Calculation of probabilities and odds in poker. What is probability theory, outs and pot odds in poker

The basic Foundation of poker is mathematics

Do not neglect this, because mathematics in poker is really very importantFor every decision you make, along with psychological factors, there are also mathematical factors, which is a key element. In this article, we are going to analyze the probabilities and odds in poker. This will include the probabilities of poker combinations, i.e. how often you will get some hands, as well as the probability of winning poker with those hands, i.e. how often it will happen. We'll also look at how to calculate odds and outs, and in addition, we'll introduce you to a concept called pot odds in poker. Finally, we'll show you how understanding math will help you stay emotionally stable at the poker table, and why you should focus on decisions rather than results.

Probability is a branch of mathematics that considers the probability that one or the other outcome will occur.

For example, a coin flip has two possible outcomes: heads or tails. There is a chance that the flipped coin will fall with an eagle (one outcome out of two).) the same goes for tails.

When working with a deck of cards, the number of possible outcomes is clearly much higher than in the example of a coin.

There are fifty-two cards in each poker deck, each marked with one of four suits (clubs, diamonds, hearts and spades) and one of thirteen ranks (numbers from two to ten, Jack, Queen, king, ACE). Thus, the odds of getting any ACE as the first card are in (.), while the odds of getting any spade as the first card are in. Unlike coins, cards are said to have " memory»: each card dealt changes the composition of the deck.

For example, if you get an ACE as the first card, then only three aces remain among the other fifty-one cards.

So the odds of getting another ACE are in (.), which is much lower than the odds you had before you got the first ACE. To put this in perspective, when you play poker at a local casino and earn hands per hour, you can expect to earn pocket money on average once every. Unlike a specific pair, you can expect to receive any pocket pair on average once every minutes (for more information, see the igravcasino website). Players do not play poker in a vacuum, each player's hand must be matched against his opponent's hand, especially if the player is all-in before the flop. Now let's look at the odds of certain events occurring when certain starting hands are drawn.

The following table of probabilities of poker are listed some interesting and valuable mathematical data from Texas hold'em: Many poker beginners overestimate certain starting hands, such as suited cards.

As you can see, cards of the same suit do not collect a flush very often. In addition, a pair improves to a set on the flop only of the time, so low pairs are not always profitable to play.

Now take a look at the diagrams of General poker mathematics and probability theory, which list a variety of probabilities and odds for many Texas hold'em events.

These poker tables include, in addition to the two tables above, different probabilities of starting preflop hands. We recommend that you print out these tables and use them as a reference source. Note: the percentages shown above are rounded and do not take into account all possibilities. You must also take into account the number of clean suits and or the maximum number of straight outs. If you see a flop, you also need to know what the odds are on the flop. In poker terminology, an Out is any card that improves a player's hand after the flop.

One common occurrence is when a player has two matching cards and two more cards of the same suit appear on the flop.

The player has four cards of the same suit and needs one more of the nine remaining cards of that suit to complete the hand. In the case of a "flush draw", the player has nine" outs " to collect his flush. The "rule of four and two" is useful for calculating the chances of completing a hand. The player counts the number of cards that will improve their hand, and then multiplies that number by four to calculate the probability of getting that card on the turn or river. If a player has a draw on the turn, he multiplies his outs by two to find the probability of completing the hand on the river.

you or your opponent have a better hand

For example, the flush draw a chance to finish the flash is equal to approximately after the flop (outs x) and after the turn (outs x). Another important concept in calculating odds and probabilities is the pot odds (also known as pot odds). Pot odds are the fraction of the next bet relative to the pot size. For example, if the pot is $ and a player has to call a $ bet to continue playing the hand, they get a -to- (to) pot chance. If he calls, the new pot will now be $, and his call is $- of the new pot. Experienced players compare the pot odds with the chances of improving their hand. If the pot odds are higher than the odds of completing the hand, the professional player will call the bet.

if not, the player will pass.

"Bad bits" occur when a player completes a combination that initially had a very low probability of success. Probability experts explain this phenomenon by saying that an extremely unlikely event with a low probability does not make it completely impossible. The response to bad beats depends on the player's experience and maturity. In fact, many experienced players they tend to think that the reason for bad beats is that weak players remain in the game. Bad poker players often mistake their luck for skill and continue to make the same mistakes that more capable players use against them. One of the most important reasons that novice poker players need to understand what the probability function is in a poker game is that they can make better decisions during the hand. Although the odds (luck) fluctuate from hand to hand, the best poker players understand that skill, discipline, and patience are the keys to success at the poker tables. A good knowledge of poker math and probabilities will help you adjust your strategy and tactics during the game, as well as give you reasonable expectations of potential outcomes and emotional stability to continue playing smart, aggressive poker. Remember that the Foundation on which to build an understanding of the game of Texas hold'em begins and ends math. Never forget that math is very important in poker. Something did not understand a bit what is the probability we have to set (on the river, not the flop) if you have a pair preflop.

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