Online Poker Math - Poker Mathematics

Giselle Adriene
February 13, 2023

Poker is one of the world's most popular and fun games. In addition to being the most played game with friends, many people are lucky enough to earn extra income with it.

Before the age of technology, poker was only available offline in land-based casinos.

With the advancement of technology, poker progressed from splendid casino rooms to the easiness and convenience of online casino sites.

The rules and variants remain the same in both versions, and the basis of every poker game is still the math behind it. The use of mathematics applied to poker is not unreasonable since any strategy in card games is carried out by logic, which is closely related to math.

But how exactly does math relate to the poker strategy, when to use it, and how deep should you go into it? Read more to find out!

Why is math so important in poker?

Many of our readers may already know the close connection between mathematics and poker. In games of chance, the mathematical factor is significant. Everyone who wants to improve their gaming experience and increase their chances of winning should know the relationship between poker and math.

Poker is primarily based on statistical analysis and combinations. Despite being true that chance is critical in online poker for real money, the result of the hands has a lot to do with mathematical and statistical factors.

When we talk about poker online mathematics, you will find that if you know how to use it correctly, you will have the possibility of winning a large number of online poker games. The best poker players professionals worldwide have an enormous memory capacity, but above all, they know mathematics very well.

How can math improve your poker game?

In games of chance, some principles of mathematics and statistics can be applied to obtain better performance when taking action. To be successful in the game, you need more than luck on your side. It is often essential to acquire mathematical skills to improve the odds of victory.

How exactly do you manage to increase the probability of winning with math?

Probability of winning and losing streaks

Using a simple formula, you can calculate the probability of entering a streak, either positive, in your favour, or negative, against you. The formula is the following:

P = (Option to win from your bet / total options) x 100, raised to the number corresponding to the streak.


This concept is related to volatility. The greater the variance in a game, the greater the probability of having a winning or losing streak. As an example, slots have high variance. Instead, blackjack, craps or baccarat are low-variance options.


It is essential to know the volatility of the different online poker games to decide which one to play, considering your taste and budget. Progressive jackpot slots pay out big but infrequently and are a high-volatility game. By contrast, video poker is a low-volatility online casino game.

Ruin or risk of losing all money

This criterion will help you know the probability of a significant money loss in a particular game. Also, you will be able to understand your chances of doubling your balance when playing.

Checking whether a game strategy is favourable or risks the loss of all your money is recommended. There are calculators on the internet that will help you find out.

Poker Sequence Math

New poker players always need help knowing the best poker hands. However, studying the poker guides could help them greatly.

The player's main objective in Texas Hold 'em is to form the five best hands at the showdown time. The sequence goes as follows:

  • High Card
  • One pair
  • Two pair
  • Three of a kind
  • Straight
  • Full house
  • Four of a kind
  • Straight Flush
  • Royal Flush

Some players love to find the probability of a hand occurring. Although Royal Flush is one of the rarer phenomena in poker, the chances of it occurring can be estimated using probability. Being the rarest combination, it can only occur in 1 out of 649 740 hands.

Calculating pot odds in Online Poker for real money

"Pot odds" is the reference between what you bet and the amount you can receive as a win from your bet. Betting on poker online is no different than placing a bet at a bookmaker or a roulette table. The only difference is that your win depends on the amount in the pot at all times.

Imagine there is $50 in the pot on the turn. Your opponent plays first and bets half the pot. You now have to bet $25 to match it, with no one else left to bet after you. If you call the bet and win, you´ll get $100 from betting $25.That’s a $75 net profit from $25. That's a 3-to-1 chance.

How to use pot odds?

Ok, now we understand how to calculate pot odds. But how do we use this info? First, we must link the odds to our hand. After the flop, we have four hearts and are going for a nut flush. Nine hearts are left in the deck that can complete the hand. With 5 cards already revealed, there are 47 left, and 9 of them will get us the hand we want.

If 1 out of 5 cards gives us victory, 4 out of 5 don't. That's 4-to-1 odds. That’s a pretty good odd, so we should go for it and bet waiting for a heart in the turn or the river. If the odds in our favour are higher, it’s even better. If they’re lower, it’s better to play it safe and fold.

Implied probabilities

When discussing pot odds, we look at a single decision in isolation. And, of course, real poker games online are never that simple. The pot may not have the correct odds right now, but when you know you'll get called later, you can sometimes justify taking the wrong price.

For example, let's take a $2/$4 Limit Hold'em game. You are facing a $4 bet into a $16 pot. They are 5 to 1 pot odds (bet $4 to win a total of $20, or $1 to win $5). However, you may know that your opponent has invested enough in the hand that he will call another bet at the end. If that's the case, you'll win another $4, so your implied odds are 6 to 1. And if there's a raise involved, it would increase to 7 to 1.

Online Poker Math & Probability

To make these calculations, you must understand what cards are needed to improve your hand. It is not always easy to know your outs since poker involves a lot of hidden information. Sometimes you think a card is an out, but it helps our opponent too. However, as a general rule, here are the most common scenarios.

Draw a flush9 outs
Two-way straight draw8 outs
Inside straight draw4 outs
Two overcards6 outs
Flush draw plus an overcard12 outs
Flush draw plus two overcards15 outs

If you prefer to think in terms of fairness, the general rule of thumb is this: each additional out provides about a 4% chance of hitting the turn and river. So if you have ten outs, your chances of winning are about 40%.

Calculating poker odds as percentages

  1. Calculate the total size of the pot after making the call.
  2. Divide the amount of the call by the amount of the pot.
  3. Multiply the number by 100.

So if you are faced with a $5 bet into a $2 pot:

The total size of the pool = $25

5/25 = 0.20

0.20 x 100 = 20%

Determining the equity required for a call

Imagine a situation where you are facing a $50 river bet in a $100 pot. There is a total of $150 in it (the starting pot plus your opponent's bet), and you need to put in $50, so you are getting odds of 150 to 50. You can divide each number by 50 and simplify it as 3 to 1.

To calculate the equity required for the call, take the second number in the ratio (the 1) and divide it by the first number in the ratio plus the second number (3+1), giving you

1/(3 + 1) = 1/4 = 25%

This means that if your opponent is betting a stronger hand than yours less than 75% of the time, you should call because you are either making money or walking out just the same.

Expected value calculation

The expected value lets you know the probability of winning or losing when a bet is repeated a thousand times. In this formula, the negative value is set as the expected value. Knowing the house edge, this formula is one of the easiest to apply:

[(probability of amount/100) x what you can win] – [(probability of losing/100) x amount you can lose].

Imagine you are the big blind with €50 and one of the players opens a pot of €100. Let’s say you have a stack of 10 big blinds and a pair of J + J in your hand with a probability of winning of 77%. If you win, you will take 200 euros; if you lose, you will be left without the 50 from the big blind and the 50 from the call.

If we apply the formula, we get 131, a positive. This means that the decision to see the call is correct.


Mathematics has different applications in poker. It's basically about calculating the probability of winning the pot. It is impossible to avoid the question of probability since this forms the essential basis for playing poker online well.

So lose your fear of math. Players will try to convince you that poker is not based on mathematics but intuition. Your gut can't guess your odds of completing such a draw or hand; it's pure math.

Don’t hesitate to try these tactics out, and you’ll see we’re on the right here!


What do we have to know before starting to play online poker?

Make sure you’re familiar with the game rules and the card sequence. Get to know the basic strategies and when to fold and call. Once you have that practised and cleared, you can move to get to know the math behind poker.

Are poker games online only for high-stakes players?

Absolutely not. Tables and tourneys have very low entries starting from $0.10 initial bets. If you play the low tables, you usually won’t spend more than $1 - $2 per hand, but you won’t be able to win much more.

Can you win at online poker without using math?

Yes, but occasionally. While poker, like any other casino game, is partially based on chance, strategy can significantly improve your chances in the long run. Most players have their strategy and are familiar with the basic math, so not knowing it will get you to a disadvantageous position.

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About the author

Giselle Adriene

Giselle Adriene is a remarkable author who has transitioned from being an avid casino player to a highly skilled professional game analyzer. Giselle's journey began with a deep fascination for the thrilling world of casinos, where she honed her skills through countless hours of gameplay.

After experiencing the highs and lows of the casino floor, Giselle realized her passion extended beyond playing. She yearned to uncover the secrets behind successful strategies and delve into the intricacies of game design. Determined to explore this realm, she embarked on a new path as a game analyzer. With her keen eye for detail and analytical mindset, Giselle quickly established herself as a trusted authority in the field. Her ability to dissect games, identify patterns, and uncover hidden nuances allowed her to provide valuable insights to both players and casino operators.

Giselle's expertise and contributions to the gaming industry have not gone unnoticed. She has been recognized with multiple prestigious awards for her exceptional work. These accolades serve as a testament to her dedication and unwavering commitment to excellence in the field of game analysis.

With her exceptional skills, relentless pursuit of knowledge, and numerous accolades, Giselle Adriene stands as a respected figure in the gaming industry. Her passion for unraveling the intricacies of games and sharing her expertise has established her as a trusted source of guidance for enthusiasts and professionals alike. 2022 ALL RIGHTS RESERVED.