the lying move is to steal and vice versa; the stealing move is to lie.

Nick reversed this, making it so his lying move would be to share. Nick was saying, "If I lie, I lose, or win less, not more" which is an unusual place in the lying/truthful: win/lose matrix.

Classic prisoner's dilemma breakdowns are usually conditional on both parties being incommunicado, and on there being limited (usually one or few) rounds of play.

The game here allows for communication, and deal making. Which is a big relaxation on the normal prisoner dilemma constraints. As well, the game allowed them to *explicitly* bargain with each other about monetary transactions after the show. I bet Jeopardy doesn't allow that!

Everyone - players and audience alike - know that all's fair within the show, and potential damage to the player's reputations - even a lying player's reputation - is limited by the fact that everyone knows its a cutthroat game, and that it's "just" a game. By offering a deal to settle up after the show, Nick brought his real-world reputation into play. If he walked off the set with all the winnings, then didn't share them, people would find out and he'd look like a cad in real life. In promising a move to take place after the game, Nick accomplished two things: he was able to extend the limited rounds of play beyond the scope of the normal show, which in itself created at least a psychological allusion to further moves during which cooperation seems more likely to pay off. And he was also able to increase the reputational penalty he would bear in the real world if he cheated - thereby giving Ibrahim more reason to trust him.

The fact that Nick actually shared in the end was inconsequential. If he intended to split the earnings, he could have stolen, then paid out after the show. But he might as well have settled up right then and there by sharing -- and lying!

JockoApril 24, 2012 6:11 PM

What would happen if you proposed that you compare tax brackets and that you both agree to have the player with the lower tax bracket take down the whole prize? Then there would be an agreement to give over half of the after tax winnings over to the other (since it will be under the gift tax threshold... at least in the US). It might be such a seemingly honest idea that it would build trust with your opponent and make it more likely that the post game split would actually happen. It essentially goes into so much detail that it is a bigger reneg to back out of it.

AaronApril 24, 2012 6:53 PM

Re: Monty Hall above
If anyone is interested, I wrote up a simulator for this a while ago -- you can do sample sizes up to 10,000. It consistently shows ~66% success for switching and ~33% for staying.
The URL is: http://amhill.net/projects/montyhall/index.php and the source code is listed directly below the simulator.

Re: the original video
Brilliant.

As an addendum to some of the other points about Nick's cockiness -- I think he *HAD* to confidently pick his choice, whichever it was going to be, IMMEDIATELY and with confidence; if he hesitated, waffled, or gave ANY indication that he was making his choice conditional on Abraham's decision, Abraham would have *NO* reason to trust him at all. As Bruce pointed out, the elimination of the subterfuge was completely predicated on Abraham trusting Nick to be honest about his treachery.

eckenheimerApril 24, 2012 7:14 PM

On the Monty Hall problem. I didn't find Marilyn Vos Savant's argument convincing, even though she's right.

Here's my explanation: Let's say Monty's feeling generous and allows the player to pick TWO doors at the beginning. When both are then opened, the odds of winning are obviously 66.7% or 2 out of 3, and it doesn't matter in which order the doors are opened. Aren't the odds still the same if I tell Monty, "I'll pick door number 1, and if that isn't the right one, then I'll pick door number 2"? The odds are the same whether you pick the doors one at a time or both at once.

For those who insist that the odds change to 50% once there are only two doors, consider whether that is true if you start with 4 doors, or 10, and are allowed to keep choosing until only one is left. In that case, for N doors where you get to pick all but 1 of them, you have a N-1/N% chance of winning. So, for 4 doors, you have a 75% (3 out of 4) chance of winning, and for 100 doors your chance of winning goes up to 99%.

AlApril 24, 2012 7:40 PM

Why would I trust people who can't get the guy's name right? Ibrahim NOT Abraham, FFS

JoeApril 24, 2012 8:15 PM

Nick's offer to split the winnings is not really relevant; it's just a way to reinforce his commitment to choose Steal. Nick needs to convince Abraham that, no matter what, he is committed to Steal. One possible pitfall is if Abraham decides Nick is "too nice", so by offering to split the winnings, Nick makes it all the more believable that he'll choose Steal. It really doesn't matter if Abraham believes Nick will split the winnings; it only matters that he believes Nick will Steal. See Thomas Schelling's Theory of Bargaining.

Chad ParryApril 24, 2012 8:43 PM

At the beginning of any game, either player has the chance to announce that they will choose "Steal," just like Nick did. So you can define the meta-game: A player may make an irrevocable announcement that they will choose "Steal." We'll call this move "Defect." Or the player can announce that they are choosing "Split" (although in that case they are incented to lie). We'll call this move "Cooperate." If both players choose "Defect," then they get no money. If both players choose "Cooperate," then they get a better outcome: the chance to play Prisoner's Dilemma and possibly win money. Obviously the meta-game is just a round of Prisoner's Dilemma.

I recall someone making an observation about the game of Chicken. They said that the best possible strategy would be to unscrew your steering wheel from the car, and toss it out the window, in full view of your opponent. Once they know that you are committed and you can't swerve, you are guaranteed to win.

TybaltApril 24, 2012 9:30 PM

"moo, I think you'll find that a verbal contract isn't worth the paper it's printed on here..."

You'll find that's incorrect.

WernerApril 24, 2012 9:43 PM

@Cosmo Wenman: I think that's exactly the point - replacing the agreement with the game persona, who is fully expected to lie and cheat, with a public agreement with the real person, who is expected to behave.

I don't see it as a weakness on Nick's side that he chose to split. I see it as an elegant way of actually staying within the formal limits of the game, adding another twist and making him take home a spectacular psychological victory.

In the case of the poker player, this may not work, a) because she may count on her opponent to choose to split, and b) because she may consider her non-game persona to be the poker player, who is still expected to lie and cheat.

What may work in case a) is, once both sides have expressed their agreement to split, for her opponent to promise to split out of game in case he should by some twist of fate end up showing the steal ball, and to ask her to make the same promise. She should have a hard time wriggling out of reciprocating. Of course, in case b) she wouldn't keep the promise.

- Werner

Petréa MitchellApril 24, 2012 10:20 PM

Finally got a chance to watch the video!

What Nick does is turn it into an ultimatum game-- once he's declared he'll pick "Steal" no matter what, Abraham/Ibrahim has to choose between an arbitrary division (since Nick has control of the money, there's no guarantee of 50%) and a sure outcome of nothing at all.

JPWApril 24, 2012 10:21 PM

Personally I was more interested in how the contestants displayed trust toward the game show.

After all, both checked both gold balls. . . .

mathewApril 24, 2012 11:04 PM

Liv Boeree actually made a small tell

in this video. Although pretending to be open and trusting, she is actually very secretive when she flips open her ball, like a practised poker player checking her cards.

RandallApril 24, 2012 11:56 PM

Rock, Paper, Scissors, winner steals, loser splits, after both promise to split it after the show. Would that have any interesting differences in strategy or psychology?

PaulApril 25, 2012 12:05 AM

Nick actually does let Ibrahim choose first before picking up his own ball. The weird part is that Ibrahim changes his mind after Nick grabs the Split ball. I think Nick grabbing the Split ball first may have helped him if he had done it, but I don't think Ibrahim noticed and changed his mind solely on the strength of Nick's chicanery.

WernerApril 25, 2012 12:20 AM

@BCR: one way how this could be defeated is if one party swaps their balls ("own" with received) after the exchange. Of course, that would have to be done in a way that prevents retaliation by the opponent. Not sure if that's feasible within the framework of that game.

What's nice about your approach is that it doesn't even require the other side to understand how it works, as long as they agree on doing the exchange.

- Werner

QnJ1Y2UApril 25, 2012 12:58 AM

@DoubleDown
Your sidetrack resulted in a demonstration of what we should call the 'Monty Hall Law':


Every statement of the Monty Hall problem will have at least one reply that is emphatic, argumentative, and wrong.

I've had some interesting experiences with this problem. Even after I have (repeatedly) described the solution to people, they are often unwilling to move from their initial "it's 50-50" intuition. Basically, they trust their 'gut' more than they trust a logic-based argument, even when they cannot find holes in the logic.

MavisApril 25, 2012 1:46 AM

I also wonder if a key aim is ensuring the money remains 'in play'.

By picking split- What ever Ibrahim chose the money remained in play - and having set up the idea of 'splitting after the game' Nick had a chance of that happening (and thus getting something) where as once the money is back in the hands of producers - your never going to get it......

FentexApril 25, 2012 2:25 AM

This reminds me of an episode in my families life.

My parents live on a section set back from the road behind, and surrounded by, neighbouring properties.

The neighbour immediately between them and the road has a gate in their fence onto my parents driveway that provides easy access to the rear of the neighbours property.

That neighbour asked my parents to sign a legal covenant gauranteeing access to that gate so as to leave no doubt to anyone that the access was available.

My parents, being honest and trusting, were inclined to agree but us more cynical children argued to dissuade them on the basis that they would be making it easy for their neighbour to subdivide his property and possibly build multi-storied apartments that would shade and overlook them, an option unpleasant for my parents and currently limited by the difficulty of access to that properties rear.

They protested he had promised them this was not his intention, but if it was a worry could they not write something about it into the covenant?

Our reply, and this is what I think is important about Nicks strategy in this game show, was that if there was trust to be granted that my parents, knowing themselves to be trustworthy, should demand they be trusted and not sign a document that was predicated on a lack of trust in them. Let the neighbour trust in their intentions, not they in his.

Nicks attitude was similar to this argument - he knows if he can be trusted but might not expect it of anyone else.

Abraham was asking Nick to trust him, while Nick was asking Abraham to trust Nick. Why should Nick grant Abraham trust where Abraham would not grant it to Nick?

That Nick decided (and I wonder if he based his final choice on feedback from Abraham) to assume Abraham made the best possible choice giving some hope of receiving any money. That part was courageous, because assuming he was trustworthy (and given his actual choice it appears he was) he would have been safer to stick to his announced plan.

Maybe there were tax issues to consider .

There's another British quiz show that didn't last long that had a conclusion based on The Prisoners Dilemma. It's name escapes me. It involved three participants who worked together to amass a prize.

At the conclusion they had to agree on how the prize was divided among them in three separate values (something like 5/12, 4/12 and 3/12 divisions) and only when they agreed were the prizes awarded. Each was given a few words to put an argument for how the prizes should be dispersed, but after that the total prize would start decreasing in value as time passed until exhausted or they agreed on a division.

The only episode I saw had two people each refusing to allow the other to have more than themself until the total pool was almost gone. It was as elegant an argument against homo-economis I have ever seen.

Clive RobinsonApril 25, 2012 4:09 AM

The Monty Hall problem has always amused me because although you can work it out on a piece of paper by drawing a matrix it contains a simple trap which is what catches most people out.

So what is it....

Well at the start of the game the car is behind one door and (effectivly) nothing behind the other two.

Thus the player has a one in three chance of selecting the right door. These are the starting odds and they don't change through out the game.

The player selects a door (1/3).

Now at the second stage Monty opens a door which monty knows is going to have nothing behind it.

Now importantly if the play has selected a door with nothing behind it (2/3) Monty can only open one door. However if the player selects the right door (1/3) Monty can open one of two doors.

Now if you were drawing this out as a matrix you would now have 4 not 3 options. The first two options being those where the player has picked a door with nothing behind it have a probability of occuring with the original one third each. The last two come from the one third probability where the player has picked the right door BUT as these two come from an original one third they only have a one sixth probability of occuring.

So the first two options count as two thirds of the likely hood and the player needs to swap to win for those two options.

The last two options only count as one third and to win the player must not swap.

Where it goes wrong is as I said when you draw it out there are four final options that each have a "50/50" choice for wining or losing depending on if the user swaps or not. However the bit people miss because they don't write the probability down as they go along is that to get the four options you have halved one of the original three options...

The maths is absolutly sound the lady is correct, the best stratagy at two thirds probability is to swap.

But choices are not probabilities they are options or modes that have probabilities as attributes that can change with time or with which choice you are actually looking at. Sow at the end of the game you had one of four possible choices not the original three possible choices.

Why a PhD in Maths would not know this I don't know unless the person asking the question asked the wrong one. Because at the last stage of the game the player does in deed have what we often call a "50/50" choice to swap or not, but it is a choice where the probabilities have changed during the game, based on the first choice the user made.

This problem has come up on this blog before with "failure modes" and it's important to engineering and thus to security engineering.

Take for instance a 747 aircraft with four engines each engine is either working or it is not working this is a "50/50" option on it's mode. When looking at the failure modes you thus have 2^4 or 16 failure modes. But a failure mode is not a probability... each failure mode has a probability of being in the failed mode or the working mode and these probabilities are not "50/50" by any means. Thus having established your 16 failure modes you then need to work out the probability of each mode occuring at any given time, which introduces the issue of past, present and future probabilities. That is if one engine fails it increases the load on the other three making their probability of failure go up from that point onwards unless other action is then taken in the future to bring it down again.

I know people have a problem getting their heads around this and the problem is in part the "time dimension" and in part muddeling up the number of states (choices) within a system and the actual probability of each state occuring.

So firstly, they make the mistake of not realising the probabilities change with time, so another example ;)

When you buy a lottery ticket to a single prize draw, prior to the draw there are two tthings you can say about the ticket,

1, It will either win or lose (ie it's final state)
2, It's probability of winning goes down as more tickets are sold.

This gives rise to the interesting fact that the first ticket sold starts off with a probability of 100% that it will win, droping to 50% when the second ticket is sold and so on. That is it's modes (final state) are known at all times (win/lose) but the probability of each mode depends on the number of tickets sold and this changes until sales of tickets stop.

After the sales stop the win probability is known as is the lose probability but there is still only two eventual outcomes which have not changed since the ticket was purchased it will either win or it will lose and this only becomes determined once the draw has happened and the tickets win/lose mode is then and only then known.

But can the number of states the ticket can be in change?

Not in a single prize game.

So what about a multi prize game the answer is maybe...

Before the draw starts all the tickets have the same states and the same probability on each state.

Now what happens as the draw progresses is important. When a ticket is drawn and it wins a prize what happens to the ticket? does the ticket get discarded or does it get put back with the other tickets?

If it gets put back in the draw then it has the same states remaining as all the other tickets and as the same number of tickets remain for the second and subsiquent draws.

However if it is discarded it's state has colapsed to a winning ticket with no further change, that is it cannot win/lose again. As it is removed from future draws the probabilities of wining of the other tickets goes up slightly untill all the draws are compleated then the states of all the tickets are finally known.

Now for most prize draws the number of tickets involved generaly makes little or no difference to the outcome. But when the number of tickets and prizes are the same or similar it makes a lot of difference.

Getting your head around these sorts of thing without having a clear idea of what changes in terms of states and the probability asigned to each state as time goes on can be used to "game a game" by some one who can compared to some one who cann't. And uncertainty in a players mind gives rise to all sorts of "tells" which can also be exploited by another player or the person running the game (see the other naff UK "daytime game show" Noel Edmands "Beat the Banker").

JonApril 25, 2012 4:36 AM

The problem with the Monty Haul three-door game is that the definition of the problem changes halfway through the problem.

They claim there's an equal probability of the treasure being behind any one of three doors, but the door Monty opens *never* has the treasure behind it.

Therefore, that door had a probability of zero to start with, and now you've redefined the problem halfway through.

That's kinda a no-no in logic puzzles...

Jon

DerpyApril 25, 2012 4:59 AM

Amazing - and a very interesting strategy. Nick wanted to Split, but had no way of knowing what Abraham would do or whether he could trust him, and by openly announcing his intention to Split, he would've opened himself up to walking away with nothing.

So by offering a deal that would leave Abraham no worse off than a genuine Split, by making sure that Abraham believed that he couldn't do better, and by convincing Abraham that he (Nick) was not just honest but also honorable and thus trustworthy and that he wouldn't break the deal and take all the money for himself after all and refuse to share, he managed to get him to choose Split - and then went for the option that would ensure his desired outcome himself, right there in the audience and under the rules of the game.

That's brilliant - the psychological equivalent of revealing a bomb strapped to yourself and saying "I'm pushing the button, so whatever you do, don't connect that cable".

And Abraham could trust him because as soon as it was about honor and what it means to "be a man", he could be sure that Nick wouldn't embarass himself in front of his peers for the (ultimately rather measly) sum of 6800 pounds.

I'm not even sure what Adam could've done if he'd wanted the entire amount and if he'd been willing to gamble. Once Nick convinced him that he would only lose by chosing Steal, he really had no other choice anymore.

And the best thing? Despite his claims tha the was honest, Nick WAS lying; but he was also honest insofar as that he said he'd share the money with Abraham, and - well, he did.

Amazing, indeed.

wasylApril 25, 2012 5:45 AM

Some replies to the rock-paper-scissors comments about my suggestion:

a) it's not exactly RPS, as two of the "draw" choices (catch-catch, steal-steal) are actually "both sides lose" - which makes choosing catch or steal more risky than splitting (expected value 1/3 instead of 1/2 of the winnings)
b) what made me suggest this as an interesting variation is that it makes your belief that the other party is going to steal from you actionable. In the basic version, if you believe your partner is going to steal, you have no options available (and that's what made Nick's trick effective). You can also trick the other party into believing you will steal, which allows you to choose split and hope for 100% of the winnings.
c) even if it was exactly RPS, the conversation beforehand would still make it really different from a normal round of RPS - trust would be much more important than luck
d) rock, paper and scissors have no emotional meaning. Being a "thief" has, so even that is enough to differentiate the options.

I think the variation would make for a more compelling game (even if the helplessness when the other player chooses "steal" is what made the video interesting).

PybeApril 25, 2012 5:50 AM

I think it even goes further than that.

Let's say that, out of spite, Abraham chose Steal. This would be choosing "we either split or nobody gets it". This is a tough choice to make, and Abraham would have to convince himself that it's the way he wants it.

Because of this, when realizing that Nick had chosen Split, he'd probably have been so much in his "split or nobody gets it" mindset that he'd have chosen to split it anyway.

CliveApril 25, 2012 5:54 AM

The legal side of this interests me: yes, it's a game in which people lie, but arguably Nick's promise was extrinsic to the game. Jasper (the host) claimed that Abraham couldn't rely on it, but I'm not sure that's true. It was a contract to give money in exchange for a service. It was verbal, but there was an entire studio audience full of witnesses.

Supposing Nick had made a legally binding offer, he's then entirely in Abraham's hands: he gets half if Abraham shares and nothing if Abraham steals... regardless of what he himself now picks. But what he picks makes a difference to Abraham, who could still take everything if Nick shares and Abraham steals.

Abraham, however, can either take a guaranteed half by sharing, or can play double-or-quits by stealing.

So why did Nick then share, having either threatened or promised to steal? Either he's just a really nice guy, or he was hoping Abraham would be shamed into giving him some of the money if Abraham had chosen steal. Having reconfigured the game by his initial promise he had nothing to gain directly from sharing, under any circumstance. (Which is, of course, partly why the "I'm going to steal" threat had such credibility, when coupled with his promise to split his winnings.)

It is, indeed, fascinating on all sorts of levels in all sorts of ways.

IntrospecitfApril 25, 2012 9:18 AM

more interesting:
2 steals - 0
1 steal, 1 split - 15000 payout
2 splits - 5000 each

Fred PApril 25, 2012 10:06 AM

@moo - that's exactly how I originally worked through the problem, when I originally heard it; I added more doors.

Dan LewisApril 25, 2012 10:55 AM

B could also tell A 'I'm not going to pick my ball, you are. Left or right?" This forces A to pick Split to have a chance at the money, because if A takes Steal, they're leaving their fortunes up to a coin flip. B can follow up with the offer to share outside the game if by chance they turn up the Steal ball.

If B plans to renege outside the game, this would also be a strong way to renege for B, with a 50% chance to walk away with all the money.

PaulApril 25, 2012 11:00 AM

Nicks strategy was brilliant! The only way to win at a game of chicken (a version of prisoner's dilemma) is to convince your opponent you are a madman and irrational. The only choice then facing Abraham is to definitely lose (choosing steal) or hope that his opponent will pay off after the show (choosing split). If I were Abraham, I would have agreed and chosen the split ball. Nick clearly anticipated that Abraham was smart enough to figure this out. Nick was also nice/generous enough to select the split ball instead.

Nick BoneApril 25, 2012 11:07 AM

No-one has noticed here that the "Golden Balls" game is not strictly a Prisoner's Dilemma.

The "sucker's payoff" (Split when other Steals) is exactly as valuable as the "penalty" (Steal when other Steals). Further, the average of the "sucker's payoff" and the "temptation" (Steal when other splits) is the same as the "reward" (Split when other Splits).

The strategy probably wouldn't work with a true prisoner's dilemma.

VijayApril 25, 2012 11:22 AM

I do not know the history of the players (gainful employment, financial status etc.) but it would be interesting to see how the dynamics of this strategy would change if the price was more than £13600?

pebirdApril 25, 2012 11:35 AM

Here is how I think this played out (pun entirely intended):

The traditional discussion goes something like this:

A. I plan to "Split"
B. Good, so do I

... Rest of conversation A & B talk trivialities to attempt to read each others "poker face".

Obvious and boring, except for the personal touches each brings.

But what Nick did was give Abraham (or Ibrahim) an choice that had to do with trust, but also whether he could figure out what Nick was up to. So, Nick game Abraham a lot of signals in short period of time.

By saying "I am going to Steal", he first breaks the traditional game and forces Abraham to THINK. See Abraham's head blow up when he hears what Nick is proposing.

Now, if Nick had just left it at that - he would sound like a sociopath and Abraham would be forced to Steal.

But then by saying "and I promise you I will split this with you post game", Nick is signaling:

1. I have thought this through - listen to me.
2. I think I can trust you, Abraham
3. I am giving you an out for choosing a "Split", you can say you trusted me.

This is why it is so important that Nick never varies from his "trust me" talk. Any indication of hesitation or even a display of self-awareness that this is a unique gambit will place that shadow of doubt in Abraham, ensuring "Steal".

Nick plays this as well as one could possibly play. He CLEARLY has thought this through.

I don't think Nick could take this approach with any player, you can only play this way with a certain opponent, one who values trust and rationality. Which Abraham appears to fit perfectly.

What Nick is saying is:

1. I am not insane
2. I am aware that if I pick "Steal" and you pick "Steal" we both lose.
3. I am giving you assurance through my personal word/reputation, and I think you value reputation.

and most importantly:

4. If I, Nick, can be convinced that you, Abraham, will pick "Split", then I can pick "Split" safely.

And the only alternative Abraham can consider is:

1. This guy is a sociopath
2. I have misread him the whole game

Now, I haven't seen the whole game, but if Nick displayed any dishonest tendencies through the earlier game, he can't play the end game this way.

Intelligent people have a lot of difficultly discounting the understanding they have built up for a situation. Abraham is clearly intelligent and the intensity of the game requires developing a position on your opponent/partner.

Nick also paid Abraham a implicit compliment through his approach: "I think you are smart and you can figure out what I am trying to do here."

Let's not think this approach cannot be played again, but it can ONLY be played with the right set of contestants that have played the game a particular way up to that point.

What is enjoyable about watching games is not the play itself (there are only so many moves), but watching the right play at the right time in the right context.

Well done.

LintmanApril 25, 2012 12:19 PM

If I was Ibrahim, I likely would have picked Steal in that situation in disgust. My thought was that if I was going to get screwed, I'd rather it be in-game, on camera and then be done with it, than to play along and then have the guy potentially sleaze out of it after stringing me along for weeks/months. "Oh, I haven't gotten the check from them yet" "There's some tax complications I need to clear up" "I just mailed it yesterday" etc. No thanks - I'd make sure we both got nothing before setting myself up for that.

Me, cynical? Yes, but I'd have been fine with a picking split and taking him at his word that he would also. The whole "I don't trust you a lick and I'm going to screw you, but trust me anyway" thing didn't sit well with me and would make me feel like a colossal sucker for going along with it.

All that said, if I stole and he actually did pick split, I'd split the money with him.

Chris B.April 25, 2012 12:39 PM

Gawd, the Monty Hall problem again.

People don't *get it* until they *get it*. There rarely seems to be middle ground.

Probably it's because the problem is draped in misdirection. Monty's antics change nothing.

*Accept it*, the mathematicians are right and the intuitive solution is wrong. If you will accept that, you eventually have a hope of understanding it.

You have 1 door with a 1 in 3 chance of being right. Monty has 2 doors with a 2 in 3 chance of being right. Though it's dressed up in a clever way, the simple truth is, you can keep your 1 in 3 chance, or trade it for Monty's 2 in 3 chance.

That's it. That's the WHOLE problem. Everything else that happens, happens to confuse you.

The odds don't change when Monty opens a door--that's just Monty offering you *both* his doors in exchange for your one, though it looks like something else has happened.

At *no* point does your 1/3 door ever become a 50/50 door. Someone who comes by after Monty opens an empty door, and picks randomly between the 2 that are left, don't have different odds than you do; if they pick the same door as you, they have a 1/3 chance (even though they don't know it). But they only pick the same door as you 50% of the time. The other 50% of the time, they pick the door with a 2/3 chance of being right, and with enough reps, that works out to 50/50.

LintmanApril 25, 2012 12:43 PM

@Jon - there is no "no-no" here. It's a simple, real-world situation with a straightforward question of whether to switch boxes or not.

There are some implicit assumptions, though:
1) The host knows the location of the prize, and the explicitly chooses that empty box that is revealed before the switch.
2) The host (Monty Hall) makes the switch offer regardless of whether you have chosen the correct box or not. (The real Monty Hall has said he was little more likely to offer the switch when the contestant had already chosen the correct box).

It's #1 you have a problem with, but this is actually a critical piece: BECAUSE the host knows that it was empty, if collapses the 2/3 probability of the 2 unchosen boxes down into a single unchosen box.

Another way to think about it that might make it clearer: imagine that the empty box WASN'T revealed, and instead the host offered to switch the chosen box for BOTH unchosen boxes. It's a good deal - you go from 1/3 to 2/3 probability. Now, the host revealing an empty box (already known to him) doesn't change that situation at all.

Or try this: imagine that the game is played with 100 boxes and you pick one, then the host reveals 98 empties with 1 left to switch to. Switching would give you a 99% likelihood of winning.

OtterApril 25, 2012 1:12 PM

The fallacy of the Prisoner's Dilemma is not that it is a poorly understood model but that it is poor model.

Note first: that the apostrophe is placed before the "s", despite there being two prisoners. Second: the model states that the prisoner's confederate is not his friend but is untrustworthy. Note also that the term used, "confederate", is a vague abstraction whose meaning can be bent when the audience's attention is distracted. Third: the model states that the prisoner's jailer is his friend and can be trusted to deliver what he promises.

In the real world, you would cheat a rival for something very important, eg for a large amount of money, or for a (wo)man. You might cheat a friend for a trivial wager... but not very often. However, you would never cheat a friend for something merely important, unless you were to convince yourself to promote it to something very important, and worth the loss the friend.

In the real world, you would never rob a bank or throw bombs at the Tsar with a mere confederate... you would choose a friend you can trust. (Except Americans, but the FBI swoops in and arrests them before they discover the bomb is a dud... and the jailer never offers a deal.)

In the real world, the jailer is not your friend, and if he is offering you a deal, it is only because your friend has NOT betrayed you, and because it is worth a cynical try... you might be stupid.

eigenpersonApril 25, 2012 1:31 PM

As soon as I heard about this game I came up with the strategy of announcing you are going to steal. It has many desirable features if you value fairness. Not only do you get a pretty decent chance of coming away with 50% of the pot, you also get to punish the opponent if he decides to be greedy and stupid, and you also get to prove your superior moral character to your opponent when you actually hand over his half of the pot of your own free will.

However, until I watched the video, I didn't realize how hard it would be to look your opponent in the eye and explain your strategy. Your opponent would obviously be satisfied once you handed over his share, but between the time you describe your strategy and the time your opponent gets his share, you feel unclean, because you've got your grubby hands on his money. Plus, you're on television and 90% of the viewers will assume you were just bluffing about the whole "splitting the pot" thing, so everyone will think you are an asshole of the highest caliber.

I think that's why Nick chose "split" after all that. He wanted that "unclean" feeling to go away as soon as possible, and he knew that the only person who could possibly look like an asshole was Ibrahim.

cakmplsApril 25, 2012 1:38 PM

I think Nick was trying to assure as much as possible that Abraham would take the "split" ball. It might be helpful to see what went before, to see how much knowledge of each other they might have gained. Is Abraham the kind of guy who would choose "steal" if Nick gave his word he would take "split"? Is Nick the kind of guy that Abraham would trust to do what he said? Did Nick have reason to think that Abraham would trust him?

Ernst BlofeldApril 25, 2012 1:39 PM

Nick's approach is to expand the PD game into an iterative PD game--instead of a single game of PD, he is in effect proposing to engage in two sequential games of PD, in which he will defect in the first but cooperate in the second. Furthermore, he is attempting to (falsely) frame this as a game of chicken, which has a different payoff matrix.

The Nash equilibrium for N iterative games of PD is the same as that for a single game of PD: defect. One might think that the optimal approach would be to cooperate on the first N-1 games but defect on the last, since there is no possibility of tit-for-tat retaliation after the last game. But a clever player will realize this and defect on game N-2, his opponent will realize this and defect on game N-3, and so on.

GladerApril 25, 2012 3:13 PM

Regarding testing the Monty Hall problem: They did it on Mythbusters ;)
Currently available here

OtterApril 25, 2012 3:21 PM

The optimal approach is to cooperate on all N "games".

A clever player will realize that "game theory" does not adequately describe his world.

cApril 25, 2012 5:01 PM

Scientific American had an interesting variation on prisoner's dilemma - a lottery where your chance of winning was determined by random draw among the total number entries submitted. You could submit as many entries as you liked - no limit. Prize: $1M divided by the total number of entries submitted.

Author hoped that astute readers, having just read a column about prisoner's dilemma, would estimate number of readers of column (call it N), then take a 1/N chance "coin flip" (excuse the term) to decide whether/not to submit a single entry. He anticipated a handful of entries, perhaps even zero or one.

What he got was very different. He stated in later column that readers spontaneously competed in writing mathematical expressions to describe their number of entries, where it would actually be a lot of work to decide which reader had the largest number of entries (googleplex raised to the googleplex power would be a simple example). The value of the prize was thus approximately $1M/(infinity) or approximately ( a very good approximation ) zero. So the drawing was moot. I think author stopped writing column shortly thereafter.

cApril 25, 2012 5:04 PM

re: SciAm contest
forgot to mention - just submit a postcard with your name and the number of entries you want to enter in the drawing.

PrometheeFeuApril 25, 2012 5:13 PM

This is really different from a PD. In a PD, the only Nash is defect:defect. Here, both defect:defect, cooperate:defect and defect:cooperate are Nash. In all cases, you cannot make yourself better off by switching your strategy. (which is the rough definition of a Nash equilibria) What Nick does with his promise to split the money after the game is transform this into a game similar to chicken.

In chicken, your choices are swerve or hold. The outcomes for player 1 rank as follows:
hold:swerve
swerve:swerve
swerve:hold
hold:hold

This matches split and steal. If there is a chance that Nick will keep his promise to split after the show, Abraham's outcomes rank as follows: (Abraham's choice first)
steal:split
split:split
split:steal
steal:steal

Now, Nick does a classic chicken move: he commits to holding straight. Or here, to steal. That commitment is believable because without Abraham agreeing to split the prize if he wins it all, stealing is a weakly dominant strategy for Nick. (Nick is never worst off by stealing rather than splitting)

At that point, the game is really simple and the only Nash is for Nick to steal and Abraham to split. Why does Nick split then? I'm guessing he wanted to look good on TV and was sure he had convinced Abraham.

pfoggApril 25, 2012 6:15 PM

@Bruce - All that's left is not letting Nick have the money out of spite -- and that emotion seems out of place in the conversation. Abraham decides to trust Nick, because it's the only option that makes any sense.

The standard (experimental) game where one person proposes to divide some money in some proportion (e.g. 70:30), and the other either accepts (and money is divided accordingly), or refuses (nobody gains anything), shows that people are frequently willing to refuse the split to punish proposers making offers considered too greedy, self-serving, or socially unacceptable, even in a game played only once between anonymous participants. In contrast, in a single game, game theory's "rational agent" would not reject any proposal other than 100:0.

In this game, though, no 'wrong-doing' had yet occurred. Nick made a promise of a future even split (which meets the standard of fairness). He didn't even reject any reasonable propositions from Ibrahim, since (as pointed out above) he spoke first. A "rational agent" in Ibrahim's position would only pick "split", so the only remaining danger was that Ibrahim's assessment of the probabilities gave more expected value to the potential of punishment of a cheater than the potential of cash from an honest split.

The video made it look like it was a near thing.

Julien CouvreurApril 25, 2012 7:51 PM

The meta-solution to the prisoners' dilemma is to break outside of the game and change the rules.

Here the notion of splitting outside the game is introduced. In general, you could introduce contracts, deposits/guarantees (something valuable to me but not to you could be a safeguard), and third-party enforcers.

Third-parties can nicely solve this kind of trust problem because they can specialize in escrow and build a reputation over multiple transactions (not just one, as in this TV show). So even if these to contestants only transact once, the escrow's trustworthiness emerges from the separate instances of the game.

Because humans get to set and change the rules, the situation can often be avoided pro-actively. So instead of getting into a situation where individual self-interest is at odds with collaboration, you plan for such circumstance and clarify the procedure beforehand.

Jedediah SmithApril 25, 2012 8:14 PM

The only goal is to convince the OTHER person to split. Convincing them that YOU will split does not help toward that goal at all, quite the opposite. So why does everyone try to do that? The only way to convince the other person to split is to introduce some disincentive for them to steal, which is what Nick did.

Nick PApril 25, 2012 8:25 PM

Different approach

I skipped over some of the comments so apologies to anyone who said it before me. I came up with a scheme revolving around Steal b/f seeing the last vid (more entertaining scheme). In the US, there exists oral contracts. With witnesses & video, they can be very strong in court. I would scheme my way to the top to try for a high jackpot. Then, I would clearly state that I'm making an oral contract & that I'd split if they said "split" while I said "steal." Rather than a game, it's now a legally enforced agreement between the players.

(And if it turns out it wasn't, I have all the money anyway. Evil grin.)

Any thoughts? Criticisms? Commendations? ;)

BryanApril 25, 2012 10:43 PM

What if Monty's rule for the game is, "show a goat and offer the person a chance to change his pick if he picks right the first time. If the initial pick is wrong, offer the person $50 instead or stay with the box."

The problem with the all the glib probabilities is it assume you understand the rules of the game, while in Let's Make a Deal, you really didn't. Switching might be good strategy, but it's depending on your guess at what's happening in the host's head, not just a decision tree. You can only actually see the branch you're sitting on.

WernerApril 25, 2012 11:41 PM

@Nick P: are you certain that invoking some part of the law the other side may not be intimately familiar with will increase their trust in you not trying to use "inside knowledge" to cheat them ?

I'm a bit surprised that so many people in this thread consider bringing up legal constructs in the conversation. I'd expect that, if you went out on the street with a pile of contracts in which you're promising to send the person signing a small but significant amount of cash (say, USD 100) with no strings attached, most people would refuse to sign that or may give you false information. Particularly if you give them only a few seconds to decide.

- Werner

JonApril 26, 2012 1:21 AM

@Lintman

Yes, there is a problem. It is stated that there is an equal probability of the reward being behind any door, but the door that Monty opens has no probability of the treasure at all.

So there is a logical problem in the definition of the problem.

That's a no-no.

Jon

JonApril 26, 2012 1:26 AM

Incidentally, in the game show, you are correct to switch, but the problem that you are solving is not the problem you are presented with.

J.

ChristopherApril 26, 2012 1:58 AM

Haven't read the whole comments so this has probably been mentioned before, but...

"Player A gets a pot of money. He gives some percentage of it to Player B. It is then multiplied by some amount, and Player B gives some percentage of it back to Player A. In a classic rational self-interest model, it makes no sense for Player B to give any of the money back to Player A. Given that, it makes no sense for Player A to give any of the money to Player B in the first place. But if Player A gives player B 100%, and Player B gives Player A back 50% of the increased pot, they both end up the happiest.

Nick sets himself up as Player B, promising to give Ibrahim 50% of the jackpot outside of the game. Ibrahim is now Player A, deciding whether to give Nick the money in the first place. "


Ignoring the possibility Nick was just being all showbiz and entertaining and not really putting much other thought in to it....


Nick was surely Player A, in that he had no guarantee he was going to get anything, and was relying on Ibraham (B) to give him some.

Nick knows the only way to ensure any money is won is to pick Split.

In picking Split, Nick knows there's a possibility that he may leave with nothing himself. With the best play in the world, he still can't guarantee what Ibrahim will pick regardless of how he acts and what Ibrahim promises to do. So Nick's always going to pick Split, and has to ensure that, should Ibrahim pick Steal, there's still a good chance Ibrahim will share some of the winnings with Nick.

So he gives it to Ibrahim. He convinces Ibrahim he's going to leave with nothing, then through Nick picking Split he gives Ibrahim either 50% or 100%, and relies on Ibrahim giving back to Nick either 50% through Ibrahim also picking split, or Ibrahim winning the lot and taking pitty on Nick and sharing the money with Nick. The more Nick convinces Ibrahim that he'll be leaving with nothing, the happier Ibrahim will be when he finds actually Nick was always planning on allowing Ibrahim to leave with the cash, and therfore be more likely to share it with him.

That's my theory anyway. Like I say, chances are Nick never thought that far ahead. Just seemed like a cool way to play the game.

ChristopherApril 26, 2012 2:02 AM

Oh and, that would present an opposite theory to @pebird. Nick no longer has to ensure that he's seen as trustworthy, doesn't have to convince Ibrahim to do anything, doesn't have to hope Ibrahim believes him and picks Split.

He only has to hope that, either way, Ibrahim is suitably suprised and grateful Nick picks Split, by suggesting as strongly as possible he won't. Preferably in a way that suggests money could be split between the two should anyone leave with the lot ;)

ChristopherApril 26, 2012 2:19 AM

And to demo the options:

Nick:Ibrahim

Steal:Steal

Nick says he's going to steal. With the best act in the world, personally I immediately figured something was up with Nick (he's probably tricking me whatever he does). If I was Ib, I'd choose steal. Then we're either both leaving with nothing ("what do I care, nick was acting like a dick anyway, he deserved to loose") or..


Steal:Split

I pick split, Nick wins the cash, but I recon he may keep it, or at least this makes splitting it more complicated, and I already don't trust him to do what he says, and no one likes him whether he shares the money or not and i don't want his damn money anyways. With the alternative being losing everything, picking Steal is a risky option for Nick whatever happens.

Split:Split

This works well. Whether I did or didn't trust Nick, I did what he says, and through his actions Nick's already done what he promised before we even leave our chairs. Nick looks good. I'm happy. We both win.

Split:Steal

I didn't trust Nick so I chose to Steal, figuring at worst he'll look an idiot more than I do. But, hang on... I've just won the lot. I may immediately think Nick was such an idiot he doesn't deserve anything, but... I was so convinced he was trying to con me, and actually he just let me win everything, what a nice bloke. Here nick, have some money, etc.

QnJ1Y2UApril 26, 2012 3:33 AM

@Jon

In the Wikipedia article on the Monty Hall problem, there is a very careful statement of the problem. That's the one you'll want to analyze, since any statement made here the comments may be a bit imprecise.

I'll also suggest that if you see some issues with the problem statement that you'll want to discuss it there - it's getting a bit too far off-topic for this thread. There's a very robust discussion on the talk page, and there is even a sub-page for arguments about the problem.

@All

We may need an addendum to the law mentioned above. Basically: stating the 'Monty Hall Law' will not prevent the fulfillment of the 'Monty Hall Law'.

JonApril 26, 2012 3:34 AM

Back on topic, I agree with some previous comments (I admit I've not read them all in detail) that Nick was playing to avoid the 'Steal/Steal' result. I think he'd have been happier if Abraham/Ibrahim took the whole lot than the game show getting to keep the whole lot.

If he loses it all, he can at least be proud of playing. If Ibrahim/Abraham took it all, he can at least be proud that someone took the money off the show. The worst outcome, for him, is that the show gets to keep it.

Jon

GuSApril 26, 2012 4:37 AM

OK, so Nick "changes the rules". He introduces a "Meta-game". He goes outside the foreseen rule-set. Agreed.

But... What I see as the most unforeseen in his strategy is that he introduces time, into the game.

The game is, by the organizer, defined as something that will happen at a given point in time. Like, Now. While the spectators are sill around.

Nick works with different strategies of how Ibrahim will trust or distrust him, even going outside of the game hall, seeking trust in a different geographical location.

But, what the organizers of the game hadn't foreseen is that Nick says to Ibrahim: Trust and distrust plus strategies set aside, you'll get your money later. Ibrahim still must trust Nick. But now the trust must survive time too.

"Later' obviously wasn't part of the design of the game. As it typically isn't part of of door games and such.

As a matter of fact, "Later" is also what most software development designs miss out. Some Enterprise Data Warehouses may answer the question "What was the value some time ago?", but more "ordinary" software systems regularly fail to correctly answer the same question. (Assuming that the value actually has changed at least once.)

Time is a measurement of change. And since most of us agree that time goes on... Well, change goes on. Trusting future change, or the lack thereof, is less unpredictable and introduces more risk. (What if Nick has an accident in the meantime?)

GuS

GuSApril 26, 2012 4:45 AM

@Fentex

Your parents, should they have signed up, should also take time and it's related unrelated changes in consideration. (Yes, I meant "related unrelated". From your parents point of view, they're related, because such changes will concern your parents in the context of the contract. Still those changes are potentially not part of the contract.)

Change: The neighbors sell their property and all the access rights that goes with it. New neighbors may be less respectful to you parents and behave differently. Over time, it didn't turn out the way your parents had expected.

GuSApril 26, 2012 4:49 AM

@MyKeyboard

"is less unpredictable and introduces more risk"

should of course read "is less predictable and introduces more risk"

Sorry 'bout that.

Matthew WillsApril 26, 2012 5:53 AM

Mick's genius was in two things:

a) Highlighting that he wanted to share the money ('reciprocation') if Ibrahim worked with him.
b) Getting Ibrahim to highlight his commitment to his word ('commitment and consistency').

Combined, this meant that if Nick knew he was going to Share, then Ibrahim would likely keep his share.

But *if he didn't* - if he chose steal just to spite Nick - then, Nick will likely still get half of the money. Ibrahim has seen Nick's offer, and will feel (at least partially) compelled to reciprocate. Plus, he has committed to being honest and wanting to share - so to be consistent with that, he'll feel (at least partially) compelled to reciprocate.

Its almost a textbook case of chapters 2 and 3 of Cialdini's book - http://en.wikipedia.org/wiki/Robert_Cialdini#Influence .

anonApril 26, 2012 10:20 AM

Given what we know about what occurred in the show, I can't work out why Nick wouldn't choose "steal". Assuming all is fair in the game, and the goal is to maximize winnings, of course. Nick had a good strategy to ensure his opponent chose "split". Now, why not choose "steal"? Perhaps he wanted to make a good show of it.

JonApril 26, 2012 10:27 AM

@QnJ: Actually, no, it's not what I'd call a 'careful description of the problem', I'd call it a wild mishmash of a dozen different descriptions.

But you are right in that here is not the place to discuss and dissect it.

J

Nick PApril 26, 2012 11:30 AM

@ Werner

"are you certain that invoking some part of the law the other side may not be intimately familiar with will increase their trust in you not trying to use "inside knowledge" to cheat them ?"

Contracts are pretty basic, even conceptually. There's something in it for both parties, there's an agreement and there's doing it. That it's video'd with plenty of witnesses increases its confidence rating. Why would anyone be worried about being cheated? They've signed plenty of contracts before & know that you're stuck with them more often than not.

"I'm a bit surprised that so many people in this thread consider bringing up legal constructs in the conversation."

It's actually been a small portion. The rest are focused on how to be clever with game theory, model the situation with probability, and somehow win by luck + cleverness. Our side just says: make it a court-enforceable promise. There's even experts (guess who) we can hire to get the money.

Btw, the street situation is a very poor comparison. That context has con man written all over it. Of course, nobody would sign on that! However, if the guy was the banker & said they were getting paid for a survey, they might be more likely to succeed. Context is very important.

The context here is that they might get nothing, half or everything. I'm telling them I'm going to steal, regardless. I tell them I'm doing it so my strategy will work. The strategy is an oral contract between us that they'll get half of what I get after I receive it. Their options: steal + get nothing; split + probably get half. I also remind them that this isn't a bluffable promise: the courts can enforce it & seize their half just like they can take a car from someone not making payments. I figure my gambit would be more reliable than the other Nick's. After all, what choice do they have.

No OneApril 26, 2012 12:36 PM

I just watched a few SoS videos and I have to say, I think it would be more interesting if they added $1k to the pot if both players choose "split." This comes after seeing the game where one player "stole" a $2.85 pot.

I like the random-chance/partner's choice gambit if you can get your partner to understand your new game. Barring that, Nick's is a very interesting solution.

BCRApril 26, 2012 12:54 PM

I say again - A solution that does not involve trust, or chance, or bluffing or tricking the other player...

Swap balls.

I pick one and give it to you.
You pick one and give it to me.

No incentive to give the other person steal. Job done.

No OneApril 26, 2012 1:02 PM

@BCR: You're not allowed to do that by the game rules. You can't show them your balls and you certainly can't give them your ball.

No OneApril 26, 2012 1:07 PM

Sorry for the double post, but after seeing people talk about "verbal contracts" I have to say the whole show is based in deception. I highly doubt the verbal contracts here would be worth anything and here's the reason why: contestants routinely state they're going to split then steal it all. If you could enforce a promise of splitting outside the game as a verbal contract you should be able to enforce them choosing to steal instead of split as a verbal contract.

Nick LevertonApril 26, 2012 1:19 PM

Oh dear, is that what Jasper Carrott is doing these days ? What a waste ...

WernerApril 26, 2012 2:20 PM

@Nick P: we all understand promises but we may not think of them as "verbal contracts". By introducing the "oral contract" into the discussion you would probably change your opponent's focus from the promise to the legal construct.

Now, we all know that contracts can contain surprises and need to be carefully considered and carefully worded. But there is no time for that. Furthermore, the game is designed to create a con situation.

Also the possibility of enforcement through a court wouldn't convince me at all. Would I really want to go through all that trouble just for a few thousand pounds ? What if it's ruled to be a gambling debt, no matter what you said, and I lose the lawsuit ? Do we both even live in the same jurisdiction ? Are you counting on me not going to court ?

I think keeping things as simple as possible is key to this approach.

- Werner

mere mortalApril 26, 2012 2:23 PM

Re: Monty Hall

The solution becomes much more obvious using cards. Let's play a game I'll call "Find the Ace of Spades."

Step 1: I randomly choose a card from a standard deck and set it aside without looking at it.
Step 2: You look through the deck and show me 50 cards that are not the ace of spades, and set the last card aside face down.
Step 3: I decide whether to keep my card that I have not looked at or take the face down card that you have set aside.
Step 4: I reveal my choice, if it is the ace of spades, I win.

I will win 51 out of 52 times by switching to the card you set aside, and there's nothing about the flourish of Step 2 that can change that.

Nick PApril 26, 2012 9:19 PM

@ Werner

"Now, we all know that contracts can contain surprises and need to be carefully considered and carefully worded. But there is no time for that. Furthermore, the game is designed to create a con situation."

Well, certainly, there's little time & I'd use that to my advantage. I'd keep it simple. They'd know they have two choices: get nothing or maybe get something. Most people lean toward maybe get something. Additionally, I don't care about the money, so getting nothing is ok for me. Probably not for them. Most people come to those shows to make money & be on TV. Their safest bet is to accept my proposal.

"Would I really want to go through all that trouble just for a few thousand pounds ? "

Nice how you changed the argument from 30,000-50,000+ pounds to "a few thousand pounds." I'll ignore that and focus on the obvious: you must live outside the USA and/or never heard about our many frivolous lawsuits. People routinely fake injuries, physical or economic, to get money. At grocery stores, people spend 20 min griping to get a $5 refund. People on Fear Factor climb into mountains of spiders, transfer lard with their mouth, walk on broken glass, drink disgusting concoctions, etc. for $50,000. You think people won't go to court over a similar amount? (I hear that Brits and Americans are kind of similar when it comes to trying to score big payoffs.)

"What if it's ruled to be a gambling debt, no matter what you said, and I lose the lawsuit ? Do we both even live in the same jurisdiction ? Are you counting on me not going to court ?"

Good points, those. I'm counting on most opponents not knowing that. In the USA, especially in my locale, most won't. In Britain, who knows. Again, I'm putting them in a no win situation if they don't trust me & a maybe win situation if they go along with it. They have no choice. This is coercion. I have two possible goals: deny them winnings by being clever or split it with them. I win either way, as I'll tell them. "Question is, do you want to win something too? You know how. Just legally agree to the split & I'll be forced to pay you half. "

BradyApril 26, 2012 10:01 PM

Interesting, this (Nick's proposal to start) was exactly what I was thinking of doing when I started watching the video. I do a similar thing often with paper, rock, scissors (I tell the person what I will definitely throw, though I usually do throw what I state). Thanks for sharing these videos.

FigureitoutApril 26, 2012 10:58 PM

I have to say, this show brings me great pleasure when you have two contestants, staring each other in the eyes, saying "I'm gonna split, trust me. I like you, I'm gonna split, honestly" Only to have both of them pick steal and get nothing, and then the host just rubs their deceptive greed in their faces a little more.

The looks on their faces...Ah that is pure bliss to me. :)

WernerApril 26, 2012 11:32 PM

@Nick P: that game was "only" about UKP 13600 in total, 6800 per person when split. So it's basically a vacation for two people or the ability to afford some other small luxury. More pleasure than investment money.

I agree that a larger sum may change the situation, but I'm not sure whether it would make forced cooperation more or less likely.

Ego would also become a stronger factor then. If you promise to split but you choose to betray me, then I can walk away from UKP 6800 with my dignity still intact. On the other hand, if it's an amount of money that could change my life, would I be willing to submit to you, leave my future at your mercy ?

Those shows where people debase themselves may not be a reliable predictor for greed (or maybe masochism) always trumping pride, since the participants are self-selecting for tolerance towards humiliation.

- Werner

David SchwartzApril 30, 2012 6:51 PM

mere mortal: Actually, that's the broken description of Monty Haul where you can lose every time by switching. Since you didn't say I was *required* to give you the option of switching cards, for all you know, I will only offer you the option of choosing when I know the remaining card is not the Ace of Spades.

Switching is only a benefit when you know ahead of time that you are required to be given the option of switching cards. If the other person tells you that you can switch after he knows whether you have chosen correctly or not, there is no guarantee switching improves your odds.

PhilMay 1, 2012 6:03 AM

Nick chooses Split at the end as it's the only way he can guarantee that the money will come out of the game. Whatever he has said to Ibrahim, he cannot know whether he will Split or Steal. Split is his logical choice.

James_HMay 1, 2012 8:05 AM

Very fascinating show and interesting comments. Here's my take...

I sense that any player going into this scenario - evidenced by Liv Boeree's example - would already have chosen whether or not they were prepared to Steal. This choice would be based on the assumption that the other player would take the sensible, safe option to Split. Win big, Lose big/ a straight 50:50 gamble.

I don't think that any of the 'trust me' banter would actually have any bearing on this player's assessment of the risk/ reward involved - either way they have no way of knowing what the other player will in fact do. On the other hand, if a player doesn't want to take the big gamble - Win big, Lose big - they definately need to choose Split and simply hope the other player does too.

Given my assumption - and please correct me if I'm wrong - that the 'banter' is essentially irrelevant, there are only two possible winning strategies: 1. Steal and hope the other player Splits, and 2. Split and hope the other player Splits too. Either way, you lose if the other player Steals - but you have no way of knowing what that decision will be or influencing it in any way.

So the question becomes; does Nick's approach - saying he would Steal and share but actually Split (choosing Split being the most sensible choice to hedge his bet having made his initial case) - alter the game in any meaningful way? I see four possibilities:

1. Ibrahim was planning to Steal, and
a. He stuck with his original strategy.
b. Nick got him to change his mind.
2. Ibrahim was planning to Split, and
a. He stuck with his original strategy.
b. Nick got him to change his mind.

And here are the potential outcomes:

1.a, Ibrahim Wins big. Nick Loses big.
1.b, Ibrahim Wins small. Nick Wins small.
2.a, Ibrahim Wins small. Nick Wins small
2.b, Ibrahim Wins big. Nick Loses big.

So essentially, Ibrahim - without ever realising it - was actually in a no-lose situation. Whereas Nick - who had actually decided on a Split strategy - needed Ibrahim to Split too in order to win anything at all.

That strategy ultimately relied on a psychological trick that would only be effective in this scenario and with this result:

1. Ibrahim was planning to Steal, and
b. Nick got him to change his mind.

Essentially, Nick was gambling on how effectively he could convince Ibrahim NOT to Steal - if indeed he ever intended to do so in the first place.

Either way, I think Ibrahim's best strategy would have been to Steal, so in that sense, Nick's approach succeeded in getting Ibrahim to ignore the logic and secured him the result - Split - that he was after in the first place.

So what if Nick had just gone for a straight Split strategy from the outset? It would have been 50:50 whether Ibrahim would Steal or Split. So in the final analysis, Nick fancied his chances of convincing Ibrahim not to Steal thereby tipping the odds in his favour; probably something like 90:10.

tobias d. robisonMay 1, 2012 10:50 AM

re: this comment and Schneier's response:

"A more powerful variation would be to offer the same deal but without looking at the balls at the beginning, stating that you will pick one at random. The other player is then forced to split or risk walking away with nothing."
That's a really good idea, but it works less well in the context of the game show.

Suppose, at the very end, a contestant says, "Oh my god, I've forgotten which ball is which", and then makes a show of picking at random.

Larry ClappMay 2, 2012 3:29 PM

@c, re: SciAm contest

It was Douglas Hofstadter, and he reprinted the columns in his book Metamagical Themas; see chapters 30-31, most of which are available via Google Books. Dr. Hofstadter expected *lots* of entries, and in fact expected people to stumble all over themselves vying for the higher numbers (even though it would guarantee them a zero payout), which is exactly what they did.

TgrMay 4, 2012 12:58 PM

This is actually not a prisoner's dilemma game. In prisoner's dilemma, whatever the opponent chooses, you are better off stealing, so the only rational outcome is to steal for both sides (unless they have reason to think the other is not purely rational, or unless they can prove to each other what their strategy will be). In this game, if the opponent steals, both decisions lead to the same outcome for you (maybe not emotionally, but in terms of money). Once the opponent convinced you that he is going to steal, there is no strong rational reason for you to steal. The same trick would have been harder to pull off in a real prisoner's dilemma game.

FelixMay 15, 2012 1:33 PM

Alternate strategy to verbally assuring each other with words that you will both split:

Bet the other player half his winnings that he will steal.

If he takes the bet, he must steal since he could lose if he splits but cannot lose if he steals (since you will choose split, split being a lock for half the dough). If he does not take the bet, he is stealing, since there is no up side to splitting - he could have taken the bet without cost.

Therefore, the bet is essentially saying, "Take the bet, choose steal and we split the pot. Or, decline the bet and I choose whether you win everything or nothing. In any case, if you decline the bet, I know I will be getting nothing."

A possible response to the offer of the bet is to decline and then offer the same bet back. That way, you're telling the other guy, "No, I don't want you to choose whether I get everything or nothing, but rather I want to split with you. So you choose steal, and I'll go with split. Or, you can also decline and let me choose whether you get nothing or everything." If the game is set up to show the two players the contents of the balls at delayed times, then the two players can go back and forth with this bet until the balls' contents are known to them.

It's intriguing to think what Liv's response would be to Nick's offer of this bet. I'm betting she would decline but not offer it back. Then she'd go in to maximum eye-bat mode.

In any case, one thing to remember is that this game is not a two person game. It's at least a 4 person game, the show-guys and the audience being the other two players.

In particular, one might wonder if the game show guys pick greedy contestents in the hopes of giving the audience the thrill of watching two greedy people going over the cliff tightly clutching the money.

lakawakJune 7, 2012 9:38 PM

Once he decided to himself that he was going to split it with him, it really didn't matter if he was confident that the other guy beleived him. It became out of his hand at that point. He picked split. If the other guy picked steal, he got nothing. But if he suspected the other guy didn't trust him and picked steal as well, he would STILL get nothing.

To him, it makes no difference. A rational person couldn't care less what someone else gets if it doesn't change their situation at all.

Bigjeff5July 7, 2012 12:43 PM

I think a lot of you are trivializing the incredible appearance of honesty Nick creates.

Ibrahim was already afraid Nick was going to steal, that's what everyone is afraid of. That's the way the game goes - your opponent convinces you to trust them, and then it turns out they are liars and you walk away with nothing.

When Nick says he is going to steal, however, all motivation for Nick to lie in a way that harms Ibrahim is removed. That lends a whole lot of credibility to the promise of splitting after the show, so much so that Ibrahim was willing to go for it in the end. The dilemma transforms into split, and hope Nick keeps his word, or steal and force both of you to win nothing out of pure spite. Why would you spite a guy who has, apparently, been incredibly honest with you (even if the honesty is regarding screwing you over)? If you care about your own character, which Ibrahim obviously did, you can't chose steal. If Ibrahim were a hateful, spiteful person, well at least Nick could go to bed at night knowing he's the happier person.

It turns out Nick didn't steal, and in my opinion that makes it a little disappointing, but it may well have just been a convenience thing (actually splitting the money later would be a real pain in the butt, but splitting on the show is easy), a way to keep his word ahead of time.

paisielloOctober 16, 2012 12:25 AM

Excuse me in advance if someone has already stated this somewhere above but I can think of one other strategy to use. Somebody suggested for Nick to choose randomly but I think this is wrong because Ibrahim would then always “Steal” since this doubles his expected value EV= 50% vs. 25% assuming he never believed Nick would keep his promise. Even if he could somehow trust Nick 100% the most he could maximize his expected value would still only 50% so it would be better strategy for Ibrahim to “Steal” in this case.

Also Nick is taking a rather significant gamble that his manipulating strategy will work. I am confident that there are a fairly large number of people out there in the general population who are idiots and would overreact emotionally. They would pick “Steal” just to keep someone from manipulating them in anyway even if the manipulation was in their best self-interest.

However, what if Nick instead proposes to Ibrahim that they both agree to (excuse the expression) not look at their respective balls but rather both choose randomly. The expected value for both players is then equal with EV = 1/4 (0) + 1/4 (0) + 1/4 (50%) + 1/4 (100%) =37.5%. This might not be an optimum strategy since the best strategy would be able to manipulate someone into trusting you and then back stabbing them. However it does play into people’s sense of fairness and is a very reasonable strategy.

JamesMarch 21, 2014 9:16 PM

Let me start by saying that Nick has to have the intention to want to share, otherwise this is a failed plan. It all revolves around transforming the opponents choices. Ibrahim after the proposition has 2 choices with the following apparent consequences:

1. Pick Steal - Both walk away with nothing
2. Pick Split - Has a chance of getting half the money

Nick has no apparent advantage in lying about his intentions, so Ibrahim has no doubt in believing him. In Ibrahim's mind the only chance he has of getting something is to trust that Nick will share after the show. This removes the temptation to steal

Now the second part is the clever bit! Once the preposition is made, Nick has 2 choices. Splitting is the only choice at this stage to guarantee money being won. If on the off-chance Ibrahim had picked steal as he didn't believe Nick, he might feel quite bad when he sees that Nick was actually telling the truth. Therefore even if Ibrahim steals, he might end up splitting after the show.

If you incentivize bad behaviour, you get bad behaviour. If you incentivize good behaviour, you get good behaviour! Swap the incentive from the bad behaviour to the good behaviour, and hey presto!...good things happen :)

GlennnMarch 26, 2014 1:26 AM

A recent Radiolab podcast discussed this event, including interviewing the men involved. One of the interesting things for me was to hear was Ibrahim admitting he intended to steal (not split) until Nick followed his unusual strategy, essentially forcing him to split. It was also interesting to hear that aspects of Ibrahim's story (such as appealing to what his father would have said if he stole, and "wisdom" his father had passed on) were a lie. In fact, Ibrahim admitted that he didn't know his father as a child and it was a fabrication with no intent (originally) to split. Noting all that, it makes it even more clear that Nick's clever strategy converted an almost certain loss (and inability to be sure whether he could trust Ibrahim) into a win.

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