If a game were fair the payoff on a bet would be the same as

If a game were \"fair,\" the payoff on a bet would be the same as the odds for the event. In one game, the odds for winning are 1:13. If the game were \"fare,\" what would the payoff be for a $5 bet ? of course, games in casinos are designed to make a profit for the casino investors. Supposing the casino makes the payoff at 1:11 odds, what profit does the casino make on your winning bet?

Solution

Odds for winning = 1:13

prob for winning = 1/14 and losing =13/14

For a 5 bet, if k is return for winning then

E(x) = (k-5)/14 -65/14

For a fair game E(x) =0

k-5 = 65 so k = 70

When pay off is 70, it is a fair game

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When payoff at 1:11 odds

means prob for pay = 1/12