Video: strategy in a TV game show

Game theory concepts can often help when trying to win prizes on a TV game show. I have previously written about a couple of the scenarios from the U.S. show The Price is Right:

Optimal strategy in spinning the wheel

Strategy for Pay the Rent

Strictly dominated strategies in Lucky Seven

I came across another instance of game theory in a British TV show called Golden Balls. One of the games in the show is called “Split or Steal” and it closely resembles the classic game of the Prisoner’s Dilemma.

The twist in the game is that players are in the same room and can communicate, which yields some entertaining dialog and reactions.

Below is the video where one person decides whether to trust his partner with £100,000 on the line.

Video: Golden Balls – £100,000 Split Or Steal?

Rough transcript of the show

Host: This is serious, life-changing money. The jackpot today is £100,150. You have one final decision to make. You are going to play “Split or Steal.” I know you’re the last two people in the country I have to explain this to, but you have two final golden balls.

You each have a golden ball with the word “Split” written inside. You each have a golden ball with the word “Steal” written inside. You will make a conscious choice choosing the “Split” or the “Steal” ball.

–If you both choose the “Split” ball, then you split the jackpot of £100,150 and go home £50,075 richer.

–If one of you “Splits” and one of you “Steals,” then whoever chooses the “Steal” ball will go home with £100,150. The person who chooses the “Split” ball goes home with nothing.

–If both of you choose the “Steal” ball, then both of you go home with nothing.

[Note: the game resembles a Prisoner's Dilemma, with payoffs as follows (via Wikipedia):

Result Split Steal
Split 50% 50% 100% 0%
Steal 0% 100% 0% 0%

The game is a version of the Prisoner's Dilemma: it is in each player's interest to steal the jackpot.

That is, you want to trust your partner and pick split, but if you know your partner will split, then you would rather steal and take everything for yourself.

The outcome is that both players are tempted to steal, and if they do that, then both end up with nothing.

Let's see how the contestants fare on the show, and whether they can cooperate.]

Before I ask you to choose, I want you to look at your golden balls and make sure you know which is the “Split” and which is the “Steal” ball. This is very important, and make sure you don’t show it to us.

Before I ask you to choose, I think you have some talking to do to each other.

[Important background note: Both Stephen and Sarah are returning contestants from previous games who all "Split" where their opponent "Stole."]

Sarah: Stephen, I just thought they weren’t puppy dog tears and they were real tears, and that you were genuinely going to split that?

Stephen: I am going to split this. 50,000, I’m just, it’s unbelievable. I’m very, very happy to go home with 50,000.

Sarah: You’re telling me you are going to split?

Stephen: If I stole off of you, every single person would come over here and lynch me.

Sarah: There’s no way I could. I mean everyone who knew me would just be disgusted if I stole the money.

Stephen: When people watch this, they are not going to believe it. Sarah, I can look you straight in the eyes and tell you I am going to split this money. I swear to you.

Sarah: That’s great.

Host: This is serious money. Sarah, Steve, choose either the “Split” or the “Steal” ball now. Hold it up.

Stephen: We are going home with 50,000 each. I promise you that.

Host: Split or Steal?

Stephen holds up SPLIT
Sarah holds up STEAL

Host: You never know what’s coming up in this game. Congratulations Sarah, you have just won £100,150. Stephen, I am so sorry, commiserations. You have just lost. So an unfamiliar feeling for one of you, but a horribly familiar feeling for another.

Stephen: Golden Balls has taught me that some people look for revenge quite easily. And greed knows no bounds.

Sarah: When I saw Stephen hold up the “Split” ball, I wasn’t proud, I wasn’t happy about what I had done. But having been stabbed in the back last time, I just couldn’t put myself through that again.

It’s a bit painful to see how the game turns out. Stephen tried his best, but ultimately he faced a no-win situation because Sarah could not overcome having been betrayed in a previous game. Sarah was clearly not playing the game at hand but instead considering a bigger game in which she wanted to avoid being double-crossed again.

It would have been nice to see them cooperate, but the true nature of the game is not always pretty.



Share this post:

| More

Previous post:

Next post:



  • Sameer

    This comment has nothing to do with game theory, but somehow when I saw her say “please”, I suddenly became certain she was going to steal.

  • http://purplepawn.com Yehuda Berlinger

    Frankly, I think this is a dumb decision. The difference in value between n and 0 is far more than it is between 2n and n. If the difference were an order of magnitude, it might actually be interesting.

    Here’s what you have to realize: the moment you decide to steal, your opponent gets nothing. If she decides to split she gets nothing. If she decides to steal she gets nothing. By you taking steal, you are damning your opponent and she has no recourse.

    The above woman who said “having been stabbed in the back last time” is not doing herself any favors by stealing (the difference between 2n and n, which is not much) but simply stabbing someone else – who doesn’t deserve it – in the back.

    But here’s what you also have to realize: the sum total of what the show will pay out is X or 0. If either or both players split, the show will pay X. If both players steal, the show keeps the money.

    My goal would simply be to ensure that the show doesn’t keep the money. I would lift up the “split” ball and SHOW it to my opponent and say “Here, you’re talking nice, but let’s simply split the money, whether you choose split or steal, ok? I’m going to ensure that, between the two of us, we get the money and the show doesn’t get to keep it. Now your ball is irrelevant. If, on the other hand, you choose to steal after seeing that I put the split ball in, and you actually insist on keeping the money afterwards, then you’re an asshole.”

    Yehuda

  • http://www.mindyourdecisions.com/blog/ Presh Talwalkar

    Yehuda: Your comment reminds me about the magna called Liar Game in which some players realize the goal is to maximize the surplus and not fight amongst each other to mutual self-destruction.

  • Jeff

    My thoughts are that you could guarantee a win by taking charge(and changing the game).

    Convince your opponent that no matter what, you are going to steal. That way their options are between $0 and $0. However, then tell them that if they hold up share (so that you win all the money), you will give them X% after the show.
    Now the game has transformed into an Ultimatum game, where you just have to figure out how little they will accept.

  • http://purplepawn.com Yehuda Berlinger

    Jeff, I woke up and came here with the exact same thought as you: that the only way to convince the other person that you weren’t trying to trick them was to swear that you are going to put in the steal ball. My offer to the other person would be 50% (again, $n is not much versus $n + $x, but game theory tells us that even if $x is $1, the other person is likely to screw both of you simply because he feels like he’s getting an unfair distribution), and I would be willing to give show them a check for the amount or a signed contract to the effect.

  • Pingback: How to beat the Prisoner’s Dilemma in the TV game show Golden Balls - Mind Your Decisions

Previous post:

Next post:

This site is for recreational and educational purposes only (privacy policy)

Powered by WordPress