9711

Spin Game

A player spins the pointers on two disks as follows. The game starts with the first disk. If the pointer stops:
• in the green area, the player stays with the same disk and spins the pointer again
• in the blue area, the player moves to the other disk and spins its pointer
• in the red area of the first disk, the player wins and the game stops
• in the red area of the second disk, the player loses and the game stops
You can set the probabilities of the green and blue areas with the sliders.

SNAPSHOTS

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DETAILS

Snapshot 1: if the probability of moving from disk 1 to disk 2 is zero, the probability of winning is 1
Snapshot 2: if the probability of moving from disk 2 to disk 1 is zero, the probability of winning does not depend on the probability of continuing with disk 2
Snapshot 3: if we always continue with disk 1, the probability of winning is indeterminate because the game never ends
Snapshot 4: if we always continue with disk 2, the probability of winning is likewise indeterminate because it is possible that the game never ends
Snapshot 5: if we always move from disk 1 to disk 2 and from disk 2 to disk 1, the probability of winning is again indeterminate, because the game never ends
The Demonstration is based on [1, pp. 28, 244–247], where the probability of winning the spin game is calculated by a clever method (note the misprint in the boxed probability on p. 245: in the denominator should be ).
Reference
[1] P. J. Nahin, Digital Dice: Computational Solutions to Practical Probability Problems, Princeton, NJ: Princeton University Press, 2008.
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