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- Why calculating probabilities in poker
- Probabilities of getting specific combinations in poker
- Chances of getting certain starting hands
- Probability of winning preflop
- Postflop opportunities to improve
- Probabilities of opponents’ behavior
- Poker odds calculators
- Online poker winning probability calculators
- Frequently Asked Questions About Poker Odds
- Is it even possible to calculate probabilities while playing poker?
- Do high chances of winning guarantee you the win?
- Is it possible to win at poker without a math background?
- How to learn to calculate probabilities in poker?
Why are odds so important in poker? It is very simple. A player who has an idea of the odds of getting a particular combination will always win in the long run over someone who plays randomly.
What should you pay attention to? You can calculate the probabilities in poker yourself, but there is little point in doing so. All such calculations have been made for you long time ago. Therefore, it is better to memorize the key numbers, and you can always use special software to get the rest.
Why calculating probabilities in poker
In poker, every player faces uncertainty because he does not have complete information about his opponents’ hands. So the decisions are made based on probabilities analysis. After all, players have accurate information only about their own cards and, possibly, about some common ones.
The probability theory in poker is a percentage value that shows what the chances are of a particular situation. Understanding the prospects, the player can evaluate his chances not emotionally, but logically and mathematically.
In practice, in poker, it may also happen that you do not get pocket aces for 40 consecutive hands. However, this does not mean that you are being deceived. The actual probability of getting a pair of aces in any given hand is just 0.45%, meaning that on average you only get them once every 222 hands.
In poker, every situation depends on mathematics, or rather on the probability theory. These tools allow you to predict the likely outcome of a hand as a percentage, which helps determine your chances of getting the right card or even hand. All calculations take into account cards in the deck, suits, and players in the hand and so on.
Calculating the probability of getting certain cards in poker helps the player evaluate the chances and determine the most profitable solution in a given situation. When the chances of success on the flop reach 90%, it makes sense to put more money into the pot. However, with only a 30% chance of winning in poker, the risk is not justified, and it is better to refrain from large bets.
Obviously, the calculations will be approximate, since we do not have information about the opponent’s cards. At the same time, you can improve accuracy if you adequately determine your opponent’s hand range, as well as take into account the nuances of his strategy and HUD stats.
Beginners should refer to the already compiled tables with calculations of poker probabilities for various scenarios. When using visual cues, the player gradually absorbs information and accumulates experience, which contributes to his development. There are a huge number of tables; we will present those that will be useful when starting to study probabilities.
Probabilities of getting specific combinations in poker
Information about the possibilities of making different hands helps to understand hand rankings and the possibility of being behind with certain combos.
| Combination | Probability |
| Royal Flush | 0.003% |
| Straight Flush | 0.027% |
| Four of a kind | 0.17% |
| Full House | 2.6% |
| Flush | 3.03% |
| Straight | 4.6% |
| Three of a kind | 4.8% |
| Two pairs | 23.5% |
| Pair | 43.8% |
| Nothing | 17.4% |
Chances of getting certain starting hands
The likelihood of getting specific hole cards depends on the poker format you play. For example, in Texas Hold’em, everyone receives only two cards.
In Omaha, depending on the specific version, the number of hole cards dealt to each player can range from four to seven. The probabilities are also different in the Hold’em versions. The classic version is played with a deck of 52 cards (from two to ace), while the short deck is played with a reduced deck (from six to ace).
Let’s look at some examples of winning probabilities for classic no-limit Texas hold’em, the most popular poker type:
| Starting hand | Probability |
| AA – pocket pair of aces | 0.45% |
| KK or AA – pocket pair of kings or aces | 0.90% |
| 22-AA – any pocket pair | 5.90% |
| AKs – ace-king suited | 0.30% |
| AKo – ace-king offsuit | 0.90% |
| J3s – any suited hand | 24% |
From this table it is clear that in reality the player will not get strong hands too often, less than 25% of the times. Therefore, you need to develop a strategy where you raise a tight range in early position and wider range in late positions. At the same time, you should try to steal the blinds.
Probability of winning preflop
When people stack off preflop, there are some common spots. For example, 2 high cards against a pair (AK vs TT) or a high pair against a low one. In modern poker rooms, the software shows the equity of your hand. This is the probability of winning in the current pot with your hand.
At the very beginning, each starting hand has a chance to improve and outperform stronger hands. Let’s look at the chance of winning in situations with common preflop stack offs. Here are some typical situations:
| Preflop situation | Chances of winning |
| “Coin flip” – pocket pair against 2 high cards (88 against AK) | 54% / 46% |
| High pocket pair vs. low one (KK vs. 99) | 81% / 19% |
| Pocket pair versus 1 high card (JJ versus A9) | 71% / 29% |
| 2 low cards vs 2 high ones (56 vs JQ) | 37% / 63% |
| 2 mid cards versus 1 high one (JT versus A5) | 45% / 55% |
| Dominated hand (QJ vs AQ) | 26% / 74% |
| 1st and 3rd highest cards vs. 2nd and 4th (T8 VS 97) | 63% / 37% |
Postflop opportunities to improve
There are rare cases when a poker player gets a made hand on the flop. Much more often, there are various draws where one more card is required to complete combinations.
To calculate the profitability of a call, a player must know the pot odds taking into account his outs, the number of cards that can potentially improve the hand. For example, when hitting a flush draw on the turn or flop, a poker player will have nine outs to make a complete flush. Probably, the actual numver f outs is going to be higher, because some pair outs may give us the best hand.
The probability of improving on the flop is different for different starting hands. For example, for unsuited disconnected hands, chances are quite low, and suited hands hit the flop much better.
To prove this, we provide a comparison table:
| Flop situation | Probability % | |
| Suited connectors | Offsuit connectors | |
| Complete flush | 0.94% | – |
| Hitting a flush draw | 10.94% | 1.1% |
| Hitting a backdoor flush draw | 41.6% | 12.8% |
| Complete straight | 1.3% | – |
| Hitting an open-ended straight draw | 10.45% | 9.71% |
Playing many suited connectors is justified by the chances of hitting a flush by the river. Before the flop, the chance is 6%. In the case of an offsuit hand, it is significantly less – only 1.8%.
Probabilities of opponents’ behavior
The importance of the psychological aspect of playing poker cannot be overestimated. However, it often overshadows the calculations and charts. Poker game is an interaction with others, all of whom are subject to emotions and stress. Only experienced poker players are able to control their emotional state and remain calm at the table.
For a poker player, passion is the main enemy; it is well known even amongst the beginners.
Analyzing the behavior of your opponents at the table through statistical data rarely produces positive results, since each player has unique style. However, keeping personal statistics using special poker trackers can help identify the strengths and weaknesses of your opponents and use them to your advantage.
Poker odds calculators
Those calculators are basically tools that calculate chances for different poker situations (odds, outs and other probabilities) based on available data or information entered manually. These tools are important for both beginners who have not mastered poker mathematics and experienced players, making it easier to perform detailed probability calculations in various situations:
Online poker winning probability calculators
Web calculators automatically, online, analyze the gaming situation based on data from the table, providing quick and accurate calculations of the chances of winning.
Finding a Russian-language online poker calculator today is easy: there are many similar programs on the Internet. However, it is important to remember that not all of them are of equal quality and accuracy. Programs that provide correct results are often not free. Usually, you can purchase a subscription for a month or a year.
Here are the most popular poker calculators at the time:
- Poker Calculator Pro.
Software from PokerProLabs, a developer known for such popular tools as Tournament Shark and TopShark. This software has extensive functionality, but requires payment – $49.9 per year.
- Poker Wingman Pro.
Powerful software that not only makes accurate calculations, but also provides betting strategy advice for every situation. Works both online and offline. Trial version is available.
- Poker Hound.
Software that is famous for its flexibility. It works for Sit n’ Go tournaments, limit cash games and short stack No-Limit games. Subscription cost is $19.99 per month.
- Calculatem Pro.
A powerful program that can determine the chances of winning, calculate the number of outs and offer advice on game actions. A trial version of this software is available.
- Hold’em Genius.
One of the most popular software among poker players. Automatically synchronizes with the cash tables you play in real time, displays information about the pot odds on each street, shows the probability of collecting different combinations, estimates the real strength of the hand and can work with a large number of tables. This software has a Russian-language version and supports 250+ online rooms.
- Offline poker calculators:
To calculate the probability percentage in poker, some players use offline software.
Poker Studio is one of the most popular programs in the segment. It is easy to use and it performs detailed mathematical odds calculations developed by renowned gambler Dan Harrington. All information is presented in a convenient format, which makes it easier to assess the situation at the poker table.
Similar software – Poker Stove, Poker 4h Calculator, Turning River Calcs.
There are also more complex poker probability calculators. They are equipped with additional analytics functions. With their help, you can not only calculate odds, but also get advices on the most appropriate moves. In addition, such software calculates equity for all possible options at the moment. It allows you to work in more detail with hand ranges. Simply put, such programs have some analytical options available only to poker managers. These include:
- Cardrunners EV.
Offline calculator, recognized as the best at the moment. It is convenient to use in both cash games and tournaments. The program is based on a powerful mathematical engine, so calculations are made in just a couple of minutes. All data is as accurate as possible and presented in a convenient format. The software supports a trial version.
- Flopzilla.
Software for Texas Hold’em, which allows you to quickly determine the mathematical expectation of a hand and the chances of winning with different sets of cards. In addition, the program is ready to analyze your own game and provide valuable recommendations on the best moves.
- PokerStrategy Equilab.
An effective poker analysis tool, ideal for calculating equity and other key parameters. A special feature of the software is the presence of a simulator. With its help, poker players master the skill of making the necessary calculations on the go.
Frequently Asked Questions About Poker Odds
Is it even possible to calculate probabilities while playing poker?
While calculating odds is prohibited in some card games, in poker it is not only allowed, but an integral part of the game. It determines the level of players and their chances of winning. Poker is a sport where success comes from good strategy and mathematical theory.
Do high chances of winning guarantee you the win?
Definitely not. Moreover, an incomplete understanding of this fact leads to an overly emotional reaction to a loss with a high equity advantage.
Beginning poker players mistakenly take high chances of winning as being close to 100%. Even a pocket pair of aces in all-in loses to weaker hands 1 time out of 5, which needs to be clearly understood.
Is it possible to win at poker without a math background?
Sure, math skills are a benefit, but they are not a prerequisite for winning. However, for the greatest success, it is still recommended to understand the basic poker theories.
How to learn to calculate probabilities in poker?
To apply the probability theory in poker correctly, you need to practice a lot away from the tables. You can do manual calculations, because, despite the fact that various software significantly simplifies the process of finding the right solution, novice poker players need to improve their own calculating skill.
Poker programs are also important – they help develop strategies. However, until the player has his own clear strategy, it is better to use only equity calculators. It is also useful to study materials about poker mathematics. Videos, books, articles on probability in the game provide good support in the analysis and search for profitable solutions. Well, don’t forget that theory is more important than practice, especially for beginners. It takes twice as long to study it as it does to play.
Initially, it may look overwhelming, especially for a beginner, when there are so many numbers and calculations in front of him. However, in reality, mastering all this information is not that difficult. Over time, you will find that you can quickly estimate the approximate odds without spending a lot of time and effort.
