Recreational Math

Card and Dice Games

What are the probabilities and odds of being initially dealt certain hands in five-card poker and bridge?

Because there are a certain number of cards in a playing deck, mathematicians have worked out the probabilities and odds of being dealt certain hands for certain games. The following explains the odds in terms of “chances against : chances for.”

In five-card poker the probability of drawing a royal flush (a poker hand with the ace, king, queen, jack, and 10 all in the same suit) is 1.54 × 10-6, with odds of 649,739:1. For a straight flush (a poker hand with consecutive cards in the same suit, but not a royal flush), the probability is 1.39 × 10-5, with odds of 72,192.3:1. Three of a kind (three cards with the same value) has a probability of 0.0211, with odds of 46.3:1, while one pair (two cards with the same value) has a probability of 0.423, with odds of 1.366:1.

In bridge 13 top honors has a probability of 6.3 × 10-12 and odds of 158,753,389,899:1. A 12-card suit, ace high, has a probability of 2.72 × 10-9, and odds of 367,484,697.8:1. Getting four aces has a probability of 2.64 × 10-3, with odds of 377.6:1.



Close

This is a web preview of the "The Handy Math Answer Book" app. Many features only work on your mobile device. If you like what you see, we hope you will consider buying. Get the App