Texas Holdem Straight Flush Probability
Playing poker is about playing the odds. The following list gives the odds for outcomes in Texas Hold’em hands. When you realize how heavily the odds are stacked against you, you may want to rethink going all-in before the flop with two suited cards. Use the odds to your advantage:
- Texas Holdem Straight Flush Probability Rules
- Texas Holdem Royal Flush Odds
- Texas Holdem Straight Flush Probability Calculator
- Ultimate Texas Holdem Royal Flush Odds
- Texas Holdem Straight Flush Probability Distribution
- Texas Holdem Straight Flush Probability Chart
Calculating the odds of a straight flush overall depends on the number of different combinations of three cards that provide a straight flush, so it’s important to know what your ‘outs’ are. Generally, the odds of forming a straight flush are 1 in 6,180,020, or 4.62%. 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.
1 percent (1-in-100): Percentage of time that no player holds an Ace or a King at a table in a 10-handed game
1 percent (1-in-100): Percentage of time that if you hold two suited cards, you’ll flop a flush
6 percent (about 1-in-20): Percentage of time that five community cards will give pocket suited cards a flush
6 percent (about 1-in-20): Percentage of time that you’ll be dealt a pocket pair
8 percent (about 1-in-12): Percentage of time that you’ll hit at least trips after having a pair on the flop
12 percent (about 1-in-8): Percentage of time that you’ll flop trips if holding a pocket pair
12 percent (about 1-in-8): Percentage of time that two more cards will flop in the same suit as a suited pocket pair
19 percent (about 1-in-5): Percentage of time that the five community cards will at least trip your pocket pair
32 percent (about 1-in-3): Percentage of time that you’ll pair one of your cards on the flop (with no pocket pair)
33 percent (about 1-in-3): Percentage of time that you’ll make a full house or better after having trips on the flop
35 percent (about 1-in-3): Percentage of time that you’ll make a flush on the turn or river if you have four cards to a flush after the flop
- 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.
- See also: sample space and event (probability theory). Straight flush — Each straight flush is uniquely determined by its highest ranking card; these ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits. For any particular suit where the straight flush is ace-high, the extra 2 cards may be chosen from the remaining 47 cards.
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
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
Texas Holdem Straight Flush Probability Rules
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 |
Texas Holdem Royal Flush Odds
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 |
Texas Holdem Straight Flush Probability Calculator
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 |
The following table shows the number of combinations for each hand of player 1 by the winner of the hand.
Ultimate Texas Holdem Royal Flush Odds
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
Texas Holdem Straight Flush Probability Distribution
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 |