This is great. The Show offers each player with three possible outcomes, which makes negotiation hard because the highest incentive is on getting all the money (choosing Steal while tricking the opponent into choosing Split), while the lowest incentive is on nobody getting anything.
What Nick does by saying that he will definitely Steal is reducing the choices for Abraham to two: Split or Loose. Actually just one: Loose, albeit with a promise to also split.
The cunning bit about the plan, of course, is that Nick never intends to choose Steal. Choosing Steal is foolish to begin with: There is a 50% chance that nobody will get anything if you choose steal, so by default, players should stay away from it. "Count your blessings", so to speak.
What is clever about this is that Nick has replaced the technical bet with a social one: He has done something that appeals to his opponent, by challenging his intellect, turning the game on its head. For Nick, the chances are now that either he gets half or nothing. He, internally, accepts a lower possible payout to himself to maximize the probability that the "group" will cash out. In any outcome, this would mean that it's no longer "He tried to get the money", but "He tried to make sure we get the money". I would say there is a pretty good chance that Abraham would have decided to give him half, even had he decided to Steal, basically matching Nicks generosity. This is supported by the fact that Nick really did end up displaying the Split - Had Abraham revealed a Steal at that point, he surely would have felt like quite bad about this ("He did it to help us both, after all!").
Nick has simply maximized the chances of a Split on all available vectors.
I think this game is actually pretty close to a prisoner's dilemma. Why wouldn't you choose steal if you've managed to convince someone to choose split? If they didn't chose split, you'd still lose anyway.
In very basic, almost evolutionary terms, the dumbest thing to do is both choosing Steal, because that would mean that there are two losers. Only choosing split yourself makes sure that there is a winner.
Steal only seems sensible if you care about winning yourself.
I think you are making a big assumption with your number of "50%". It's true that there are two possible outcomes for either choice I could make. But what makes you say they are equally likely? To my mind, the estimating of that probability is actually the crux of the game.
Yes, that was what I was talking about - If you make a choice and then depend on another person making a choice, your chances are precisely 50/50. That's the prerequisite of the game.
Of course, it gets a lot more complicated after that, particularly because you can talk to your partner. (That's kind of why I wrote "superficially", but it seems that word has triggered the downvote police.) Not sure whether it changes much of the math, though - after all, anything that you weigh in favor of something could always be a lie.
I was pointing out that of the basic choices that are offered to you, one is very disadvantageous, so it should be an advantage to prevent it from even possibly happening by choosing Split. You can literally prevent 1 in 4 outcomes with your decision. This realization, paired with some very social engineering in the example is what made this so impressive to me.
in the case of the show there is a third player that loses when you both split so it is not clear that steal is only sensible if you care about winning yourself. :)
What Nick does by saying that he will definitely Steal is reducing the choices for Abraham to two: Split or Loose. Actually just one: Loose, albeit with a promise to also split.
The cunning bit about the plan, of course, is that Nick never intends to choose Steal. Choosing Steal is foolish to begin with: There is a 50% chance that nobody will get anything if you choose steal, so by default, players should stay away from it. "Count your blessings", so to speak.
What is clever about this is that Nick has replaced the technical bet with a social one: He has done something that appeals to his opponent, by challenging his intellect, turning the game on its head. For Nick, the chances are now that either he gets half or nothing. He, internally, accepts a lower possible payout to himself to maximize the probability that the "group" will cash out. In any outcome, this would mean that it's no longer "He tried to get the money", but "He tried to make sure we get the money". I would say there is a pretty good chance that Abraham would have decided to give him half, even had he decided to Steal, basically matching Nicks generosity. This is supported by the fact that Nick really did end up displaying the Split - Had Abraham revealed a Steal at that point, he surely would have felt like quite bad about this ("He did it to help us both, after all!").
Nick has simply maximized the chances of a Split on all available vectors.