Do you need to know maths to play poker well?

Anyone who plays poker is at least a little familiar with the basics of probability theory. "What is the probability that your opponent has a better hand?", "Am I likely to win this one with two pairs sweat?" - these are the questions that probably everyone asks themselves during the game. Well, probability theory and probability calculations are, after all, real mathematics. So there may be a preconception that without a deep understanding of mathematics and a solid theoretical background it is impossible to play poker well. Is this really true? Different sources have different opinions, but let's try to find the right one.
Mathematics in poker

In this article, we'll answer the basic question - is it necessary to know complex formulas and mathematics to play poker well?

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The history of mathematics in poker

XIXa. With the introduction of modern 52-card decks in the mid-19th century, it was not until around the second half of the 19th century that a whole mathematical and game theory associated with poker emerged. Theory and the emergence of the game went hand in hand, with the first real book of theory dating back to 1875, so it is fair to say that it was not long before the players noticed the benefits of certain calculations and theories on the game.

Later, as the theories developed, and especially as computers and more literature became available, the information became accessible to everyone, and in the 21st century, every poker player can not only buy literature, but also software that does the calculations for him in real time.

We already know that for those who are too lazy to gather knowledge, all the necessary information will be provided by Holdem Manager 3, PokerTracker 4 or other poker software, but what about when you want to play in real time, when you want to calculate value, bet size, probability and other relevant aspects. So, do you need to know maths or is maths not needed in poker?

The success factor is not enough to outweigh the need for maths

The fiercest critics of maths in poker say that it is not needed when a player is lucky. But luck is usually not just a set of blind coincidences. Luck is far more often the result of the right decisions, made at the right time. The best succeed, not just anyone. It is difficult to say exactly how much of the game is luck and how much is mathematics, but the optimal calculation is to say that theory and fundamentals lead to at least 90% of wins, and up to 10% of luck and fortune.

The need for mathematics in poker

One handWhile it may be possible to win one game, or maybe one tournament, on the basis of intuition rather than conventional calculations, in the long run such a game is hugely unprofitable, and no professional or experienced player will rely on such a strategy all the time. But this is not super significant news. We are more interested in getting the facts straight: do you need a background in mathematics to win at poker?

The real benefits of game theory in practice

The best researchers and mathematicians in game theory and mathematics around the world are scientists and mathematicians from prestigious universities in the USA and around the world (MIT, Harvard, Cambridge, Oxford, etc.). But without an internationally renowned mathematician Alan Bustany (based at the University of Cambridge, UK), it is hard to find any more famous poker players who are mathematicians. This means that it is not enough to be good at maths to be a successful poker player. Otherwise, every mathematician from a prestigious university would be winning millions of prizes every year.

Poker mathematics

Mathematicians themselves say that in poker, it is not enough to know dry theory. Professional poker players echo them. Mathematics will not guarantee 100% wins because In poker, it is also important to understand the psychology of the players, to analyse the bluff and mask emotions, not to give yourself away to the other gamblers at the table, whether you are playing virtually or actually.

Probably the best known game theory figure in poker is J.F.Nash. This is the 20th century. Nash Equilibrium is the 20th century scientist whose formula linked opportunity theory and other mathematical functions to poker.

Essential probabilities

The fundamental principles, and the mathematical constants, theorems and formulae that follow from them, involve the probability of certain scenarios. It is worth knowing the basic probabilities. For example you have:

  •       17,4% probability of having no pair or high card;
  •       43,8% probability of having one pair;
  •       23,5% probability of having two pairs;
  •       4,83% probability of having three of a kind;
  •       4,62% chance of having straight'ą;
  •       3,03% probability of having flush;
  •       2.6% chance of having a Full House;
  •       0.168% probability of having four of a kind;
  •       0,0279% probability of having straight flush;
  •       0,0032% probability of having royal flush.

Pot odds

Knowing these probabilities can help you plan your game better. But even more important than these probabilities are pot oddswithout which no player would dare to move forward. Pot odds is a fairly simple probability, which is the ratio of your call bet to the size of the total prize pot. For example, if your bet is €10 and the pot is €40, then Pot odds is 4:1 or 25%.


The King of Wines and 10Oh, and you also need to know all about "outs", or those cards that, when turned up to river, JYour hands become happy. Let's say the player has a 10 and a K in his hand. Almost all the cards on the table are face up (the last one is missing) and now our player has four wines and wants to collect flush. Let's also assume that there is a so-called overcardwhich means that if you don't fall out flush you have a back-up option - a high pair (K pair), which, if dropped, would also improve the odds.

When you see a hand like this, you can be sure that if the right card is dealt, it is almost impossible for someone else to have a better hand (remember the probabilities of combinations). We calculate the probability and see that there are currently 4 cards of the same suit (4 wines) on the table. Which means that there are 9 wines left in the deck. We have 9 outs (autus). There are 3 kings left in the deck, so we have 3 more outs. We have a total of 12 outu and from this number we can calculate the probability of your card coming up. Calculated using rule of four ( rule of four) and the binary rule (rule of two).

The Quartet rule applies after flopand the twentieth - after turn.

  •       After the flop - Outs * 4
  •       After the turn - Outs * 2

So, we can see that the probability that the flop we will need you outs or in other words, the cards we need are 48%, followed by turn - 24%. Admittedly, the calculation is simplified and the true probabilities are slightly adjusted for error, but to give you a better idea, here's a table with the exact percentages of how likely it is based on outs by calculating that the card you need will come up.  

After Flop (two cards left) After turn (one card left)
Number of Outs Probability by the rule of fours Exact probability Number of Outs Probability by the binary rule Exact probability
1 4 % 4.5 % 1 2 % 2.3 %
2 8 % 8.8 % 2 4 % 4.5 %
3 12 % 13.0 % 3 6 % 6.8 %
4 16 % 17.2 % 4 8 % 9.1 %
5 20 % 21.2 % 5 10 % 11.4 %
6 24 % 25.2 % 6 12 % 13.6 %
7 28 % 29.0 % 7 14 % 15.9 %
8 32 % 32.7 % 8 16 % 18.2 %
9 36 % 36.4 % 9 18 % 20.5 %
10 40 % 39.9 % 10 20 % 22.7 %
11 44 % 43.3 % 11 22 % 25.0 %
12 48 % 46.7 % 12 24 % 27.3 %
13 52 % 49.9 % 13 26 % 29.5 %
14 56 % 53.0 % 14 28 % 31.8 %
15 60 % 56.1 % 15 30 % 34.1 %
16 64 % 59.0 % 16 32 % 36.4 %
17 68 % 61.8 % 17 34 % 38.6 %

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 How do professionals do it?

Again, there are many professionals, all of whom may have different views and opinions. The old school often tends to think that poker can be feel and predict the course of events without relying on maths. The new school, on the other hand, pays less attention to instinct and takes a pragmatic approach to situations. If the numbers say yes, then the next solution is ineffective.

Jonathan Little
Jonathan Little

Take the example of a good player. Jonathan Little is a two-time WPT champion and the author of various books on poker. In one of his interviews 888Poker The poker player gave his views on whether maths is necessary in the game, how important it is and how he uses it to his advantage.

As J.Little says, the essence of all essences is precisely pot odds and outs Calculation. He always thinks about how realistic and how likely it is that he will win the round before each decision, based on the probability of outs calculation. According to my husband, there is no way around this. The poker veteran can't imagine trying to achieve serious results in the poker arena without the basics. According to the American, such knowledge is what defines professionalism and determines results.

However, during the interview, the player also revealed that it is very easy to get lost in the shadows if you devote yourself to finding mathematical solutions in poker. To begin with, it's enough to simply memorize outs the probability table (available in this article) and pot odds a formula for calculating the. Failure to do so can lead to catastrophically unsuccessful phases in your game. Once again, there is no getting away from these things.

How can I improve my knowledge of poker math?

According to experienced poker players, instead of just learning the theory and calculations "on paper", you're better off practicing by playing outside of real money or by having the deck in front of you. You will develop a visual and hunch-based memory that will help you develop the gaming instincts you need to succeed. With enough experience, you can be guaranteed to make the best decisions about 4 times out of 5 without even thinking. Some people learn Read more atothers need to see things visually. But practice makes perfect, so by playing, taking your time at first, and counting, you will be able to best remember the probabilities and the steps you need to take in order to win.


To answer the main question - do you need to know complex formulas and maths to play poker well? No, it is not necessary to have a very deep mathematical knowledge, but it is certainly necessary to understand pot odds and outs calculation, otherwise you risk being exploited by stronger players and not being successful in the long term. Master the basic formulas and remember the percentage probabilities and you will have a solid foundation for a serious poker game. If you want to improve and play better tomorrow, absorb all the information written here and you will see the improvement will be clearly visible.