• Texas Holdem Math Book
• Understanding Texas Hold'em Math
• Texas Holdem Percentages
• Texas Holdem Probability Chart
• Texas Holdem Math Pdf

In a Texas Holdem cash game, the chips you have in front of you are valued in real dollars, when you bet a $5 chip – that’s the equivalent of a real five bucks from your pocket. This means that decisions you make cumulatively win or lose you that money. Any player can hit some nice cards and walk away with a profit in the short-term. Using pot odds in Texas Hold’em will certainly help you beat the tables. While No Limit Hold’em may use more implied odds principles (as you can stand to win much more by being able to freely choose exactly how much you want to bet or raise at any given point), Limit Hold’em uses the concept of expressed pot odds incredibly well!

Texas Holdem Math Book

Poker is a purely mathematical game, even if it doesn’t look like it on the surface. Everything at the poker table is based on math, and if you learn how to use this math the right way you’re guaranteed to win in the long run.

I know it’s a big promise to guarantee that you can win, but that’s the way that math works. If you use math facts the right way, there’s nothing that can change them.

This article serves as an introduction to basic poker math that you need to know about. It’s not everything that you need to know, but you can’t learn more advanced techniques correctly until you learn these 6 poker math facts.

1 – Basic Poker Card Math

Everything that you need to know about using math when you play poker starts with the way the cards that are used are designed and how they work. All of the most common poker games use the same deck of 52 cards.

Poker uses both the 13 card ranks and the 4 card suits to build hands. The harder a poker hand is to complete, the higher it ranks.

The power of poker math and the deck is about what can and can’t happen when the next card or cards are dealt. You know what’s left in the deck and what’s not in the deck based on what cards you have and what cards you’ve seen.

If you have a pair of jacks in your hand in a Texas holdem game before the flop, you know that there are 50 cards that you haven’t seen and that exactly 2 of those cards are jacks. The deck only has 4 jacks, and you have 2 of them.

The rest of this article goes into more detail about different situations at the poker table. But you need to spend some time thinking about what you learned in this section. Every time you play a hand of poker think about what can happen, what can’t happen, and how you can use this information to make better decisions.

2 – Odds on the Flop

In Texas holdem and Omaha poker, the 2 most popular poker variations, there’s a flop containing 3 cards, followed by a turn and river. The odds of things happening are slightly different in Texas holdem than Omaha because you start with 2 cards in holdem and 4 in Omaha. I’m using Texas holdem for the odds discussions on this page.

When you start a holdem game with 2 cards and stay in the pot to see the flop, you can get an idea of the odds of improving your hand on the flop. This is important because once you learn how likely or unlikely a hand is to improve it helps you learn when to stay in a hand and when to fold.

If you have a pair in your hand, the best thing that can happen on the flop is to get quads or a set. The odds of flopping quads are very low. The odds of flopping a set aren’t great, but they’re better than flopping quads.

You have to look at each card on the flop to consider odds. The odds of getting a set on the first flop card are 2 out of 50. The odds on the second card are 2 out of 49, and the odds on the third card are 2 out of 48.

This averages out to basically 6 out of 49. In other words, you’re going to flop a set almost 1 out of every 8 times you have a pocket pair.

This is just 1 example of using odds on the flop. Deal out practice hands and determine the odds of improving using this method until you understand how likely your hand is to improve.

3 – Odds on the Turn and River

Using odds on the turn and river is easier than determining them on the flop. You know the value of more cards and there’s only 1 card on the turn and 1 on the river.

On the turn, there are 47 cards that are possible. On the river there are 46 possible cards.

All you have to do is figure out how many cards help your hand in total.

If you have a flush draw with 4 cards of the same suit and 2 high cards that can form a high pair if you match 1, you have 9 cards that can make the flush and 4 cards that can match either of your high cards, for a total of 13 cards.

The odds of getting 1 of these 13 cards on the turn are 13 out of 47. If you don’t get 1 of these cards on the turn, the odds on the river are 13 out of 46.

Run the odds for every hand as you practice. This is going to help you learn which hands are worth drawing to and which ones you should fold.

4 – Odds of Completing a Flush

A flush draw is a common draw in poker. I touched on it in the last section and it’s a good example of using odds so I want to cover it more here. And this same method can be used for any type of draw once you see how it works.

On a flush draw you have 4 cards of the same suit out of a total of 13. This means you have 9 chances left in the unseen cards to complete the flush. This means that you’re never the favorite to complete a flush because there are always more cards left that don’t complete it.

But this doesn’t mean you should always fold when you have a flush draw. Sometimes it’s profitable in the long run to draw. You’re going to learn more about this in the next section.

On the turn you have 9 out of 47 chances to complete your flush, and on the river you have 9 out of 46 chances.

5 – Poker Pot Odds

Now you know how to run the odds for poker hands on the flop, turn, and on the river. But how do you know when you should stay in the pot and when you should fold?

Pot odds compare the odds of completing your hand and hopefully winning against the amount of money you can win. When the amount of money you can win is better than the odds of drawing the card you need you stay in the pot, and when the money you can win is worse than the odds you should fold.

Look at the odds of completing your hand. In the case of a flush on the river, you have a 9 out of 46 chance. Now look at how much is in the pot and how much you have to put in to see the river.

For example, the pot has $400 in it and your opponent bets $50. This means you have to call $50 and the pot now has $450 in it. This is a ratio of 1 to 9. Your odds of hitting the flush are 1 to 5.11. This is better than the ratio of money you call against the money in the pot, so the pot odds say this is a profitable call in the long run.

Understanding Texas Hold'em Math

6 – Poker Expectation

Poker expectation is a way to determine the average profit or loss for situations in poker. In the last section you saw an example of pot odds. Here’s how you can determine how much this situation is worth in the long run.

The deck has 46 unseen cards. So you’re going to run the exact same situation 46 times using each of the possible cards on the river to see the average profit per hand.

It’s going to cost you $50 for each of the 46 hands for a total of $2,300. You lose 37 times out of the 46. On the 9 times that you hit your flush you’re going to get $500 each time. This is a total return of $4,500.

This is a total profit of $2,200 on 46 hands. This is an average profit of $47.83 per hand. This is how you use expectation in poker to make better playing decisions.

Conclusion

Poker math starts with an understanding of the cards used in the games. The deck of cards unlocks all of the secrets about poker math you need to use.

A deck of poker cards is built in a way that lets you determine odds of what can happen on the flop, on the turn, and on the river. It also lets you use 2 powerful mathematical concepts called pot odds and expectation.

With these poker math tools you can quickly learn how to be a profitable poker player.

Poker is a game of skill, that’s why your abilities to read situations and opponents will give you an advantage in each and every hand. Moreover, poker is a game based on mathematics, where you would need to be able to calculate your odds and probabilities of your hand, and the hand of your opponent in every specific situation. In this section of our site you’ll be able to find all the necessary information about the mathematics of poker.

Will poker math help you to win more money?

Texas Holdem Percentages

This is a fairly common question. You’ll be able to win money in poker even without a good grasp of mathematics of course, but the knowledge and understanding of its basics, such as pot odds, implied odds, probabilities of improving your hand and your opponent’s hand, equity, fold equity, expected value and many others, will help you to win even more money in poker and will significantly improve your game. Mathematics in poker will give you an advantage over those opponents who do not want to devote it their time.

Almost all players use mathematics during the game even without knowing that they do it.

Where mathematics is used in poker?

Math and draw hands

Mathematics in poker can be used in a wide variety of situations. The most common example of using math in poker is calculating your equity with draw hands (flush draw or straight draw). When your opponent makes a bet and you, having a draw hand, do not know if you should call his bet hoping to improve your hand or fold your cards and give away the pot to an opponent.

In such a situation the player who is familiar with mathematics of poker will always know what he should do. At the same time a player not familiar with the math of poker will make his decision based on his feelings and lose in the long run.

Expected value (EV)

There are other situations where mathematics of poker is used more widely, for example, to calculate your expected value (expected profit). Imagine that you have a lower pair on the river and your opponent bets $4 into $10 pot. What should you do? If you don’t have any weighty proofs that one or another action from your side will be better than the other, just stick to the poker math and you’ll find the correct answer.

An example of using poker math

You should assess the likelihood of your opponent bluffing or having the weaker hand for starters. Let’s assume:

• Our opponent plays aggressively and likes to bluff. We will have better hand on showdown once in three times.
• That means, that the chances of getting the strongest hand for us equal 1 to 4
• Thus, our odds to losing are 3 to 4
• That means that we will lose 3 times and win 1 time (3 to 1)

As a result we can calculate that if we will call and have the best hand, we will win $14 per hand, but if we will call and lose, then we will lose $4 three times. Thus, if we will call every time we will lose $12 every 4 hands (3 x $4) and win $14. Net income will be $2. That’s how with the use of simple poker mathematics we have determined the profitability of the action.

Few nuances about poker math

A key moment that you should remember when using mathematics in poker is that decisions you made on the poker table will have no impact on your winnings short term.

Just because you have correctly calculated your winning odds in one specific hand and made a correct call doesn’t mean that you will win that hand. It also does not mean that you have made wrong decision if you had lost. If you will continue to make correct decisions based on odds, you will surely make profits in the long run, so try not to let your short term results have an impact on your game.

Studying poker mathematics may seem difficult, but we strongly encourage you not to be discouraged, because it will help you to become a winning player in the long run.

Texas Holdem Probability Chart

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