Poker Hand Probability Table

Poker Hand Probability Table 9,0/10 1637 votes

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.

May 23, 2017 There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. Three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise. If you play poker for a long time, you might notice sometimes the hands at the tables which seem to be far from reality and not being defined by the mathematical laws. In this article we will tell you about various kinds of poker probabilities. The probability theory plays a huge role in poker. Poker is a game based on odds, probabilities and math.

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

EventPaysProbability
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

EventPaysProbability
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

Reference
EventPaysProbability
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

EventPaysProbability
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

EventPaysProbability
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

EventPaysProbability
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

See All Results For This Question


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

EventPaysProbability
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

EventPaysProbability
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

EventPaysProbability
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

Poker Hand Probability Table Calculator

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

Cached
EventPaysProbability
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

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 1WinTieLoss
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 HandPlayer 1TiePlayer 2Total
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

Written by: Michael Shackleford

The poker hand probability chart shows the odds of making a specific hand type by the showdown. It is valid for any 7-card poker variant, including Texas Holdem and 7 Card Stud.

The chart assumes that you have a random hole cards. Some hole cards (for example pocket pairs), are more likely to make a good hand by the river. This is why playing tight is such important in poker.

The cumulative odds column displays odds to make a particular hand or better. For example, the probability for making four of a kind or straight flush or royal flush is 0.0311%.

The total number of unique 7-card hands is 133,784,560. Suits have no relative value in poker, so by ignoring them the total number ot unique 7-card hands drops to 6,009,159.

Since in poker you can use only 5 cards out of 7 to make the best hand, there is a further reduction in possible combinations, making the total of 4,824 unique poker hands.

An interesting fact is that you are more likely to make a pair than a high card by the showdown in 7-card variants. This is a bit against the poker hand ranking, which was originally built with the assumption that the less frequent hand beats the more frequent one.

The ranking was correct for 5-card poker variants, which were dominant at the times the ranking was created. Maybe people that invented 7-card variants forgot to update the ranking, who knows?

Poker hand probability chart

HandOddsCumulative
Royal flush0.0032%0.0032%
Straight flush0.0279%0.0311%
Four of a kind0.168%0.199%
Full house2.60%2.80%
Flush3.03%5.82%
Straight4.62%10.4%
Three of a kind4.83%15.3%
Two pair23.5%38.8%
One pair43.8%82.6%
High card17.4%100%

More articles on poker probability:

Poker Probability - Wikipedia

Poker odds calculator
Poker outs and odds
Pot odds and expected value
Sklansky bucks
Implied odds
Reverse implied odds
Common preflop odds chart
Common flop odds chart
Pocket pairs - flopping overcards odds

See Full List On En.cardmates.net

Go back to the Online Poker Strategy.

Comments are closed.