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The question that arises therein is this: how long should the players wait to steal the pot?Īll this should be sounding familiar.

By passing the pot, each player is increasing the payoff they could receive, but in the end only one player walks away with the pot. In layman’s terms, a Centipede Game is any game in which there are two or more players, and each player, when given the pot, has the option to either pass the pot, adding to its value, or take the pot for themselves.

The payoffs are arranged so that if one passes the pot to one's opponent and the opponent takes the pot on the next round, one receives slightly less than if one had taken the pot on this round. In game theory, the centipede game, first introduced by Robert Rosenthal in 1981, is an extensive form game in which two players take turns choosing either to take a slightly larger share of a slowly increasing pot, or to pass the pot to the other player. What exactly is a Centipede Game? Well, here’s how Wikipedia puts it:

In analyzing the Button, one can’t help but categorize it as a Centipede Game. Here, we will be discussing the timing of the press.

Graycism aside, I try my best to approach the Button rationally. Like the prior post, which can be found here, I will preface my post by confessing that I am a Follower of the Shade and, out of pragmatism, a Gray Hopeful. Welcome to part two of my series on Button Game Theory.