# Probability, poker odds made easy

Aug 4, 2009 5:05 PM
by George “The Engineer” Epstein |

Quick, easy ways to do poker math

Reading about probability in a poker magazine, I found the discussion somewhat confusing. But these concepts can be easily understood. (I taught it to kids under 13 in the Intergenerational Summer Day Camp and they got it!)

Because it is important in our game of poker, I thought it appropriate to better explain the concepts and practical application of probability and poker odds for GT readers.

First Some Basic Definitions

Chance is the likelihood that an event will occur.

Probability is chance in the long run, on the average.

Luck is chance right at this moment – now.

Odds are the likelihood of the event NOT occurring relative to the likelihood that it will occur.

Rather than use coin tosses or horse racing to explain the concepts to poker players, let’s stick with a standard deck of cards.

What is the chance – the likelihood – of cutting the ace of spades from the deck? One out of 52. That’s also the probability of this happening. We can express this probability as a fraction (1/52), as a decimal (1 divided by 52 is 0.0192); or as a percentage (1.92%). If it happens on this cut of the cards, you had good luck.

What are the odds against it happening? There are 51 cards that are not the ace of spades; only one of the cards in the deck is the ace. There are 51 ways to miss; only 1 way to "hit." So the odds against you are 51-to-1. That’s easy to understand.

Applying These Concepts to a Typical Hand

Example: Starting with A-J suited, on the turn the board has two more cards of "your" suit. Now you have four-to-the "nut" flush! You have seen your two hole cards plus the four cards on the board – six in all; there are 46 unseen cards (52 – 6).

Of these, any one of nine (13 – 4) cards will give you the flush. So the probability of catching the nut flush on the river is 9/46; that’s 19.6% More important, what are the odds against catching the flush on the river? There are 9 cards that are favorable; 37 cards (46 – 9) that are not. Therefore the odds against catching the flush on the river are 37-to-9, just over 4-to-1; that’s the card odds.

How to Use this Information

An opponent bets; should you call? The card odds against you are approximately 4-to-1; there must be enough chips in the pot to justify calling a bet to see the river card. Let’s say the pot contains 10 times the amount of the bet. You are getting 10-to-1 pot odds. Since that is more than the card odds, calling would be a positive-expectation bet. In the long run, you will make money by calling. Let’s hope you’re lucky.

Comments? You can reach George "The Engineer" at [email protected].