Poker Hand Probability Table
Mark Brader has provided the following tables of probabilities of the various five-card poker hands when five cards are dealt from a single 52-card deck, and also when using multiple decks.
The traditional hand types are described on the poker hand ranking page. These include one hand that belongs to two types at once - a straight flush is both a straight and a flush. With two or more decks, it is possible for other combinations to occur, such as a hand that has both a flush and a pair (such as 4-6-6-8-9 all of one suit). The left-hand tables include these composite hand types for multiple decks; in these tables 'plain' means a hand that is not a flush.
The hands are listed in descending order of probability, which could be used as the basis for their ranking order in multi-deck poker variations. It can be seen that as the number of decks increases, flushes become easier to make than straights, and sets of equal cards become more common.
Here is the Perl program that produced the tables. Mark Brader has placed both the program and the tables in the public domain.
- So the probability to make the winning hand is 100% – 45.9% = 54.1%. This means that on the flop, having both an open-ended straight and a flush draw, you can call an all-in regardless of pot odds, because you will win in more than 50% of cases.
- Poker Hands Probability. OPN NewsDesk January 19, 2016. The table below will help you decide which hands to play according to their winning percentage preflop.
Introduction
This page examines the probabilities of each final hand of an arbitrary player, referred to as player two, given the poker value of the hand of the other player, referred to as player one. Combinations shown are out of a possible combin(52,5)×combin(47,2)×combin(45,2) = 2,781,381,002,400. The primary reason for this page was to assist with bad beat probabilities in a two-player game, for example the Bad Beat Bonus in Ultimate Texas Hold 'Em.
For example, if you wish to know the probability of a particular player getting a full house and losing to a four of a kind, we can see from table 7 that there are 966,835,584 such combinations. The same table shows us that given that player one has a full house, the probability of losing to a four of a kind is 0.013390. To get the probability before any cards are dealt, divide 966,835,584 by the total possible combinations of 2,781,381,002,400, which yields 0.0002403.
Table 1 shows the number of combinations for each hand of a second player, given that the first player has less than a pair.
Table 1 — First Player has Less than Pair
A “poker hand” consists of 5 unordered cards from a standard deck of 52. There are 52 5 = 2,598,9604 possible poker hands. Below, we calculate the probability of each of the standard kinds of poker hands. This hand consists of values 10,J,Q,K,A, all of the same suit. Since the values are fixed, we only need to choose the suit.
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 164,934,908,760 | 0.340569 |
| Pair | 228,994,769,160 | 0.472845 |
| Two pair | 43,652,558,880 | 0.090137 |
| Three of a kind | 7,303,757,580 | 0.015081 |
| Straight | 26,248,866,180 | 0.054201 |
| Flush | 13,060,678,788 | 0.026969 |
| Full house | - | 0.000000 |
| Four of a kind | - | 0.000000 |
| Straight flush | 85,751,460 | 0.000177 |
| Royal flush | 10,532,592 | 0.000022 |
| Total | 484,291,823,400 | 1.000000 |
Table 2 shows the number of combinations for each hand of a second player, given that the first player has a pair.
Table 2 — First Player has a Pair
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 228,994,769,160 | 0.187874 |
| Pair | 574,484,133,960 | 0.471324 |
| Two pair | 270,127,833,552 | 0.221621 |
| Three of a kind | 47,736,401,832 | 0.039164 |
| Straight | 50,797,137,096 | 0.041676 |
| Flush | 30,076,271,352 | 0.024675 |
| Full house | 15,829,506,000 | 0.012987 |
| Four of a kind | 586,278,000 | 0.000481 |
| Straight flush | 214,250,184 | 0.000176 |
| Royal flush | 25,380,864 | 0.000021 |
| Total | 1,218,871,962,000 | 1.000000 |
Table 3 shows the number of combinations for each hand of a second player, given that the first player has a two pair.
Table 3 — First Player has a Two Pair
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 43,652,558,880 | 0.066798 |
| Pair | 270,127,833,552 | 0.413355 |
| Two pair | 246,286,292,328 | 0.376872 |
| Three of a kind | 31,155,189,408 | 0.047674 |
| Straight | 18,549,991,152 | 0.028386 |
| Flush | 14,200,694,712 | 0.021730 |
| Full house | 28,751,944,680 | 0.043997 |
| Four of a kind | 653,378,400 | 0.001000 |
| Straight flush | 109,829,304 | 0.000168 |
| Royal flush | 12,673,584 | 0.000019 |
| Total | 653,500,386,000 | 1.000000 |
Table 4 shows the number of combinations for each hand of a second player, given that the first player has a three of a kind.
Table 4 — First Player has a Three of a Kind
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 7,303,757,580 | 0.054369 |
| Pair | 47,736,401,832 | 0.355348 |
| Two pair | 31,155,189,408 | 0.231918 |
| Three of a kind | 27,586,332,384 | 0.205352 |
| Straight | 3,310,535,196 | 0.024643 |
| Flush | 2,606,403,900 | 0.019402 |
| Full house | 12,910,316,760 | 0.096104 |
| Four of a kind | 1,705,867,680 | 0.012698 |
| Straight flush | 19,970,844 | 0.000149 |
| Royal flush | 2,304,216 | 0.000017 |
| Total | 134,337,079,800 | 1.000000 |
Table 5 shows the number of combinations for each hand of a second player, given that the first player has a straight.
Table 5 — First Player has a Straight
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 26,248,866,180 | 0.204299 |
| Pair | 50,797,137,096 | 0.395362 |
| Two pair | 18,549,991,152 | 0.144377 |
| Three of a kind | 3,310,535,196 | 0.025766 |
| Straight | 25,219,094,136 | 0.196284 |
| Flush | 3,229,836,828 | 0.025138 |
| Full house | 975,510,000 | 0.007593 |
| Four of a kind | 43,198,800 | 0.000336 |
| Straight flush | 98,961,348 | 0.000770 |
| Royal flush | 9,485,064 | 0.000074 |
| Total | 128,482,615,800 | 1.000000 |
Table 6 shows the number of combinations for each hand of a second player, given that the first player has a flush.
Table 6 — First Player has a Flush
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 13,060,678,788 | 0.155206 |
| Pair | 30,076,271,352 | 0.357410 |
| Two pair | 14,200,694,712 | 0.168754 |
| Three of a kind | 2,606,403,900 | 0.030973 |
| Straight | 3,229,836,828 | 0.038382 |
| Flush | 19,608,838,592 | 0.233021 |
| Full house | 1,102,206,960 | 0.013098 |
| Four of a kind | 50,221,200 | 0.000597 |
| Straight flush | 191,762,164 | 0.002279 |
| Royal flush | 23,604,264 | 0.000281 |
| Total | 84,150,518,760 | 1.000000 |
Table 7 shows the number of combinations for each hand of a second player, given that the first player has a full house.
Table 7 — First Player has a Full House
| Event | Pays | Probability |
|---|---|---|
| Less than pair | - | 0.000000 |
| Pair | 15,829,506,000 | 0.219222 |
| Two pair | 28,751,944,680 | 0.398185 |
| Three of a kind | 12,910,316,760 | 0.178795 |
| Straight | 975,510,000 | 0.013510 |
| Flush | 1,102,206,960 | 0.015264 |
| Full house | 11,661,414,336 | 0.161499 |
| Four of a kind | 966,835,584 | 0.013390 |
| Straight flush | 8,767,440 | 0.000121 |
| Royal flush | 993,600 | 0.000014 |
| Total | 72,207,495,360 | 1.000000 |
Table 8 shows the number of combinations for each hand of a second player, given that the first player has a four of a kind.
Table 8 — First Player has a Four of a Kind
| Event | Pays | Probability |
|---|---|---|
| Less than pair | - | 0.000000 |
| Pair | 586,278,000 | 0.125418 |
| Two pair | 653,378,400 | 0.139772 |
| Three of a kind | 1,705,867,680 | 0.364923 |
| Straight | 43,198,800 | 0.009241 |
| Flush | 50,221,200 | 0.010743 |
| Full house | 966,835,584 | 0.206828 |
| Four of a kind | 668,375,136 | 0.142980 |
| Straight flush | 390,960 | 0.000084 |
| Royal flush | 44,160 | 0.000009 |
| Total | 4,674,589,920 | 1.000000 |
Table 9 shows the number of combinations for each hand of a second player, given that the first player has a straight flush.
Table 9 — First Player has a Straight Flush
Poker Probability - Wikipedia
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 85,751,460 | 0.110699 |
| Pair | 214,250,184 | 0.276582 |
| Two pair | 109,829,304 | 0.141782 |
| Three of a kind | 19,970,844 | 0.025781 |
| Straight | 98,961,348 | 0.127752 |
| Flush | 191,762,164 | 0.247552 |
| Full house | 8,767,440 | 0.011318 |
| Four of a kind | 390,960 | 0.000505 |
| Straight flush | 44,354,840 | 0.057259 |
| Royal flush | 596,856 | 0.000770 |
| Total | 774,635,400 | 1.000000 |
Table 10 shows the number of combinations for each hand of a second player, given that the first player has a royal flush.
Table 10 — First Player has a Royal Flush
| Event | Pays | Probability |
|---|---|---|
| Less than pair | 10,532,592 | 0.117164 |
| Pair | 25,380,864 | 0.282336 |
| Two pair | 12,673,584 | 0.140981 |
| Three of a kind | 2,304,216 | 0.025632 |
| Straight | 9,485,064 | 0.105512 |
| Flush | 23,604,264 | 0.262573 |
| Full house | 993,600 | 0.011053 |
| Four of a kind | 44,160 | 0.000491 |
| Straight flush | 596,856 | 0.006639 |
| Royal flush | 4,280,760 | 0.047619 |
| Total | 89,895,960 | 1.000000 |
Poker Hand Probability Table Example
The following table shows the number of combinations for each hand of player 1 by the winner of the hand.
Table 11 — Winning Player by Hand of Player 1 — Combinations
| Player 1 | Win | Tie | Loss | |
|---|---|---|---|---|
| Less than pair | 76,626,795,600 | 11,681,317,560 | 395,983,710,240 | 484,291,823,400 |
| Pair | 496,857,988,764 | 38,757,694,752 | 683,256,278,484 | 1,218,871,962,000 |
| Two pair | 419,896,266,012 | 34,054,545,168 | 199,549,574,820 | 653,500,386,000 |
| Three of a kind | 97,664,829,948 | 4,647,370,128 | 32,024,879,724 | 134,337,079,800 |
| Straight | 103,685,076,072 | 15,662,001,240 | 9,135,538,488 | 128,482,615,800 |
| Flush | 71,523,195,288 | 2,910,219,176 | 9,717,104,296 | 84,150,518,760 |
| Full house | 62,810,500,464 | 5,179,382,208 | 4,217,612,688 | 72,207,495,360 |
| Four of a kind | 4,240,864,800 | 198,204,864 | 235,520,256 | 4,674,589,920 |
| Straight flush | 734,237,144 | 35,247,960 | 5,150,296 | 774,635,400 |
| Royal flush | 85,615,200 | 4,280,760 | - | 89,895,960 |
| Total | 1,334,125,369,292 | 113,130,263,816 | 1,334,125,369,292 | 2,781,381,002,400 |
The following table shows the probability for each hand of player 1 by the winner of the hand. The bottom row shows that each player has a 47.97% chance of winning and a 4.07% chance of a tie.
Table 12 — Winning Player by Hand of Player 1 — Probabilities
| Player 1 Hand | Player 1 | Tie | Player 2 | Total |
|---|---|---|---|---|
| Less than pair | 0.027550 | 0.004200 | 0.142369 | 0.174119 |
| Pair | 0.178637 | 0.013935 | 0.245654 | 0.438225 |
| Two pair | 0.150967 | 0.012244 | 0.071745 | 0.234955 |
| Three of a kind | 0.035114 | 0.001671 | 0.011514 | 0.048299 |
| Straight | 0.037278 | 0.005631 | 0.003285 | 0.046194 |
| Flush | 0.025715 | 0.001046 | 0.003494 | 0.030255 |
| Full house | 0.022582 | 0.001862 | 0.001516 | 0.025961 |
| Four of a kind | 0.001525 | 0.000071 | 0.000085 | 0.001681 |
| Straight flush | 0.000264 | 0.000013 | 0.000002 | 0.000279 |
| Royal flush | 0.000031 | 0.000002 | 0.000000 | 0.000032 |
| Total | 0.479663 | 0.040674 | 0.479663 | 1.000000 |