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Solutions to the Spin Game

To theoretically analyze the spin game described at the end of the introduction, start by defining P as the probability of the event that the player, starting with disk 1, wins. Then we can write, as follows, all the ways that event can happen:

(1) the pointer stops in area p11 n times in a row, where n = 0, 1, 2, 3 ..., and then the pointer stops in area x1;

(2) the pointer stops in area p12, followed by the event that, if the player starts with disk 2, he wins the game (i.e., the pointer stops in area x1);

(3) the pointer stops in area p11 n times in a row, where n = 1, 2, 3,..., and then (2) occurs.

If ...

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