Feb 14, 2022
Casino Blog

How to Count Probabillity in Poker

Math should be and fundamental pillar for any good poker player. As with blackjack, it should have a lead in every decision you make. In today's article, we'll show you how you can use probability to improve your poker game.

Just for completeness, let's say something about probability as such. Probability indicates to us how the chance that a specific phenomenon will occur. As a rule, the value is written in the range from 0% to 100% (or from 0 to 1) with the fact that the indicator 0% means that the situation will not occur and on the contrary the indicator 100% means that the situation will definitely occur.

The easiest way to describe is with the coin flip. It has only two possible results - head or tails. Both results have the same probability of 1/2 (50%) that they will occur. In other words, depending on the probability, every second throw should be, for example, the head. Of course, this will not be the case in the short term, but the longer you will be flipping the coin, the closer the results will be to this probability.

Probability and Cards

If we look at the probability problem for a deck of cards, it is clear that the number of possible outcomes will increase rapidly compared to the coin flip. Poker is played with a deck of 52 cards, four suits and 13 values. This results in the following changes:

  • Getting an ace (or any individual card) from the deck: 4/52 = 0.0769 (7.69%)
  • Getting the spade: 13/52 = 0.25 (25%)

Unlike coin flip, roulette or slot, for example, a card deck has something of "memory". Respectively, this means that previous results have an impact on current and future results. This is because the dropped card from the deck and will change the default situation. Let's look at an example where an ace was drawn as the first card from a 52-card deck (chance 7.69%). The probability that an ace will be drawn from the deck again as the second card will now be different. After the first turn, the number of aces dropped to 3 and the number of cards to 51. So we calculate the chance as 3/51 = 0.0588 (2.88%).

Probability Before the Flop

Now that we've outlined how the probability of a deck of cards works, let's get to practical use. First of all, we will show you how to calculate the probability that you will get a pair. (for example, the already widely mentioned aces). In this case, we have to multiply the individual chances.

(4/52) x (3/51) = (12/2652) = (1/221) = 0.004524 (0.45%)

To give it a little perspective, if you play poker in a casino where about 30 hands are dealt per hour, you get a pair of aces about once every seven and a half hours of play.

So what is the chance that you will get any of the thirteen possible pairs? We can start from the possibility is 1/221 for any pair (see the formula above). There can be a total of 13 of these pairs, so the formula for the calculation will look like 13/221 = 0.0588. You can expect a pair once every 35 games.

Probability in Player-to-Player Game

However, poker is a multiplayer game that usually plays against each other. So here is a selection of the most common pre-flop situations.

Your Hand Opponent's Hand Probability of Winning
High Pair Two Low Cards 83%
High Pair Low Pair 82%
Middle Pair High, Low Card 71%
Two High Cards Two Low Cads 63%
Two High Cards Low Pair 55%

Probability Calculation According to "Outs"

If you manage to see the cards on the flop, you will undoubtedly be interested in what your chances are of improving your hand. In this case, we will talk about so-called "outs". The term refers to all cards in poker that can help you. This can be the case when a player holds two cards of a suit and two more cards of the same suit appear on the flop. The player then has nine outs, so there are nine cards left to form a flush.

Number of Outs Flop - Turn Turn - River Turn a River
20 42.6% 43.5% 67.5%
19 40.4% 41.3% 65.0%
18 38.3% 39.1% 62.4%
17 36.2% 37.0% 59.8%
16 34.0% 34.8% 57.0%
15 31.9% 32.6% 54.1%
14 29.8% 30.4% 51.2%
13 27.7% 28.3% 48.1%
12 25.5% 26.1% 45.0%
11 23.4% 23.9% 41.7%
10 21.3% 21.7% 38.4%
9 19.1% 19.6% 35.0%
8 17.0% 17.4% 31.5%
7 14.9% 15.2% 27.8%
6 12.8% 13.0% 24.1%
5 10.6% 10.9% 20.3%
4 8.5% 8.7% 16.5%
3 6.4% 6.5% 12.5%
2 4.3% 4.3% 8.4%
1 2.1% 2.2% 4.3%

There is a very easy method for calculating the probability for outs, thanks to which you can handle calculations directly at the gaming table. It is generally called the "four and two" rule. After the flop, the player simply multiplies the number of outs by 4 to determine the probability for a turn and river. If the player does not get the card on the turn, he/she just multiplies the number of outs by two and finds out the approximate probability of getting the card on the river.

Again, we can mention this as an example where you have four cards of the same suit after the flop. Your outs are nine cards, and the chance of a flush after the turn and river is 36% (9x4). Let's say you didn't get a card on the turn. In that case, we'll then multiply the outs by two and find that we have an 18% (9x2) chance of running out of cards on the river. As you can see in comparison with the table, this method is straightforward, but on the other hand, inaccurate, but it can be used.

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