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 GeoAstro Applets |
 Astronomy |
 Chaos Game |
 Java |
 Miscel- laneous |
Gambler's Ruin Applet
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A gambler
starts with a stake of size S.
He repeatedly plays a fair game, with 0.5 probability of winning or losing 1 dollar, until his capital reaches the value M or until going broke (capital 0). |
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button starting a single game, the diagram is showing the current capital button to stop the game |
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select the value S
of the initial stake |
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select the value M
of the final capital the player tries to reach |
Statistical analysis:
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button starting a set of N games |
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the numbers N of games can be selected from the menu |
The probability of winning a capital M starting
expected duration of a fair gambling game
P = S / M
expected duration of a fair gambling game
If the gambler starts with S dollars and plays until he is broke (lost) or has a capital of M dollars,
he can expect n = S·(M-S) steps
expected duration of a fair gambling gam
expected duration of a fair gambling
The green line is computed from the blue and red one by:
n = Pwon·nwon + Plost·nlost = (S/M)·nwon + (1-S/M)·nlost
which agrees with n= S·(M-S)
Updated: 2023, Oct 06
