# On average how many games of bridge are necessary before a player is dealt three aces?

A bridge hand is 13 randomly selected cards from an ordinary deck of 52.

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- Jay VLv 49 years agoBest Answer
just multiply the number of ways of choosing 3 aces from 4 and 10 cards from the remaining 52

C(4, 3)*C(48, 10) = 4 * 6540715896

this gives you number of ways to get only 3 aces but if you want at least 3 aces then add

C(4, 4)*C(48, 9) = 1 * 1677106640

then divide this number (sum) by C(52, 13) to get the probability of accuring one of these hands.

The expected number of trials before success = 1/P(aquiring a success) = inverse of the above calculated number.

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