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Poker Math 101

Poker is a game of feelings and intuition.  Especially when we play online poker, where we can’t see our opponents, we have to observe them in different ways.  These ways are mostly feelings and intuition.  Even in land-based casino poker, when we feel that an opponent has shown us a tell, we feel that way through intuition. 

Poker Success Can Come Via Mathematical or via Common Sense Analysis

Although poker is at base a game of feelings and intuition, math has come to play a very important role in modern poker, especially in tournament poker.  As much as you’ll use feelings and intuition to determine many actions, many players feel that it is important to learn the basic mathematics of poker if they want to achieve ongoing success playing poker.

Poker Math Faces Daunting Complexities

Math is, in a real sense, a rigid set of principles so poker math works equally well when we play poker online or on land.  If you try to look up the mathematics of poker on the internet, you’ll likely find many sites that use jargon and esoteric language to explain the mathematical concepts that can determine the best course of action.

Having said that the mathematics of poker is important to learn and, having said that poker is at base a game of feelings and intuition, we need to explain this seeming contradiction.  After all, at every stage of a poker hand, the number of possibilities increases by the millions of unique units.

Even the greatest mathematical mind could not go through so many millions of permutations in the time allowed for a single decision.  So, let’s understand the word “intuition” to mean “insight” and let’s understand “feelings and insight” to mean conclusions arrived at through inductive reasoning.

Probability and Odds

These are the first math terms you need to learn in order to begin using poker math but they are confusing to many players.  Probability is expressed as a percentage while odds are expressed as a ratio of one event versus another, in the case of poker the ratio of winning chances to losing chances.

Both can also be expressed as the opposite.  For example, if you have a 20% chance of getting the card you need to win a hand, you also have an 80% chance of not getting the card.  A 4-1 chance of not getting the card is the same as a 1-4 chance of getting it.

Some players understand the hand as a percentage, in other words as their probability of winning while others understand it better as the odds of winning.  Many strategy analysts insist that we all learn to express our status in a hand in both ways but that is not necessary.  Follow your skills in both intuition and math!

In order to know your chances of winning, you need to know how many outs you have.  However, when you’re playing against real opponents you never know how many of the cards you need are still available since you don’t know which cards have been folded.

So players go from calculating the odds to calculating the amount of money you stand to win or lose if you call or raise a bet.

Pot Odds

Pot odds are another way to calculate the probability or ratio of winning versus losing a hand.  Simple probability takes into account your outs.  Pot odds takes into your outs and the cost of seeing another card based on the size of the pot and the amount you need to bet to stay in the hand.

Therefore, determining the pot odds is a better way to mathematically calculate and express the value of staying in a hand over simple probability and simple odds.  Calculating pot odds is confusing to even experienced players.

You add the bet you need to make to the money already in the pot and divide that into the bet you need to make.  So, if you have to bet $10 to stay in a pot that has $90 in it, your fraction is 10/100 or 10%.  The ratio way of expressing this is 90:10 or 9-1.  What exactly does this tell us?

The fact is that if you feel that you have the stronger hand, pot odds don’t tell you much.  If you feel that you have the weaker hand, pot odds tell you the cost of seeing one more card.  That is valuable information.


This is another term that poker analysts use that confuse a lot of players simply because it is used differently in poker than it is used in real life.

In real life, your home equity is all the money you have invested in the house minus your interest payments.  You can also say that any expected profits from the sale of your home can be part of your equity but that latter number is wildly unreliable as American homeowners found out in 2007 and 2008. 

In poker, equity is the probability that you’ll win the hand.  In practical terms, it is impossible to accurately calculate the probability that you’ll win the hand for reasons.  One, you don’t know which cards have been folded.  Two, you don’t know exactly what range your opponents are playing with.  Three, you don’t know which opponents might fold after the next street.

For many players, trying to accurately calculate probability, pot odds, and equity take away from their ability to observe their opponents and make a reasonable decision based on observation.

Common Sense

There are other mathematical concepts that poker players use to determine the correctness of any play.  However, there is still the common sense approach to poker play.  This approach also has a fancy modern term—heuristics—but it is really just good old fashioned common sense.

Our everyday language has other ways to describe this approach: hands on, learning from experience, the school of hard knocks, trial and error, and lateral thinking.

The mathematical approach is disinterested; the heuristic approach is interested.  In the great novelistic book of philosophy, Zen and the Art of Motorcycle Maintenance, the author talks at great length about the vital need to be interested.  In fact, he places caring and interest at the top of his philosophical hierarchy.


If you have fully understood the math of poker and can apply it in a wide variety of hands, then it can be very valuable.  Most players cannot do this but that doesn’t mean that most players are doomed to lose.  Before the math of poker was fully developed there were great poker players who used a common sense approach to poker decision-making based on observation.

You can become a very successful poker player doing the same.