Many people who know poker only by hearsay believe that anyone can win at poker and all it takes is a little luck. Indeed, poker is interesting because it is impossible to predict in advance who will win. A striking example was the victory Qui Nguyen in the final event of the WSOP series in 2016.
Luck plays in poker enough significant role, but not decisive. After all, every year the number of poker players increases, and the world's largest tournaments are constantly replenished with new participants, but the same people are always among the prizes. They may not win regularly, but consistently reach the final rounds and receive a good monetary reward. And the point is not that they are luckier than others.
The thing is that they have good mathematical abilities, soberly assess the situation and can quite accurately calculate the probabilities in poker. And thanks to their skills they have good chances get far enough in the tournament, where in an equal fight they can lose to no less skilled players, but with better cards.
No one knows which card will appear on the board next, but after analyzing probability of getting a combination in poker, a participant can estimate his chances of winning a particular hand. Today, in order to become a good player, you do not need to be a mathematical genius and carry out complex mathematical operations in your head. Everything has long been calculated and summarized in specific tables. A good memory is very necessary for a poker player, and you can start training it by remembering what the probability of getting draws in poker or a strong combination is.
If a player takes part in an online poker tournament, then the calculation probability of making a combination in poker it gets even easier. Programs have long been developed and exist that help instantly calculate the chances of success in the game, and for the required map to appear. They show the real picture, but even if the chances are 80% to 20%, this does not mean that these 80 percent will be decisive. That's the beauty of poker. Even with all the advanced developments, it is impossible to give a 100% guarantee of success.
Probability of getting a pair
The most common poker combination is a pair. It is quite strong in the poker hierarchy and is also not as difficult to collect as flush or straight. Many people have been calculating the probabilities of poker combinations since preflop and the appearance of pocket cards. Particularly lucky players may immediately land a pocket pair.
The probability of a pair in poker at the pocket cards stage is quite low. The total number of pocket pairs is 13, and the chances of such a local success do not reach 6%. The calculation is carried out using simple mathematical operations.
We know that there are 13 pairs in total, while there are 52 cards in a poker deck. Divide the number of pairs by the total number of cards and multiply by 12 and 51. Twelve means number of remaining pairs in the deck or in the hands of other participants, and fifty-one is the number of all cards minus one that has already been dealt to the player. Some quick math shows that the probability of a pair in poker preflop is no greater than in one hand out of seventeen.
Of course, ideally it would be nice to get a pair of aces preflop. But the chances of this are negligible - less than 0.5%. Pair probability in poker on the flop or rever it increases significantly. On the flop, in 32% of cases you can make a pair, and two pairs at once, one of which is a pocket – 16%. On the river the chances are even higher. A pair occurs in 46% of hands, and two pairs, if one of them is pocket, in 40%.
Flush probability
A flush is higher in the hierarchy of poker combinations than a pair. It is much more difficult to assemble it, but if you succeed, then the chances of success are very high. In order to collect a flush, the player must have combination of 5 cards of the same suit. The value of the cards does not matter, but if several players managed to collect a flush at once, then the winner is the one with the highest card.
The probability of a flush in poker is very small. Pocket cards play an important role. Naturally, they should be of the same color. If a participant has a pair, then the option with a flush should be immediately discarded. The chances of a flush on the flop are already less than one percent. But if you figure it out, what is the probability of draws in poker for a flush, then it will be a little more than 10%.
If a poker player hopes for flush on the river, then you need to understand that at best chances of success no more than 7% and this is provided that he has two pocket cards of the same suit. If the pocket cards are of different suits, then the chances of a flush are no more than 2%.
Street odds
Street can also in 95% of cases guarantee the poker player success in the hand. This combination also consists of five cards, but in a clear sequence, the chain of which should not be interrupted. The Ace in this hand can be the highest card or the lowest.
A straight can be eliminated on the flop, if your cards contain a pair or random cards of different or the same suit. Random cards mean that the gap in card value will exceed 3 cards, and it cannot be replenished with the help of three community cards.
Chances of collecting straight will depend on the gap in connector values. If the gaps are from three to 1 values, then the probabilities of a poker combination range from 0.64% to 1%. If the pocket cards are consistent, then a straight draw on the flop can be hit with a probability of almost 10%.
On the river the participant has the greatest chances on the street with two cards of consecutive value. They make up 10%. As you can see, the probabilities in poker of making a straight, even under the most optimal hands, are very low and do not give you the opportunity to hope for success more than in one out of 10 cases.
Results
A player's mathematical chances of making a hand in poker increase as they move down the hierarchy of hands. Also, a lot will depend on what pocket cards the player received and what type of poker is played at the table. Eg, probability of winning combinations in five-card poker will be calculated separately at each stage of the game as cards appear on the board. We advise you not to try to constantly collect Royal Flush or Four of a Kind, because in the long run it will only bring losses. The probabilities of such combinations in poker are very low.
Flush draw is a term often used during the game. Many beginning poker players are interested in the meaning of this concept. This is what we will talk about today.
Chances of making a flush
- two suited cards as pocket cards provide a 1% chance of making a flush on the flop;
- two suited cards increase the chance of adding a draw to 12%;
- with two different pocket cards, the chance of making a flush on the flop is 2%;
- two offsuit cards increases the probability of a flush draw on the flop to 24%;
- the chance of hitting a flush on the river reaches 36% if the player hits a draw on the flop;
- with a draw on the turn, the probability of making a flush on the river is 20%;
- with a draw on the flop, the chance of making a flush on the turn is also 20%.
A flush draw is a frequently used term in poker that describes an incomplete hand consisting of five suited cards. There are several varieties of draw, but the best of all is the variant with two pocket suited cards - this well masks an incomplete combination.
The positive outcome of a poker game depends on mathematical calculations. Poker is based on error-free calculations, so the player is not recommended to rely on intuition.
The probability of winning combinations in poker is an assessment of the chances of winning in a particular game. Experts have carefully studied these theories and presented them in special tables. They make it easy to calculate your own acceptable chances and opportunities in the gameplay.
In addition to tables, experts have developed computer programs and applications with the help of which any poker player is able to create an unbiased picture of his personal gaming situation when random cards appear.
In five-card poker, the probability of forming combinations on each street is calculated separately, since the position changes with the addition of new cards to the board. Consequently, the chances of forming the required combination, which are expressed as a percentage, also change.
Probability of combinations preflop
First, let's look at combinations in the poker game with the probability of hitting preflop. In a word, it is necessary to understand the number of different combinations that can be dealt to a gamer preflop. The original deck contains 52 cards. One of them will be handed over to the poker player without fail.
The second card will be one of the 51 cards that remain. Since the order does not matter here, there will be 1326 (52x51:2) different combinations of pocket cards.
Based on the calculation of 4x3:2, a certain pocket pair can be obtained in six variations. In accordance with this, the player will have a certain pair every 221 hands. We obtained this figure based on the calculation 6:1326=1:221. Since any pocket pair will occur every 17 hands, there are 13 legal pairs (221:13).
Any unpaired cards of the same or different suits can be dealt in 16 variations. You can win any two cards of the same suit in 23.5% of cases (12:51), and you can get a pair of cards of one suit or another with a 5.9% chance.
Probability of combinations on the flop
Now we need to consider the probability of hitting poker combinations on the flop. Here the gamer can see three of the five cards. This makes it possible to confidently state that the flop is considered the most significant moment in the theory of probability. Since a huge part of the gameplay is left behind, it is necessary to decide to extend it here.
In the event that a poker player does not have a pair in his hands, then the following chances are provided for gaining strength on the flop:
- Couple can be hit on the flop with a 26.94% probability.
- 2.02% on what the poker player will gain Two pairs, where a pair of cards will be revealed on the board, and the third card will correspond to one of those cards that his hands have.
- Also in 2.02% of cases the poker player will gain two cards that match the board.
- Collect Trips(when the gamer's card matches the one on the flop) is possible in 1.35% of cases.
- For education Full House there is only a 0.09% chance.
- And for the formation Kare only 0.01% remains.
Thus, the probability of getting a boost on the flop without a hole card is exactly 32.4%. The chances of forming a Flash or Straight are not taken into account here.
Odds with a hole card
With a pocket card, the variations on getting one or another combination will be as follows:
- Two pairs with a pair on the flop and a poker player’s pair – 16.16%.
- Set – 10,77%.
- Full house, where the pair is on the table and the match to the gamer’s pair is 0.74%.
- Full house, where the poker player has a pair and there are three cards of identical rank on the board – 0.25%.
- Kare – 0,25%.
A player with suited cards can build a Flush on the flop with 0.84% probability. But there is already a 10.94% chance of making a Flush Draw. With cards of different suits, a Flush Draw can be formed in 2.25% of cases.
If a poker player has connectors in his hands, then his chances of making a Straight or Straight Draw from the flop will be as follows:
- Connectors without a hole: Street's formation has a 1.31% chance. Straight Draw formation – 10.45%.
- Connectors with a single hole: Straight – 0.98%, Straight Draw – 0.08%.
- Connectors with a pair of holes: Straight – 0.65%, Straight Draw – 5.22%.
- Connectors with three holes: Straight – 0.33%, Straight Draw – 2.61%.
The probabilities of getting combinations in poker by the river are especially interesting (the turn in few cases becomes decisive). If the gameplay reaches the showdown, then it is with such combinations that the player will need to open up. When there is no pair in hands, the chances of strengthening by the river are as follows:
- Becoming the owner of a Pair – 46%.
- Become the owner of Two pairs – 22%.
- Become a Troika owner – 4.5%.
- Becoming the owner of Full House – 2.2%.
- Become the owner of a Four of a Kind – 0.1%.
In the case when a poker player has a pocket card in his hands, then he has the following probabilities for improvement by showdown:
- In 40% of cases he will be able to make two pairs.
- In 12% of cases - Seth.
- In 8.5% of cases he will be able to form a Full House.
- With a 0.84% probability he will be able to collect Four of a Kind.
With a pair of cards of the same suit, he can be 6.6% sure that he will make a Flush by showdown. If only two cards are missing for a Royal Flush, then there is a 0.05% chance that this combination can be obtained before the river. Trying to get a Straight Flush with connections of the same suit, the poker player will have 0.2%. In two percent of cases, you can make a Flush by having cards of different suits in your hands.
There is no need to talk about such combinations as Royal Flush and Straight Flush. The probability of their formation is almost zero. Given the connections, there are the following probabilities for a Street meeting:
- 9.1% – connections without holes.
- 7.8% – connections with a single hole.
- 6.5% – connections with a couple of holes.
- 5.1% – connections with three holes.
The probability of winning combinations in poker is an incredibly important and integral element of poker science. By understanding all the statistical nuances, a poker player will be able not only to prevent risky situations, but will also be able not to miss his chance of luck.