Player with Greatest Capital wins Fair Game

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