Texas Holdem Straight Flush Probability
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.
8-to-1 12.00% Inside Straight 4 400-to-1 0.25% Overcards 6 118-to-1 0.85% Open-ended Straight 8 9-to-1 10.90% Four Flush 9 15-to-1 6.50% Straight & Flush Draw Straight / Flush or Better 15 Three of a Kind Hope to Make Full House Suited connectors Two suited cards flop a four flush (flush draw) Connected cards, 10 or better Any pair One or more Aces. The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739: 1. When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be.
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
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.
Texas Holdem Straight Flush Probability Chart
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.
Texas Holdem Straight Flush Probability Calculator
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 |
Texas Holdem Straight Flush Probability Rules
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
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 |
Ultimate Texas Holdem Royal Flush Odds
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
Texas Holdem Straight Flush Probability Distribution
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 |
Written by: Michael Shackleford