Player with Greatest Capital wins Fair Game
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Theorem
Let $G$ be a fair game between two players $P_1$ and $P_2$.
Let $P_1$ have greater capital than $P_2$.
Then in a sequence of instances of $G$, $P_1$ has a greater probability of ruining $P_2$ than the other way about.
Proof
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Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): fair game
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): fair game