Many beginner players do not attach much importance to probability theory. Moreover, most of them see nothing in common between this science and the game of poker. A weak player thinks this way: it succeeds, it doesn’t work out, it can work out, or it may not work out. And this is good, if he has any experience in playing, it means that intuition can sometimes lead him to make a mathematically correct decision. But what if there is a completely green beginner at the table? Find out about this and much more in the full news!

## Introduction

It is safe to say that without knowledge of probability theory and the basics of arithmetic, the actions of poker players will be very negative, which at a distance will lead to a huge loss of money. Some experienced players can make informed decisions based on their superior feelings and knowledge of the game, but most of us must rely on math to make decisions that are close to the right ones.

A person starting to play poker needs to learn exactly, and most importantly, quickly evaluate his chances. I am sure that any average player pays tribute to this science and successfully applies it in practice. There is nothing complicated here! In this article, we will repeat all the most important poker odds that players regularly encounter. Many have known these numbers for a long time, while the rest will need to replenish their baggage of poker knowledge if they want to play good, positive poker.

Odds and probabilities are not the same thing. Probability tells you how many times this incident happens. For example, you will receive a pocket pair every 17 changes or approximately 6% of the time. The chances are the opposite - how many times this case does not happen. It turns out your odds are 16 to 1 against the fact that you get a pocket pair. We will operate with probabilities, it is much more understandable and clear.

So, we continue to talk about the probabilities of the arrival of certain cards preflop. The opportunity to get two suited cards is 12/51 or 24%. Then the chance to get cards of a certain suit will be four times less - 6%. Two aces will be handed out to you on average every 220 hands, i.e. 0.5% of the time. An ace with a king will come to us on average once for 83 distributions or 1.2% of all distributions. For clarity, let’s try to manually calculate the possibility of getting, say, a lady and jack of the same color. The first card suits us with any queen and any jack, i.e. only eight cards, we get the fraction 8/52. Suppose a queen of spades has come. This is a black suit, so now we are satisfied with only two black jacks (jack of spades and jack of clubs), we get the fraction 2 51. Multiply: 8/52 × 2/51 = 4/663 = 0.6%.

Let's say we are interested in how likely it is that at least one out of ten players was dealt an ace. The easiest way to solve the problem is “on the contrary”, that is, we will find out what are the chances that no one has received the ace. They are equal to (1-0.15) ^ n, where ^ n is the power of the number of players. That is, the possibility that the ace was dealt to at least one of the ten players = 1-0.85 ^ 10 = 81%. In fact, this number is somewhat underestimated. In fact, the probability of getting an ace by one out of ten players is 87%. That is, on average, an ace will be dealt to one out of ten players in 9 cases out of 10.

These probabilities are not so important, but knowing them is still useful. For example, knowing that your opponent will receive aces or kings three times less than an ace with a king, you will always be more accurate when reading his hand. Now let's talk about postflop odds. Three community cards are laid out on the flop, as a result of which you see more than 70% (5 cards of seven) of possible information. Opportunities on the flop are most interesting for players.

First, consider two random unpaired cards:

- Getting a pair on the flop = 32%.
- The ability to buy two pairs on the flop (regardless of whether it is a pair on the table + a match or two matches with the board) = 2%.
- Getting thrips = 1.35%.
- Full house = 0.09%.
- Four of a kind = 0.01%.

If you have a pocket pair, then the chances of further improvement are as follows:

- Getting two pairs (pocket, plus a pair on the table) = 16%.
- Opportunity to buy set = 12% on the flop.
- Getting a full house (coincidence plus a couple on the table) = 0.74%.
- Full house (three on the table) = 0.25%.
- Four of a kind = 0.25%.

If you have suited connectors, say 8-9s, then:

- Getting flush on the flop = 0.84%.
- Street = 1.3%.
- Flush draw = 11%.
- Bilateral straight draw = 9.3%.

- Getting a flop with two cards of the same suit = 55%.
- Flop of the same suit = 5%.
- A “tight” coordinated flop (for example, 10-J-Q) = 2%.

I think many will be interested to know the chances of collecting a certain combination on the river. The calculation procedure is the same as when calculating on the flop. It is only necessary to add two more cards during all calculations. If you want to check any of the numbers obtained by calculations, you can use one of the special programs that allow you to calculate probabilities in a matter of seconds, analyze and calculate various options, combinations of opponent cards.

## Probability indicator: what is it

The probability in the game is a certain indicator that starts from 0 and reaches 100 percent. Thanks to the numbers you can find out **how often a particular event occurs** in a poker game.

Professional players using probability in poker can evaluate each situation, the further development of events and the prospect of a future bet. A correctly made decision guarantees success and stable wins. Thanks to the theory of probability, you can calculate the odds of the bank and know how much money you need to put on a certain combination in poker.

## How to count the probability in poker

You can calculate probabilities in poker on your own in the mind. To do this, you need to know the principle and formula. To simplify the process, you can use a certain software for calculations. They fast **determine the exact indicators to win**. Programs will be indispensable for online poker games. However for tournaments *"Live"* will have to use their own knowledge.

## Variations of poker tables

**There is no universal standard probability table** winning poker. Otherwise, there would be no losers and winners, there was no point in the game itself. There are a lot of calculation options. Each player chooses his own principle of determining chances and probabilities.

Professionals have identified some variations of probability in poker:

- The odds of playing preflop.
- The probability of losing combinations in poker with two cards of different suits.
- Odds with a pocket pair on hand.
- Probability with suited cards.
- The appearance of two unpaired cards on the table.

In fact, there are many more variations. These are the most common and often used. **Information about the chances will allow the player to assess the situation** preflop, flop and turn, and make the right decision.

## Probability to preflop

Some options for chances to collect a combination at the preflop stage:

- Three suited cards, which subsequently give a flush - a probability of 6%.
- The loss of all cards of completely different stripes is 40-50%.
- Set collection - less than 1% chance.
- Collecting 2 suited cards on the flop - more than 50%.
- Two cards in a row - the probability in poker is 40%.
- Three cards in a row that may form a straight in the future - less than 3%.
- The discrepancy of cards in order and height is about 60%.

Knowing the approximate probability of a flop, you can evaluate your chances before betting. Pairing is the easiest. But to collect the combination above **not so often.**

## Chances to improve poker hand

Sometimes on the flop a player collects a small combination or draw (incomplete high combination). Before you bid, you need to know which **the chances of improving this “hand”.** Here is a list of some poker odds on improving the card on the turn:

- Get full house from the set - a chance of about 15%.
- Upgrade 2 pairs to full house - no more than 9%.
- To make the draw flush on the flop become a full flush on the turn - 20%.
- Improve two-way draw straight (when one card is missing from the bottom or top) - 17%.
- Strengthen the gutshot street (one card is missing in the middle) to a full straight - 8%.
- The pair will be a set with a probability of 4.5%.
- Any card on hand will become a pair - 13% chance.

These poker odds **help the player make the right decision** About bid. If you need to report 100% of the money to the bank, and the chances of winning are 4%, then it is logical to fold. Even if the combination still comes together, it will be a rather rare case. And the player will bet a large amount each time. Total losses will exceed the probable gain.

## Opportunities for improving the flop to the river

If the player on the flop thinks to go before the showdown, then he will come in handy the probability table in poker for improving the combination on the river:

- Set will become a full house with a probability of 33%.
- Get a full flush from a draw - 17%.
- Strengthen two pairs of full house - a 35% chance.
- A two-way straight draw to a full straight is a 17% chance.
- One of the cards on the hand will become a pair - 24%.

As you can see, a normal entry into the game with 2 cards with a 24% probability will give you at least one pair. Therefore, when entering with overcards (ace-king, king-queen), you can count on the TOP pair and have high chances of winning.

## Probability in poker: turn to river improvement table

After the turn there is an opportunity to see only 1 river card before the showdown. Sometimes many players rely on her. Having an incomplete combination, there are chances of its strengthening on the river. However, to get to the last step, you need to put a lot into the bank. To rate your **real chances of getting a combination**, see the table of probabilities in poker for improving the hand from the turn to the river.

Experienced players know the exact percentage of each improvement and can use this information to make a decision. It will never be possible to determine the exact probability in poker, since the player does not know the cards in the hands of the opponents. If the opponents have one of the cards we need, then the chances immediately decrease.

Math calculations **necessary for a stable victory** and assessing your real odds. You need to put off gambling thinking and always turn to numbers. Do not be afraid to think long before making a decision. Each thought in poker forms a specific player experience, brings it closer to achieving the goal.

## How to independently calculate the chances

If a player has forgotten the poker odds table, **you need to take the odds yourself**. The main thing is to include logic and minimal knowledge of mathematics. Perhaps the calculation will not be the most accurate, but it will give the player an indicative idea of their chances.

*Calculation example:* player is trying to collect a flush. He has 2 peaks on his hands and 2 peaks on the table. One spade is missing for a better combination. What are the chances that it will open on the table? To begin with, we determine how many cards of the deck will help us improve the hand: 13 spades in the deck minus 4 already open. There are 9 possible peaks that suit us. There are 52 cards in the deck. We take away already open cards (2 on hands, 3 on the flop). There are 47 cards left (these are our 100%). Now an easy mathematical calculation: multiply 13 peaks by 100% and divide by 47 cards. In the mind, you can make approximate calculations. It turns out about 25%. Now the player knows his approximate chances of winning and will be able to make the right decision.

## Use the odds wisely

Many beginners diligently calculate the chances of improving the combination and **do not always follow the game itself**. Sometimes even the improvement of a certain hand will not give exact guarantees for victory. *Example:* the player collects a draw straight, calculated his chances and waits for a card to win. But he does not notice that there are 3 suited cards on the table and perhaps one of the opponents already has a flush or another draw. In this situation, it is foolish to collect a weaker combination.

Need to **apply knowledge of probabilities in poker is appropriate** and try to evaluate the chances of the card only with confidence to win. Trying to “catch” weak combinations against a strong table is a big mistake for beginners.

## Chances of improvement to showdown

So, again, two random unpaired cards - the results will be as follows:

- The probability of getting one pair = 46%.
- Two pairs = 13%.
- Trips = 4%.
- Full house = 2%.
- Kare = 0.1%.

If you have a pocket pair, then the chances of improving to showdown are:

- The probability of getting two pairs = 40%.
- Set = 20%.
- Full house = 8%.
- Four of a kind = 0.8%.

If you have multi-suited cards in your hands, then the probability of collecting a flash is about 2%, and if the cards are suited, then approximately 7%. If you have connectors on your hands, then you will collect a street in approximately one case out of ten or 9.5% of the time.

Some more useful statistics and probabilities:

- The probability that KK will be an over pair on the flop = 78%.
- That Q-Q will be an over pair on the flop = 60%.
- That J-J will be an over pair on the flop = 43%.
- That 2-2 will win A-Ko = 53%.
- That the weakest hand (2-7 °) will win the strongest hand (AA) = 13%.

The best hands that are against aces are suited connectors, for example, 9-10s will win AA in 23%, while KK will beat the strongest hand only in 19% of cases.

General chances in duels - the error can be 1-5%, which is not very significant:

- The oldest couple versus the youngest: 82:18.
- For example: 7-7 vs 5-5.
- Couple versus two Auvers: 55:45.
- For example: 5-5 against K-8.
- Pair versus high and low cards: 70:30.
- For example: 5-5 against A-3.
- Pair versus two lower cards: 84:16.
- For example: 5-5 against 2-3.
- Two high cards versus two low cards: 60:40.
- For example: K-10 vs 7-9.
- High and low cards versus two middle ones: 56:44.
- For example: K-4 vs T-5.
- Kicker Domination: 70:30.
- For example: A-10 vs A-5.

## Conclusion

Poker is based on elementary probability theory. Whatever difficult decision you were to make, the first thing you should determine as accurately as possible is your chances of winning, how you stand against your opponent’s alleged hand, what is the probability of improving to the necessary combination, etc. These and many other figures must be fully known and be prepared to put them into practice. Finally, we recommend that you read the book by Roman Shaposhnikov and Sergey Kolykhmatov, “Poker. Texas Hold'em Course ”, where all emphasis is placed on probability theory, I’m sure that a player of any level will find for himself something interesting and useful from this textbook. We wish you success in the game!