Here's How Likely Each Poker Hand Is

Poker is a fantastic game, particularly alluring to competitive, creative types who love numbers. Business Insider’s Eugene Kim has profiled some of Silicon Valley’s biggest poker fans, and the game is also huge draw with the Wall Street crowd.

While I’m far from a serious, professional poker player, I do occasionally get a chance to enjoy a game with friends. And I also love maths and statistics.

So I decided to look at some of the basic mathematics of the game. Here, I go through the probabilities of drawing each five-card poker hand from a deck of cards. These probabilities are handy to have in the back of your head in a poker game, and they are the reason why hands are ranked the way they are: a straight flush is way less likely than a pair, so this is why the straight flush wins.

How To Find Probabilities

Finding The Number Of Hands

Order Doesn't Matter

Getting Rid Of Order

The Magic Number

Straight Flushes

Probability Of A Straight Flush

Four Of A Kind

Full House

Full House Part 1: Three Of A Kind

Full House Part 2: Pair

Flush

Counting Flushes

Probability Of A Flush

Straight

Probability Of A Straight

Three Of A Kind

Counting The Triples

The Other Two Cards

Order Doesn't Matter Again

Probability Of Three Of A Kind

Two Pairs

Counting Pair Ranks

Counting Pairs

Probability Of Two Pairs

One Pair

Counting Rank Options

Probability Of One Pair

High Card

Probability Of High Card

All The Probabilities

This Is Just The Beginning...

Sources

We based our calculations on this article by mathematician Brian Alspach.

Card images come from this collection by Iron Star Media.

Now check out some more maths!

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