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The box means NOTHING

Posted By: Timothy Chow
Date: Saturday, 29 August 2009, at 2:17 a.m.

I just read Phil Simborg's entertaining article on chouettes. He makes the point that "the box means NOTHING," and of course the general drift of his point is correct. However, it seems to me that it may not be quite correct mathematically. Suppose you are noticeably stronger than the other players. Then surely your expected earnings for the session will be higher if you stay (or get into) the box. One way to model this fact would be to give you a fixed "bonus" B for winning the game. In certain situations, this bonus could affect the play. In the limit as B gets large, the box's checker play would focus just on the win, but the cube would still be live---a rather strange situation.

Of course in practice, B is probably not that large, and it is psychologically easy to make the mistake of overestimating B. Moreover, there are many other factors at play in chouettes that are more important than this one. Still, it's interesting to contemplate what "correct" play would look like under the assumption of a bonus B for winning.

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