In poker, the probabilities of each type of 5 card hand can be calculated by calculating the proportion of the hand of that type among all possible hands.
Video Poker probability
Histori
People think about probability and gambling long before the invention of poker. Gambling led to the development of probability theory in the late 1400s. When playing games with high stakes, players want to know what the chances of winning. In 1494, Fra Luca Paccioli released his work Summa de arithmetica, geometria, proportioni e proportionalita, which is the first written text on probability. Motivated by the work of Paccioli, Girolamo Cardano (1501-1576) made further developments in probability theory. His work of 1550, entitled Liber de Ludo Aleae , discusses the concept of probability and how they are directly related to gambling. However, his work did not receive recognition because it was not published until after his death. Blaise Pascal (1623-1662) also contributed to the theory of probability. His friend, Chevalier de Mà © à © rà © Ã… ©, is a fond gambler with the goal of getting rich from him. De MÃÆ'Ã… © rÃÆ'  © tried a new math approach for gambling game but did not get the desired result. Determined to know why his strategy did not work, he consulted Pascal. Pascal's work on this issue initiated an important correspondence between him and fellow mathematician Pierre de Fermat (1601-1665). Communicating by mail, the two continue to exchange their ideas and thoughts. This interaction leads to the conception of a basic probability theory. To this day, many gamblers still rely on the basic concepts of probability theory to make decisions while gambling.
Maps Poker probability
The 5-card poker hand frequency
The following chart mentions the (absolute) frequency of each hand, given all combinations of 5 cards taken randomly from the full deck 52 without replacement. Wild cards are not considered. In this chart:
- Different hands are the number of different ways to draw hands, not counting different clothes.
- Frequency is the number of how to draw a hand, including the same card value in different settings.
- The possibility of to draw a given hand is calculated by dividing the number of how to draw a hand ( Frequency ) with the total number of 5-card hands (sample space; ). For example, there are 4 different ways to draw a royal flush (one for each setting), so the probability is 4 2,598,960 , or one in 649,740. One would then expect to draw this hand about once in every 649,740 series, it's almost 0.000154% of the time.
- Cumulative probability refers to the possibility of hand drawing as good as or better than specified. For example, the probability of drawing three types is approximately 2.11%, while the probability of drawing hands at least and three types is about 2.87%. The cumulative probability is determined by adding a one-handed probability with the probability of all hands on it.
- Odds is defined as the ratio of the number of ways not to hand drawing, to any number of ways to draw it. For example, with a royal flush, there are 4 ways to draw one, and 2,598,956 ways to draw something else (2,598,960 - 4), so the chance of drawing a royal flush is 2,598,956: 4, or 649,739: 1. The the formula for assigning an opportunity can also be expressed as (1/p) - 1Ã,: 1 , where p is the probability.
- The values ​​provided for Probability , Cumulative probability , and Opportunities are rounded for simplicity; Hand different and Frequency values ​​are correct.
Fungsi nCr pada sebagian besar kalkulator ilmiah dapat digunakan untuk menghitung frekuensi tangan; masukkan nCr dengan 52 dan 5 , misalnya, menghasilkan seperti di atas.
Royal flush is a straight flush case. This can be formed 4 ways (one for each setting), giving a chance of 0.000154% and chances 649,739: 1.
When ace-low straights and ace-low straight flushes are not counted, each probability is reduced: straight and straight flushes respectively to 9/10 as normal as it should be. The four longitudinal faces that disappear into flushes and 1,020 are passed straight into no pairs.
Note that since clothing has no relative value in poker, two hands can be considered identical if one hand can be changed into the other hand by swapping settings. For example, hand 3? 7? 8? Q? A? is identical to 3? 7? 8? Q? A? for replacing all the clubs in first-hand with diamonds and all the shovels by heart generate second-hand. So eliminating the identical hand that ignores the relative suit values, there are only 134,459 different hands.
The number of different poker hands is even smaller. For example, 3? 7? 8? Q? A? and 3? 7? 8? Q? A? is not an identical hand when ignoring task settings because one hand has three settings, while the other hand has only two settings - it can affect the relative value of each hand when more cards come. However, although the hands are not identical from that perspective, they still form an equal poker hand because each hand is the hand of a high A-Q-8-7-3 card. There are 7,462 different poker hands.
The frequency of 7-card poker hands
In some popular poker variations, a player uses the five best poker cards from seven cards. Frequencies are calculated the same way as those shown for 5 hand cards, unless additional complications arise due to two additional cards in 7-card poker hands. The total number of different 7-card hands is . It should be noted that the probability of unpaired couples is less than the probability of a pair or pair of two-paired hands.
Flush straight-straight or high Royal flush slightly more often (4324) than the lower straight flushes (4140 each) because the remaining two cards can have any value; flush straight king-high, for example, can not have Ace from its suit in hand (because it will make it an ace-high instead).
(The exact freq given: probability and probability is approximate.)
Since clothing has no relative value in poker, two hands can be considered identical if one hand can be changed to another by swapping suits. Eliminates the identical hand that ignores the relative suit value leaving 6,009,159 different 7-card hands.
The number of different 5-card poker hands that may be of 7 cards is 4,824. Perhaps surprisingly, this is less than the number of 5 hand poker cards out of 5 cards as some 5-card hands are not possible with 7 cards (eg 7-high).
Handball frequency 5 low card balls
Some poker variants, called lowball, use low arms to determine the winning hands. In most lowball variants, the ace is calculated as the lowest and straightest card and the flush is not counted with low hand, so the lowest hand is a five-height hand A-2-3-4-5 , also called wheels . Probability is calculated based on , the total number of 5-card combinations. (The exact given frequency; the probability and chance is approx.)
As can be seen from the table, more than half the time a player gets hands that have no spouse, three or four-of-a-kind. (50.7%)
If the ace is not low, simply rotate the hand description so that 6-high displaces 5-high for the best hand and ace-high replaces the king-high as the worst hand.
The 7-card hand frequency of low ball poker
In some variants of poker, players use the five best low cards chosen from seven cards. In most lowball variants, the ace is calculated as the lowest and straightest card and the flush is not counted with low hand, so the lowest hand is a five-height hand A-2-3-4-5 , also called wheels . Probability is calculated based on , the total number of 7-card combinations.
The table does not cover up to five hand cards with at least one pair. "Total" represents 95.4% of the time a player can choose 5 low cards without spouse.
(The exact freq given: probability and probability is approximate.)
If the ace is not low, simply rotate the hand description so that 6-high displaces 5-high for the best hand and ace-high replaces the king-high as the worst hand.
Bluff
The bluffing frequency can affect the chances of an opponent calling a bet or folding. A player can bully at frequent § Optimal bully to try to eliminate any advantage to his opponent.
See also
- Possible
- Opportunities
- Sample space
- Events (probability theory)
- Binomial coefficients
- Combination
- Permutations
- Combinatorial game theory
- The complexity of the game
- Set theory
- Math game
Note
External links
- Brian Alspach's math page and poker
- MathWorld: Poker
- The probability of poker includes conditional counting
- Many poker probability tables
- 5, 6, and 7 poker card probabilities
- Odds Poker for Dummies
- The 7,462 and 4,824 equivalence classes
- Preflop, After Flop and Opportunity to Create a Hand Opportunity
- Odds and Outs probability table
- Poker probability calculator 5, 6 and 7 cards
- Odds visual calculator
Source of the article : Wikipedia
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