[SumZero]

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Her argument was based arround the fact that she is not willing to risk any amount of money on a +10% wager, when the coin is only going to be flipped once. It was this element that prolonged the argument, because she valued risk aversion much higher than the EV of a single coin flip. Not necessarily because she doesn't know the concept of +EV, but because there was no guarantee of outcome on a single flip. I asked her what +% would she need in order to take the flip, but she wasn't able to answer. For the same reason I'm sure - it would still be a single flip. She did however say that she would flip the coin 100 times. But definitely not once. As was said already, beyond bankroll issues there really is no way to justify this.

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This is just stupid if what you've stated is true. If she'd accept the 100 flip game then she certainly should accept a 1 flip version where she wins more than 1 / 2^100 times (I.e., the chance that she'd lose all 100 flips). And she should likely accept much more than that. No matter how you define +10%, her chances of being negative after 100 flips are pretty high. If you define +10% as risking 10 to win 11 then there is a greater than 27% chance she is negative after 100 flips (and often times negative by a lot). If you define +10% as a 55% chance to win each flip then there is a greater than 13% chance she's negative after 100 flips. Even at 60% likely to win any individual flip she's more than one and two thirds percent likely to be negative.