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Golden Balls

So, this thing has been on my mind ever since my Esquire/ESPN pal Chris Jones sent it my way: There was a British game show that had the unfortunate name of “Golden Balls.” Ah, those cheeky Brits! Best I can tell it ran for two years, and it had this somewhat uneven plot where two people would open these, well, golden balls and build up money in what was sort of a joint bank account. It’s actually a bit more convoluted than that, but for the point in this post that doesn’t really matter. Just know that money gets piled up. And then, at the end of the show, you have two people who have up to now been working together, and an amount of money that would range somewhere between 10,000 pounds and, maybe, 120,000 pounds.

Then, they play the final round — which is what is absolutely fascinating in that Lady and the Lion sort of way.

See the final round of Golden Balls is basically a psychological death trap. It’s a financial and even more freaked out version of the famous prisoner’s dilemma that is often used for game theory. In that one, you have two prisoners charged with a crime.

— If they both confess to the crime, they each get two years in prison.

— If one confesses and the other denies, the confessor gets three years in prison and the denier is let free.

— If they both deny, they each serve one year in prison.

In Golden Balls, like in the prisoner’s dilemma, each person has two choices: Split or Steal. But the outcomes are even more unbalanced than in the prisoners dilemma.

— If they both choose to split the money, they will split the money.

— If one chooses to split the money and the other chooses to steal, the stealer gets everything.

— If they both choose to steal, nobody wins any money.

It took me a few moments to fully appreciate the stark and bare humanity that is exposed by this choice. And they do it in a dramatic way (for TV, of course). Basically, the two players are reminded of the rules, and they are given two Golden Balls — one split, one steal. They are told to secretly look inside so only they would know which is which. And then they are told to talk with each other. Only after they are finished talking will they each decide what to do. And then, after some grueling TV pauses, they each unveil their ball at the same time.

Again, the possibilities using Player A and Player B.

…Player A… …Player B… Result
Split Split Split the money
Steal Split Player A wins all
Split Steal Player B wins all
Steal Steal No one wins anything

I’ve watched a bunch of Golden Balls endings and it usually goes like so: Both players say they will definitely split the money. They promise they will split the money. They talk about how their friends would never forgive them if they don’t split the money. They talk about how half the money could change their lives. They talk about how they would never in a million years cut the other person out; they would never be able to live with themselves. They beg each other to please, please, please split the money.

And then at reveal time, well, you can go on YouTube to see the pain — I don’t want to ruin it for you. It’s just fair to say that sometimes they do split the money. Sometimes they don’t. Sometimes they both try to steal and lose everything. I have to say, it really is human nature on display in all its generosity and treacherousness. I’m shocked this show hasn’t made it to America yet.

But, what really got me was the crazy Golden Balls finale I have linked below. It seems to say a lot not only about human nature, but about sports and how teams can be successful.

In this game, the two men are playing for 14,000 or so pounds. So not as much money as other games, but still a pretty sizable chunk. They start to talk, and you expect this to be the usual blather about how they have a baby at home, and they want that baby to look up to them, and they would never, ever steal money from a grandmother of five and so on. Only it isn’t like that at all.

One player, Nick, starts the conversation like this: “Ibrahim, I want you to trust me, 100%, I’m going to pick the steal ball.”

Ibrahim, expecting Nick to have said something different, does a comical silent film double-take and then says, “Sorry, you’re going to pick …”

And Nick confirms: “I’m going to choose the steal ball.”

Yep, he’s going the other way. Here’s Nick’s deal. He promises Ibrahim that he is absolutely going to choose the steal ball. But he also promises Ibrahim that he will split the money with him after the show. Ibrahim looks at him like he’s some kind of nutter. The host, clearly taken aback, reminds Ibrahim that Nick would be under no legal obligation to split the money — something Ibrahim already knew. He’s outraged. But Nick doesn’t seem to care. Nick says the decision is entirely up to Ibrahim. He can choose steal too and they will each walk away with nothing. Or he can choose the split ball and trust Nick to split the money with him.

This concept is so fascinating that, as I said, I’ve been thinking about it way too much the last couple of weeks. Let’s try to break this down for a minute. If you are playing Golden Balls, your only goal is to get your opponent/partner to choose the split ball. That’s the only way you can win any money.

If opponent chooses split ball:

You choose split: You get half the money.

You choose steal: You get all the money.

If your opponent chooses the steal ball, though, you only have two bad choices:

If opponent choose steal ball:

You choose split: You get no money, opponent gets it all.

You choose steal: Neither of you get a dime.

So, your only hope in this game is to somehow, someway get your opponent/partner to choose the split ball. Well, how do you do that? That’s the essence of the game. Most people would say that way to get your opponent to split is to convince your opponent/partner that you are honest, and you will definitely choose the split ball. That’s the strategy almost everyone uses. But there’s a big problem with that strategy: If your opponent KNOWS you are going to choose the split ball, you are giving them the choice to be kind and split the money with you or just take all the money for themselves. That’s hardly a choice you want to give people, is it?

But what else can you do? You see people beg and plead and make the most intense promises. Sometimes, it works. And sometimes, it doesn’t.

Nick changed the entire drift of the game. He reversed the rules. It seems to me that’s what great coaches and managers can do sometimes. Nick told Ibrahim straight out that he would steal. He did not back off of it no matter how angry Ibrahim got and no matter how much Ibrahim tried to reason with him. He left Ibrahim with absolutely no doubt that he would steal, which left Ibrahim with only two choices.

1. He could choose split and hope that Nick really would give him half the money, which seems kind of a sucker’s bet.

2. He could steal and walk away knowing that, at the least, he prevented that nutter Nick from getting the money.

See the difference? Instead of Nick appealing to Ibrahim’s essential goodness like everyone else does, he challenges Ibrahim’s fury. OK, he’s basically saying, I’m telling you straight out I’m going to steal. I know that ticks you off but, frankly, I can’t help that. I’m stealing. Now, what are you going to do? How badly do you want to punish me for choosing steal? Are you so angry that you will choose steal yourself, assuring that neither of us will get a dime? Or will you choose split and take the chance — however low you might believe it to be — that I really will give you half the money?

What does Ibrahim do? How does it end? I don’t want to ruin it for you. Let’s just say that it’s pretty great. You can skip ahead to 2:35 and watch the psychological drama unfold.

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39 Responses to Golden Balls

  1. Rob Smith says:

    That was unexpected and pretty much genius. I imagine nobody else ever thought of that!

  2. Jeff Russell says:

    Joe, you say that instead of Nick appealing to Ibrahim’s essential goodness like everyone else does, he “challenges Ibrahim’s fury.” Based on your description of the game, I know what you mean, but I think it’s the exact opposite of that at its core. I think Nick is banking on Ibrahim’s goodness even more than normal participants do. I think he believes that the best way to guarantee that Ibrahim chooses the split ball was to say he’s taking the steal ball in order to present Ibrahim with these two alternatives:

    1) choose the steal ball and look rash and spiteful in front of a national/international audience; or
    2) choose the split ball and look like the good guy, and possibly (although not certainly) scoop up half of Nick’s bounty after the show (with some chance that Nick is yanking his chain and will pick split anyway)

    In essence, I think Nick is banking on Ibrahim’s GOODNESS, i.e. his ability to NOT be rash and spiteful, as what will be the most likely to cause him to pick the split ball. Time to watch what happens…

    • Rob Smith says:

      Concur. But also Nick really has to sell that he’s choosing Steal and leave no doubt that this is what he’s going to do. That’s the essential element. Nick had to leave no doubt, which he did well. Ibrahim was a good guy, but he also realizes that his only chance for a win was to trust that Nick wasn’t a total tool. If Ibrahim chooses steal, he KNOW that he loses, so being spiteful gives him no benefit. Nick really thought this through and was completely committed to his strategy. So, it worked.

  3. Austin says:

    I think your prisoner’s dilemma description is wrong. If one of them confesses and one denies, the one who confesses goes free and the other gets 3 years.

    • brhalbleib says:

      Yeah, I am pretty sure Joe has something backward there, because it doesn’t present the dilemma as well as if some things are reversed

    • rcharbon says:

      The Wikipedia article that Joe used as a reference is one of the poorer, less clear, efforts.

    • berkowit28 says:

      Yes. There’s no risk to denying. At best you go free, at worst you get 1 year. Whereas if you confess, at best you get 2 years, at worst 3 years. So there’s no dilemma: deny. All results are better than if you confess.

      There must be a different, correct version of this.

    • Richard S. says:

      The actual “Prisoner’s Dilemma” has that instead of confessing, you rat on your “partner”. You go free in exchange for providing evidence; your partner who kept silent gets the maximum penalty. If you both rat on each other, you each get the lesser penalty. If you both keep silent, the law has nothing to pin on you so you both walk.

  4. Ed McDonald says:

    I had not heard of that show before. It couldn’t air in the states, someone would end up murdered.

    • Rob Smith says:

      I believe Bachelor Pad had that element at the end. The “couples” were presented with similar choices and could share or steal the cash prize. I think it’s come up in other minor reality shows as well.

  5. invitro says:

    If I were on this show, I would say “I’m going to flip a coin, and if it’s heads, I’ll pick the one on my left, and if it’s tails, I’ll pick the one on my right.” And then I’d do just that.

    • Joshua says:

      That’s actually the worst possible strategy. If you do that, an intelligent opponent will simply pick steal and guarantee you get nothing. Since you haven’t committed to picking split, there’s no moral pressure on him to pick split as well. At that point, if he steals he has a 50% chance of getting everything and a 50% chance of getting nothing, whereas if he picks split he has a 50% chance of getting only half and a 50% chance of getting nothing. Stealing is the easy and obvious choice, and guarantees you get nothing.

    • invitro says:

      Relieving “moral pressure” is the point.

    • schuyler101 says:

      Sounds like relieving moral pressure and guaranteeing you come with nothing is the point

  6. I think Nick is also relying on Ibrahim’s goodness in another way. He says he’s going to pick steal but he has promised Ibrahim that he will split the money with him after the show. But Nick knows he’s actually going to pick Split, so he knows that they’re not both walking away with nothing. Either they’re actually splitting or Ibrahim will get it all. So yes, he’s banking on Ibrahim deciding not to be spiteful and choose split, but at least a small part of Nick knows that even if Ibrahim chooses steal (and thus gets it all) there will be some moral pressure on Ibrahim to then share it with Nick because Ibrahim (and the whole world) will see that this was all just Nick’s strategy to try to get Ibrahim to split the money and that Nick was willing to risk Ibrahim getting it all do that.

    • Rob Smith says:

      I think Ibrahim was both a good guy and intelligent… pretty fast on the uptake. Ultimately he did believe Nick, and Nick sold the story well, so Ibrahim calculated that he had nothing to gain by choosing steal, since it guaranteed him to receive no money…. and people don’t go on that show to come home with nothing. This was the crux of Nick’s strategy. Otherwise, I gather, people can, and do, make all sorts of rationalizations not knowing what the other person was going to do.

  7. Why isn’t Nick’s promise enforceable?

  8. Sean says:

    I’d never heard of Golden Balls, but I’d watched a couple episodes of “Friend or Foe” years ago in the States, and I figured even then that this would be the best strategy. I just assumed that it wasn’t allowed by the rules of the show since nobody was trying it.

  9. FranT says:

    C’mon, Joe, the British don’t use a dime as currency.

  10. jim says:

    Is anybody willing to start a Kickstarter campaign to buy Ned Yost a calculator and a fucking lesson in algebra? The baseball season is 162 games. Winning .500 percent means winning 81 games. Thus, when you win 86 you are five games above .500. Not ten. Yet I keep seeing his “Ten games over .500, it’s a significant first step” quote over and over and over again. Winning ten more games than you lost is not the same thing as being ten games over .500. If he can’t get this math right, no wonder he can’t get any of the rest of it correct. Fucking sigh.

    • Of course you’re correct. However, I’m going to give Ned Yost a pass. He’s hardly alone in this particular misusage. Indeed, I think this misusage is nearly universal. Almost everyone throughout baseball would describe the Royals as 10 games over .500. They almost all refer to the difference between wins and losses as being identical to a team’s position relative to .500. So I can’t get on Ned Yost for making the same mistake that almost everyone makes.

    • Chad says:

      I’m going to have to disagree with you. If you are 86-76, how many games would you have to lose to fall to a .500 winning percentage? The answer is 10.

      I get what you’re saying … if 5 games had gone differently, you’d be at .500, but I think Yost is correct.

    • Dan Shea says:

      One of my favourite baseball stats when I was a kid was Games Behind Leader. And we all know how that works. I don’t see why Games Over .500 should play by a different set of rules.

    • Dan Shea says:

      Interesting Wikipedia bit –

      “The “games behind” number is sometimes made in reference to a standard “winning percentage”, although in this particular context, the word “behind” is replaced by “under” or “below”. In making this calculation, however, the division by two is not done. For example, a team with a record of 19 wins and 20 losses is considered as being “one game under .500”, in contrast to being “one-half game behind” a team with a “.500″ record of 20 wins and 20 losses.”

    • Thanks for calling this to my attention, Joe. (The reference in paragraph two is to Frank Stockton’s “The Lady or the Tiger?”, first published in 1882, assigned in freshman high-school English for generations, perhaps still.)

    • Chad says:

      After thinking some more, at 86-76, it should be phrased “We are 10 games over .500” or “We are 5 games BETTER THAN .500”

    • jim says:

      Chad, think some more: Saying the Royals are 10 games above .500 implies they could have lost ten more (won ten fewer) and would have still been .500. If the Royals lost ten more they would have been 76-86, or five games under/worse than .500.

      It really is just simple algebra.

    • Chad says:

      Sorry, not buying it. 10 games above .500 means they could lose 10 more games and still be .500 … the real issue is you’re changing the outcome of games played, as opposed to looking to the future.

      I’ll go with you if you say 5 games better than .500; this, to me, says if 5 games had different outcomes, they would be .500

    • jim says:

      Chad, why can’t you see that after 162 games there are no more games! If you add ten more games, you are changing the denominator!

      After 162 games .500 equals 81 wins. (so 86 wins is 5 games above .500)
      After 172 games .500 equals 86 wins. (so 86 wins is equal to .500)


    • Chad says:

      Good thing one of their wins wasn’t rained out, or else they would have finished only 4.5 games above .500. :/

    • schuyler101 says:

      Semantics, not algebra.

  11. yeah, i haven’t heard that show too..


  12. Jason Dennis says:

    The most famous episode of this is the one with the now professional poker player Liv Boeree. It’s a very easy game theory problem. The math solution is to choose steal. I have actually said I would employ a strategy similar to this post in a message board. I’m absolutely certain the show is scripted though.

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