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Basics of Math in Poker

your brain on pokerA proper understanding of the basics of poker math will take you a long ways in your poker career. Not only will it help you at the tables but it will also help you get a better grip on the poker strategy you study during your time away from the tables. These concepts all sound difficult at first but they actually only involve basic math.

Expected Value

This term is thrown around a lot at poker strategy forums and it is one of the most important poker math concepts. Expected value takes a long term look at the profitability of your actions at the poker table. It describes the average gain or loss of an action over the long term.

An example would best explain this concept:

Let's say you enter into a proposition bet against another person. He says he'll pick a number between 1 and 10 and you have to guess the number he's picked. If you lose, you have to pay him $5 but if you win, he'll pay you $50. What is your expected value?

In this example, you can expect to guess incorrectly 9 times out of 10 and guess correctly 1 time out of 10. The 9 times you lose will cost you a total of $45 but the one time you win will earn you $50. Your total expectation is +$5. Divide that $5 by the ten trials and you'll get an expected value of +$0.50 per guess. In theory, you're gaining 50 cents per guess.

The actual results of your bet will vary widely over the short term but as you play this game more and more, your actual results will more closely resemble your expected results. Over hundreds and thousands of trials, you'll end up with a correct guess 10% of the time. Therefore, your expected value is 50 cents per guess.

Pot Odds

When you hear a poker player mention his "pot odds" he's referring to the size of the pot in comparison to the size of the bet he must call. Let's say your opponent bets $50 into a $50 pot. The pot would now be $100 and you must call $50 to stay in. All you do is slap these into a ratio and reduce it. 100:50 reduces down to 2:1 so you'd think to yourself "I'm getting 2:1 pot odds."

Pot odds are most commonly used to determine the profitability of a call based on the chances that you'll win the hand. So if you have a flush draw on the turn and your opponent bets a small enough amount to give you pot odds better than 5:1, you can call and make a profit over the long term. Check out my pot odds article for more details on this concept.

Pot Equity

This concept confused me for the longest time until I actually took the time to research it - then I found out how simple it is. Pot equity simply describes your share of the pot based on the chance you have of winning the hand.

Let's say you and an opponent are playing in a $100 pot and you think you have a 75% chance to win the hand. To calculate your pot equity, all you do is multiply the pot times the percentage. In this example, 100 x .75 = $75. Your pot equity is $75.

Poker Concepts Worth Knowing