High-stakes one-shot Prisoner's Dilemma on a British game show with an astounding strategy

A British game-show called "Golden Balls" concludes each installment with a single-shot version of the Prisoner's Dilemma in which the two players' choices can result in a large cash prize being awarded to both of them, neither of them, or just one of them. The players are allowed to tell each other what they plan on doing, but they are also allowed to lie and try to trick the other player into making a choice that would leave the whole pot in the trickster's hands.

In this remarkable clip, a player named Nick runs an extraordinary end-game that has to be seen to be believed. As Bruce Schneier says,

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.

Once you've watched the clip, check out Bruce's spoiler-y discussion of what is going on there.

Amazing Round of "Split or Steal"


  1. This isn’t really the prisoner’s dilemma though… two really important differences:
    1) In the show, people can talk. if, in the prisoner’s dilemma, the two could discuss their choices beforehand, then the average outcome might be different.
    2) Most importantly – you can’t split jail time. One of the main reasons that this worked on the show was the other guy had a reasonable reason to believe that he might get the “reduced” option even if he chooses the split choice. In the Prisoner’s Dilemma, even if the two could talk, there is no option to give the other person 3 of the years you’ve gotten taken off of your sentence.

    Still really smart, though

    1. The dilemma is not so much about jail time, but any scenario with a potential all or nothing outcome involving two people that do not trust each other 100%.

      1. No, for this to be prisoner’s dilemmea, there would have to be four different outcomes, ranked like this:
        1. You steal, while the other splits.
        2. Both split
        3. Both steal
        4. You split, the other steal

        No matter what the other player does, your outcome will be better if you steal. However, if both people act “rationally” to improve their own outcome, they will get a lower result than if both act “irrationally”. That’s the whole point of the dilemma.

        In this version there are only three outcomes, ranked like this:
        1. You steal, while the other split
        2. Both split
        3. Both steal, or you split while the other steal

        If the other person split, your should steal, but if the other person steals it doesn’t matter what you do. This is a different game, not prisoner’s dilemma. Anyway, it isn’t what a game theorist would call prisoner’s dilemma.

        1. Is it just me, or is your second option 3 actually two options?

          Also: if Bruce Schneier thinks that it’s Prisoner’s Dilemma, then that’s good enough for me.

          1. I’m not talking about options, but outcomes, the value you receive given the decisions the person takes. Zero money equals zero money, and is the same outcome.

            I know I’m sort of splitting hairs here, but this game doesn’t fall under the definition of prisoner’s dilemma.

            EDIT: Oh, and I see that Bruce Schneier also makes this distinction: “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).” So there you go.

        2. You’re confusing yourself. This is exactly the same. In this game, there are four options:

          1. You steal, while the other splits.
          2. Both split
          3. Both steal
          4. You split, the other steal

          In every case you are either equal or better off if you steal. So “rationally” you should always steal. But if both players act “rationally” to improve their own outcomes, they get the lowest result.

          So you could suggest there’s a tiny difference with the fact that in this game you are “either equal or better off if you steal” instead of simply always better off if you steal, but that actually doesn’t matter because it still means that the “rational” choice is always to steal, because it means that in all possible worlds you put yourself in the best possible position you could be in.

          And the crux of the paradox is similarly exactly the same: the “rational” choice is only rational if you don’t recognize that all rational actors will opt to do the same thing.

          1. I should have expressed myself more clearly. I blame it on the late hour (middle of the night here). Yes, both games have the same solution. But no, that doesn’t make them into the same game. Repeated prisoner’s dilemma is often used as a game theory experiment, and if you repeat this version you’d have a totally different situation, one where cooperation is much easier to reach, since the split option is less risky. You absolutely need the four different outcomes, ranked in the order I described.

            EDIT: Note that outcome isn’t the same as option. If two options give equal outcome, they only count as one.

  2. Just elegant. It’s also fascinating to watch Nick staring him down like a prize fighter before the bell.

  3. I didn’t think of it as it was leading up to it, but it makes 100% perfect sense.

    It makes no sense to agree to split, because both of you have a strong incentive to lie. Just like in the classic case, you are always better off in every possibility Ii.e. whatever option your opponent picks) if you choose to steal. Therefore you should assume that if you agree on split, the other person will opt to steal and you’ll end up with nothing.

    In this case, by promising to steal, the only reason the other person has to steal is out of pure spite. The other person is guaranteed not to get anything in any case. So their options are to get nothing at all, or to get nothing and trust the other player. There’s really no reason for anyone not to pick option 2, except spite.

    Further, I would trust the person’s word that they will split the money later far more than an empty promise that they will split. Within the confines of the game, lying is expected. Outside of the game, it would be considered crass.

    It’s a pretty perfect strategy. I wonder if there’s much point in having the contest in the future.

    1. To add on:

      Player A is left to choose between spite (and no one getting the money) or going with it, and having a CHANCE of getting the money.

      Very few people would choose spite, if they thought about it.

        1. The strategy worked because there is a difference between guilt and shame. Many people experience guilt, before they’ve even picked, by contemplating the Steal option, and choose to pick Split, unless they feel that being taken advantage of, will make them look the fool. Then they would feel shame.

          Rick, clever boy, took away any possibility that his colleague could experience guilt or shame, UNLESS he picked the Steal ball. If he picked the Steal ball, after Rick guaranteed him, 100%, that he’d choose Steal and would split the money with him afterwards no matter what, then he’d only experience shame if Rick picked Steal but failed at his word to split the money, or if he acted publicly out of spite and lost the money because he chose Steal and so did Rick, or if he chose Steal and Rick actually chose Split. (The redeemed scoundrel stereotype for Rick).
          Cad Cad Cad Duck. It takes a terribly unbright sociopath to not be able to do the shame math (Bright sociopaths feel neither guilt nor shame but have figured out what happens to people who publicise that they’re monsters) to choose anything but Duck Split.
          Because Rick was carrying the entire burden of shame unless his colleague acted the cad.

    2.  “It’s a pretty perfect strategy. I wonder if there’s much point in having the contest in the future.” Agreed. He’s found the corner “X” in the first tic-tac-toe move. I get the feeling the show will have to change to rules to keep the gameplay internal to the show, forbidding reference to events outside the game.

      1. The game is kind of too limited anyway because all that is really interesting about it is the interaction of the two people’s personalities. If it were really about effective manipulation there would need to be more variables to really disorient one of the people. It seems the key to this game is to draw out that discussion till you can get out of it and then do what you were going to do anyway. Which, because this final match kind of ruins the concept of the prisoner game since you can’t refuse and you have no trust to demolish, would logically be steal because you at least have a shot of winning that way and it isn’t like you can trust the other person.

        1.  Variables that disorient a contestant would disorient the audience as well, and make the show less accessible. I think they should separate the contestants and allow no communication between them.

           In the actual Prisoner’s Dilemma, the jailer is the one who can lie about the actions of either party, and there is nothing to be fairly divided afterward.

      2. I disagree. Now that you know all this, the key is the play the part of Ibrahim right down to the “all right, I’m going along with this,” only in the end you’re holding the Steal ball. There’s no guarantee following the same song and dance will always lead to the same outcome.

    3. I kind of *don’t* get it. But maybe I’m just spiteful. He jumped in to talk first, which immediately means he’s trying to take control. So I’d probably have said “that’s funny, I’m going to steal also. Guess we’ll both go home with f*ck all!” Balls are back in his court then. But maybe that’s just me :/

    4. Not sure it’s a “perfect” strategy.  If Ibrahim had caught on to the fact that Nick’s strategy was to lie about steal to guarantee a split, then the best option is to pick steal, knowing that you’ll get the whole thing.

      1.  It’s not about “How do I get the money?’. It’s about “I’m on national TV, my friends and co-workers and potential dates are watching.” Which is not a bad motive to act from.

    5. And yet, if you look at the papers analyzing the results (I peeked at the first linked one, didn’t look at the second), it looks like they awarded about 75% of the jackpots.  More of them went to one contestant than got split between both, but only in 25% of cases did both contestants choose to steal.

    6.  Well now that this has been done, a contestant could choose “spite” thinking that the other person is using the same trick.  Now the spiteful person does have a chance of walking away with everything or nothing.

  4. At least part of the fun of watching this was seeing Jasper Carrott, whom I’ve been a fan of since 1991. Unfortunately after this he’ll probably be out of a job because everyone now knows the way to win. 

    1. Ah, but now that someone has used this strategy, everyone who goes on the show will know about it. So now if Player A tells Player B that they are going to pick steal, B knows that A might be using this strategy. Therefore A will pick split and B is safe to pick steal, taking all the money.

      1. “… “Never get involved in a land war in Asia”! But only slightly less well known is this: … “

    2.  I think Golden Balls is finished anyway, they don’t seem to stick with these afternoon gameshows for long at all.

      Was given a tape of Carrotts standup when i was teenager (early 80s), played it to death. Shame he kind of got sucked into light entertainment shows. Not that he was ever particularly edgy (no Bill Hicks… ;)) but a talented observational comic/storyteller all the same.

  5. I don’t agree that this admittedly clever tactic spoils the game for future rounds. Imagine more contestants go this route. Sooner or later the person acting as the dominant side will be greedy and pick STEAL. Or the submissive side will pick STEAL to win it all since the expectation is the dominant will pick SPLIT. So you’re back once again to whether you trust the person or not.

  6. I’m very curious to see what happens in the next episodes after people have been exposed to this strategy.  Too bad I don’t live in Britain, though I’m sure more clips will end up on Youtube.

    1. At the end of the day it was lucky that those two acted that way. Most of the time, when I’ve seen it, one person steals and one person splits and the person who stole says “Oh, I thought you were going to steal” then scoots off with all the money anyway.

      The pressure to not give the other person the benefit of the doubt – and to stop them taking any money – seems to override a lot of people’s good judgement.

  7. Been doing some thinking about this. It isn’t the foolproof strategy you’d want it to be because of the variable of Abraham’s understanding. If Abraham sees that Nick is effectively saying, “Look, I’m working this so that we both split here and now,” then his choices are as it occurs: gamble on the split on the show, or the split following it.

    But if Abraham thinks the strategy is about manipulating trust, he can monkey wrench it by saying, “Okay, Nick, since you’ve made this about trust, why don’t we reverse it? I’ll pick Steal and split with you later,” and then put the ball back in Nick’s court. Suddenly Nick has to decide whether Abraham gets what he is up to in the metagame sense, or if he’s really banking on the trust issue. It makes Nick’s Split option much more risky.

    I still admire how he enframed the game’s rules, though. A strategy that’s literally a game-changer.

  8. Really have to watch it all the way to the end to see Nick’s reaction to the other contestant having a yacht.

  9. Yeah, I don’t think he broke the game mechanic because in fact there was still an option for him to do either, and he didn’t do what he said he was going to do which means that in the future there will be just as much incentive to cooperate or not based on the trust one player has for another. Interesting tactic guaranteed to work once though.

    I love the look on Ibraham’s face when he hears “100% I’m going to pick the steal ball” from Nick. Classic.

  10. I think that the man’s strategy was rather transparent. He was giving the other guy no choice but to pick Split under the assumption that the other would select Steal no matter what. By trying to force his hand into sharing the prize it was obvious that he was going to switch his choice at the end so that they could split the money then and there, because he was an honest man.

    Taking that information the other could’ve played a metagame and switched his choice to Steal. But because they were both “honest men” they both chose an end game that benefited them both.

      1. I actually crawled under my desk and wiggled wires, since my speaker output cuts out now and then anyway.

  11. I applaud Nick’s altruism because he rigged the game to be either split or payout for Ibriham, but I still wouldn’t fault Ibriham for choosing steal. In a sense, Nick is a liar. He promised he was going to choose steal. He swore up and down he was a trustworthy guy – but in the end he actually lied.

    1. Ish.  The payout was the same as if he hadn’t, and the effect was to immediately show Abe the content of Nick’s character.

    2. He promised to split the money.
      He promised to split the money by picking steal.

      Both statements are accurate representations of his promise. He lied about the mechanics, but the results were the same either way.

      What’s more, he lied to do less than he intended to do, and less than he actually did. He’s absolved of being a liar by both his intentions and his actions.

  12. It seems he backed Abraham into a mental, moral and ethical corner.  Intentional or not, Nick gets Abraham to make that speech about his father. “Man without his word is nothing.” How could Abraham back down from that? If he steals it hurts his honor and reputation. So, mentally the only thing he can do is split. If Nick steals and keeps the money, Abraham looks like a hero. If I went on a game show and invoked my family’s honor, I’d have to stick to it. Nick forced him into choosing the only one option. Nick reduced the variables.
    Awesome post

  13. I could swear there was a version of that shown in the US at some point in the last decade or so.  Contestants put their hands in some crazy contraption which showed people at home what they were doing.  

  14. Most people seem to be assuming that rational self-interest is the prime motive here.

    Obviously I don’t know these men personally, but it’s worth noting that Nick’s strategy made it a mathematical certainty that someone would win.

    1. And I’m aware that the same could be said of any play of ‘Split’ in any game, but by lying about choosing to steal, Nick assumed all of the risk for himself.

  15.  If I were Ibrahim I would have stolen in this case. Suppose Nick is telling me the truth and is just trying to psych me out? By stealing I deny him any money if he steals. If he actually does split while I steal, I get all the money. Keep in mind that I am strongly biased toward cooperation, but if I’m Ibrahim and facing mind games like this,  I will always steal.

    1. The default position for anyone playing the games is that the other person will  do their best to convince you to split, regardless of what they pick. You are guaranteed to be subjected  mind games. The fact that he points it out for you only changes your ability to see it coming, which you react negatively to.

  16. Low Hummmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm………………………………………………………………………………………………………………………………………………………………..

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

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

  18. I think the bigger question is ‘who stole Jasper Carrott’s eyebrows?’ Or did they just ‘split?’

  19. It’s genius. The prisoner’s dilemma is about trust. Player A de-emphasizes the trust issue by admitting to going for ‘steal’. Player B is left with a decision in which trust is less of an issue and is left with only one option to win any money at all. He is left with a probability dilemma: what is the chance he will give me a percentage of the money after the show? Say Player B thinks the probability of Player B sharing 50% of the money is about 10%; in the course of 
    ∞ games he is left with 5% of the price money. Now the only thing he has to decide is whether 5% of the price money is worth punishing the other player for being a dick by limiting your options.

  20. Nick’s strategy – explaining to the other guy that I am stealing, and the only chance they have at seeing any  winnings is to trust that I will split after the show – is essentially the same as mine.  What I don’t understand is why Nick then switches to Split, instead of Stealing, and then either splitting after the show (as I would) or not (as the case may be).

    Unless it’s a tax thing.  He doesn’t want to pay taxes on 100% of the pot, then give *more* than 50% of what remains away to Abraham, who pays taxes (again).

    1. By really choosing ‘split’ Nick guarantees that someone will take home the money: either both of them or his opponent.  And if his opponent took it, he could suggest his opponent give him half outside the game in exchange for thwarting the loss to both of them.

    2. A gameshow win would be classed as a windfall in the UK, and therefore not subject to tax (as with lottery wins).

  21. This shows why games and video games have such a hard time exploring morality. If a game allows you to be amoral then there’s tacit consent to be amoral. But, once the interaction occurs outside the game (I’ll split the money with you after the game ends), we’ve now left the realm of game and entered convention morality with all of its social pressures.

  22. “I will sell you my ‘steal’ ball in exchange for your ‘split’ ball and half the money you will win.”

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