Your expected earnings is −pX+(1−p)Y=0 Then it must be the case that p1−p=YX Or that the ratio of the payouts has to equal the odds. So consider, for example, if p1−p=2. The game is 2 to 1 against you, p=2/3; she is twice as likely to win as you. Then she will have to pay out twice as much if you win to make the game fair.