Fundamentals of Poker Mathematics


Many poker beginners often ask themselves: “At what point in time do I cease to be a fish and become a regular?” The answers can vary significantly from “when you started to be interested in poker theory and think about your own game” to “the first plus month with a decent distance.” The most universal answer that many regular poker players will be willing to agree with is: “From the moment you understood the importance of mathematics for a successful game.”

The funny thing is that many good poker players admit that they still do not know all the intricacies of the process of calculating outs, odds or potential pot odds. Then the reader’s inquiring mind will immediately formulate the thought: “If they have been playing poker for decades and do without knowledge of mathematics, then why bother with this?” It seems paradoxical only at first size. Just experienced players have learned to intuitively determine the profitability of a particular bet/call. They perform absolutely correct actions and make informed decisions on a subconscious level. But this was not always the case. If they started poker training in the correct way, they would have avoided a significant number of lost banks and stacks, for which they gained a useful, but bitter experience.

Another argument (although the opportunity to save time and money in itself looks attractive) in order to understand the mathematical foundations is the latest findings of scientific researchers. Specialists in the study of patterns of human behavior (or just habits) came to the conclusion that a conscious understanding of the sequence increases the efficiency in solving logical problems by 40-50%. Imagine making decisions at the poker table 50% faster and more efficiently than your rivals, who subconsciously understand the benefits of the action, but cannot consciously explain it. A compelling reason to spend time carefully understanding the basics of poker math. Let's go over the key concepts of poker mathematics.


Outs - the number of cards that help strengthen your hand to the best combination and win the hand. Perhaps the simplest poker concept. To accurately calculate our outs, you will need:

  • Knowledge of poker rules and seniority of combinations;
  • Determine what potential combination we can put together;
  • Be aware of which cards are in the deck (their suit);
  • Have subtraction (addition) skills taught in the first grade.

For example, if we have a flush draw on our hands, then we subtract from the total number of cards of the same suit in the deck (13) those cards that we already know (our hand and the general cards of the table). That is 13-4 = 9. We have 9 outs to gain the flush. It is worth remembering that there are outs that strengthen our hand to the desired combination, but also help our opponent. The most typical example is our straight draw flop with two spades. Here we cannot consider spades to be a full-fledged outs, allowing you to collect straight. Therefore, we must carefully approach the calculations in such a situation. Outs that help both us and the opponent are called discounted. Sometimes you can find another name - dirty outs.


Odds - the chances of the cards we need and the victory in the deal come. Usually indicated either as a percentage or as a 5:1 ratio. It is important to remember that 5:1 does not equal 1\5 or 20%, but is defined as "5 times we lose, 1 time we win", that is, the ratio is 1\6 or 16.6%. There are two options to remember odds:

  • Learn a table with exact values;
  • Use the method of multiplying by 2 or 4 (depending on the number of outs).

The second option is more approximate and serves for rough calculations during the game. The first is accurate, but will require more time to remember.

Pot odds (pot odds)

Pot odds are the ratio between the total size of the pot and the money (blinds) that we must deposit in order to continue the game. It is determined quite easily - we summarize the total size of the pot with the bets and calls of our opponents already made (this happens automatically in online poker) and divide the value that we need to call. For example - in a bank $ 20, the opponent bets half of the bank ($ 10). We need to invest $ 10 in $ 30. The odds of the bank are 1: 3 or 25%.
Outs, Odds, or Pot Odds are not important in and of themselves. The key is to calculate their ratio. The main principle of a positive game is that if the probability of collecting a winning combination is higher than the pot odds, then the action is positive. Otherwise, you should not call.

Potential Pot Odds

Quite often, there is a situation at the tables when we are not given suitable chances to call, but it can still be a plus. The reason is the high probability of further bets from the opponent. In this case, we add to the actual size of the bank its potential bets on the following streets and make a positive call. The problem is that we cannot predict the opponent’s plan with 100% probability. However, with experience you will have a good skill in determining the opponent’s intentions on the turn and river. Partly poker trackers help to solve the problem: in your Hand2Note, DriveHUD or Holdem Manager 2 there will be statistics that allow you to clearly understand the trends of opponents on turn and river.

Ace poker drills

Ace Poker Drills is a one-of-a-kind program focused on improving your poker math skills. It consists of 4 parts:
Preflop Trainer - training preflop solutions.
Equity Trainer - training to determine the equity of a hand.
Odds And Outs - training on determining outs and odds of a hand.
Equity Calculator - Equity Calculator.
The Odds And Outs functionality that interests us is available completely free even in the unregistered version of Ace Poker Drills. Training in this poker simulator in a short time will raise your intuitive understanding of mathematics. This will create a solid foundation for a successful poker career.


Poker math is the foundation of a successful and professional player. Yes, of course, playing plus is possible without knowledge of the mathematical foundations. But with them you can significantly increase the role of skill and reduce the share of gambling in your game. And with the growth of limits, it will become increasingly difficult for you to do without a clear understanding of the mathematical tricks of poker. We recommend that you do not delay the study of poker mathematics and, soon, you will be able to do all the complex calculations in seconds. This will increase your skill level, profit and become the basis for further growth in limits.