We consider the Independent Chip Model (ICM) for expected value in poker tournaments. Our first result is that participating in a fair bet with one other player will always lower one's expected value under this model. Our second result is that the expected value for players not participating in a fair bet between two players always increases. We show that neither result necessarily holds for a fair bet among three or more players.
Cubature rules and expected value of some complex functions
Expectation, Conditional Expectation and Martingales in Local Fields
The Family of Alpha,[a,b] Stochastic Orders: Risk vs. Expected Value
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