5 Mathematical Facts About Poker You Need to Know

By in Poker on
6 Minute Read
Poker Math Facts

You don’t have to have a degree in mathematics to play winning poker, but you do need to have a basic understanding to give you the best chance to win.

I’ve put together 5 math facts that you need to use if you want to win more at the poker tables. You’re also going to learn exactly how you can use each of these 5 facts. This way you can see how they work instead of just trying to memorize them and hope that they work.

1 – The Card Set Dictates Everything

1 of the best things about playing poker is that once you understand how the math behind the game works you can use it to make money. All of the math in poker starts with the fact that every game uses a specific set of 52 cards.

This is something that you already know, but have you considered how you can use this information to improve your results?

Poker Cards

Each deck of cards has 13 ranks, from ace through king, or 2 through ace depending on how you look at it. Each rank has 4 cards in 1 of 4 different suits.

The rules of poker also list a specific rank of hand values based on how hard it is to create each hand. A royal flush is the highest ranked hand because it’s the hardest to get. A full house is more difficult to get than a flush, so a full house beats a flush.

This is all common knowledge for poker players, and you need to know these things to be able to play. But the way to start winning more than most players is to start using this information in more ways. The next 3 sections teach you how to do this.

2 – How to Determine Odds

When you know the specific set of cards that are in the deck you can determine the odds of things happening. The odds of receiving an ace as your first card are 1 out of 13. The deck has 4 aces out of 52 cards, and this reduces to 1 out of 13. This means that 1 out of every 13 hands you’re dealt, the first card is going to be an ace.

You can also determine the odds of completing a hand or improving a hand.

If you’re playing Texas holdem and have 2 clubs in your hand and there are 2 more clubs on the flop, you can determine the odds of a club on the turn. And you can also determine the odds of a club on the river if the turn isn’t a club.

With 2 clubs in your hand and 2 on the flop, you know that there are still 9 clubs available. You also know the value of 5 cards between your 2 and the 3 on the flop. This means that there are 47 unseen cards.

This means the odds of a club on the turn are 9 out of 47. And if a club isn’t on the turn, the odds of 1 on the river are 9 out of 46.

Get a deck of cards and start dealing out hands. Look at each hand and determine the odds of improving. The more practice you get doing this, the better you’re going to understand how the odds work.

3 – The Pot Odds Secret

This is where the use of math and odds really starts to pay off for poker players. Once you learn how to use pot odds, you never have to worry about making the best play in a poker hand.

Most poker players don’t use pot odds. This is good news because you need as many bad players as you can find when you’re playing. These players are the ones that can help you make money at the table.

Pot odds are a calculation that uses the amount of money in the pot in combination with the odds of your hand winning or improving enough to win. Eventually you can learn how to use pot odds to make almost every decision at the poker table.

The best way to learn how pot odds work is to use an example.

In a limit Texas holdem game you have the king of spades and jack of spades. The board has the queen of hearts, 10 of diamonds, 3 of spades, and the 4 of clubs. The pot has $120 in it and you’re facing a bet of $20 from the only opponent.

You have an open end straight draw, and any ace or 9 completes your straight. You can’t determine exactly what your opponent has, but it’s safe to assume that if you complete your straight on the river that you’re going to win. It’s also possible that you might win if you pair 1 of your hole cards, but it’s not likely going to win the hand.

You have to decide if calling the $20 bet is the right play. To determine this you need to determine your odds of completing your straight. 8 cards complete your straight, and there are a total of 46 unseen cards. This means that 8 cards help you and 38 cards don’t. This is a ratio of 4 to 19. If the ratio of the reward against the amount you have to call is better than the 4 to 19 ratio it’s profitable to call the bet. If it isn’t, you need to fold.


The ratio of the amount you have to call to the amount in the pot is 20 to 140. The pot is $140 because it had $120 in it and the bet was $20.

The easy way to see if this is profitable is to run the hand 46 times, once for each of the possible cards. The cost to see the river is a total of $20 times 46, or $920. You win with a straight 8 times out of 46, and when you win you get back your $20 plus the pot of $140. 8 times $160 is $1,280.

This is more than the cost of $920, so the pot odds are showing that it’s profitable to make the call.

Use this method to practice determining pot odds. Keep practicing until you can quickly gauge the pot odds at the table.

4 – Starting Hand Math

I’m going to share a secret that many poker players don’t know. Once you hear the secret, you’re going to think that it should be common sense, but lucky for you it’s not something that most poker players know or use.

The player at the table that starts with the best hand wins more than the other players. Of course, anything can happen on a single hand, but the long term averages show the best starting hand is the most profitable.

This makes sense when you think about it. A pair of aces is more valuable than a pair of kings. Ace king wins more often than ace queen when they go head to head.

So why do so many poker players enter the pot with poor hands?

Your starting hand isn’t the only thing that is involved in winning at the poker table, but it’s something that you have total control over. You decide which hands to enter the pot with and which ones to fold.

If you play poker now and aren’t winning, the first thing you need to do is play fewer hands. Write down every hand that you’re entering the pot with now, and cut them in half. Only keep the top hands and start folding the rest.

Learn about how your position relative to the dealer button influences your profits and combine this information with your starting hand selection.

The exact percentage of hands you should enter the pot with varies based on many things, but until you start winning you should play fewer than 20% of the pots. As you learn more and gain experience you might be able to play more hands, but don’t be in a hurry to expand your starting hand range.

5 – Why Controlling Pot Size Is Important

The mistake that most poker players make is accepting that they don’t have any control over the size of the pot. While you don’t have complete control over the pot; you do have some control over it.

The basic poker strategy that you need to use is to build the pot as high as possible when you’re favored to win the hand, and keep it as small as possible when you’re behind and trying to improve to win the hand.

This might seem simple, but really all that you need to do is bet and raise when you’re favored and check and call when you’re trying to improve.

Here are the only 2 things beyond this that you need to know. Make sure you’re getting the correct pot odds when you’re behind in the hand. The second the pot odds are wrong you need to check and fold.

The other thing is that betting and raising needs to be done in a way to maximize your profits. If you push all in and everyone else folds, you probably didn’t maximize your profits. Size your bets to get as much as you can in the pot while keeping an opponent in the hand to give you more money.


The 3 main things that you learned on this page are going to improve your results at the poker table immediately. Odds, pot odds, and starting hand selection give you the tools you need to win. These aren’t the only tools you need, but you’re going to use them every time you play poker for the rest of your life.

Don’t ignore the importance of learning how to control the size of the pot. The more you learn how to influence pot size, the more profit you can squeeze out of every hand you play in. You’re also going to limit your losses when you don’t hit your draws.

Michael Stevens

Michael Stevens has been researching and writing topics involving the gambling industry for well over a decade now and is considered an expert on all things casino and sports betting. Michael has been writing for GamblingSites.org since early 2016. ...

View all posts by Michael Stevens
Email the author at: [email protected]