Texas Holdem Probability
In Texas Holdem poker, it’s essential to understand the probabilities of the most common situations. This knowledge can help you make positive decisions under some difficult circumstances. The probability of many events in Texas Holdem can be determined by direct calculation. This article will show you one simple method to compute the probabilities for many commonly occurring events in the game of Texas Holdem and provides some probabilities for specific situations. In most cases, the Texas Holdem probabilities are approximations due to rounding.
Below are two simple and easy methods to estimate your equity on the Flop and/or Turn. They work best when you deal with small numbers of outs. Also note that Multiples of 2 are generally more accurate than Multiples of 4; however, both give very good estimates.
Multiples of 4 – To approximate the equity you have on the Flop, multiply your number of outs by 4.
Example: You have an open-ended straight draw on the Flop. That’s 8 outs, so 8 x 4 = 32 percent to win by the River. The actual number is 31.5 percent (This is if you get to see both the Turn and River cards).
Multiples of 2 – To approximate your equity on the Turn, multiply your number of outs by 2.
Example: You have an open-ended straight draw on the Turn. That’s 8 outs, so 8 x 2 = 16 percent to win by the River. The actual number is 17.4 percent.
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Probabilities for Texas Holdem Poker
The following tables are the probabilities of the most common situations in Texas Holdem Poker.
1. The probabilities of improving the hand after the Flop and the Turn with respect to the number of outs.
| Number of Outs | After the Flop 2 Cards to Come |
After the Turn 1 Card to Come |
| 1 | 4.3 | 2.2 |
| 2 | 8.4 | 4.2 |
| 3 | 12.5 | 6.5 |
| 4 | 16.51 | 8.7 |
| 5 | 20.3 | 10.9 |
| 6 | 24.1 | 13.0 |
| 7 | 27.8 | 15.2 |
| 8 | 31.52 | 17.4 |
| 9 | 35.03 | 19.6 |
| 10 | 38.4 | 21.7 |
| 11 | 41.7 | 24.0 |
| 12 | 45.0 | 26.1 |
| 13 | 48.1 | 28.3 |
| 14 | 51.2 | 30.4 |
| 15 | 54.14 | 32.6 |
| 16 | 57.0 | 34.3 |
| 17 | 59.8 | 37.0 |
| 18 | 62.4 | 39.1 |
| 19 | 65.0 | 41.3 |
| 20 | 67.5 | 43.5 |
1 Two pair or gut-shot draw
2 Straight draw
3 Flush draw
4 Straight flush draw
2. The number of outs and probabilities of the most common situations.
| Number of Outs | Drawing Hand | After the Flop 2 Cards to Come |
After the Turn 1 Card to Come |
| 4 | Two pair needing a full house; an inside straight draw | 16.5 | 8.7 |
| 6 | Two overcards needing to make a pair | 24.1 | 13.0 |
| 8 | Open-ended straight draw | 31.5 | 17.4 |
| 9 | Flush draw | 35.0 | 19.6 |
| 11 | Flush draw plus a pair needing to improve to trips | 41.7 | 24.0 |
| 12 | Flush draw plus an inside straight draw | 45.0 | 26.1 |
| 15 | Flush draw plus open-ended straight draw | 54.1 | 32.6 |
3. The probabilities of your Pre-Flop cards.
| Pocket Cards: | Percentage (%) |
| AA | 0.45 |
| Any pair | 5.9 |
| AK suited | 0.30 |
| AK off suit | 0.90 |
| At least one ace | 14.9 |
| Any two cards suited | 23.5 |
4. The probabilities of improving your hand on the Flop.
| Your Hold | Flop Gives You | Percentage (%) |
| Pocket pair | Three of a kind | 9.0 |
| Pocket pair | Four of a kind | 0.24 |
| Pocket pair | Full house | 0.73 |
| Any two unpaired cards | Two pairs | 2.0 |
| Any two unpaired cards | A pair | 32.4 |
| Two suited cards | Flush | 0.84 |
| Two suited cards | Four cards to a flush | 10.9 |
| Any two unsuited cards | Four cards to a flush | 1.12 |
| Two connected off suit cards (4,5 to T,J) | Straight | 1.31 |
5. The probabilities of improving your hand on the Turn.
| You Have | Turn Gives You | Percentage (%) |
| Four cards to a flush | Flush | 19.1 |
| Open ended four card straight | Straight | 17.0 |
| Gut shot straight draw | Straight | 8.5 |
| Three of a kind | Four of a kind | 2.1 |
| Two pair | Full house | 8.5 |
| A pair | Three of a kind | 4.3 |
| Nothing | A pair with a pocket card | 12.8 |
6. The probabilities of improving your hand on the River.
| You Have | River Gives You | Percentage (%) |
| Four cards to a flush | Flush | 19.6 |
| Open ended four card straight | Straight | 17.4 |
| Gut shot straight draw | Straight | 8.7 |
| Three of a kind | Four of a kind | 2.2 |
| Two pair | Full house | 8.7 |
| A pair | Three of a kind | 4.3 |
| Nothing | A pair with a pocket card | 13.0 |
7. The probabilities of improving your hand from the Flop to the River.
| You Have | Turn or River Gives You | Percentage (%) |
| Four cards to a flush | Flush | 35.0 |
| Three cards to a flush | Flush | 4.2 |
| Open ended four card straight | Straight | 32.0 |
| Gut shot straight draw | Straight | 17.0 |
| Three of a kind | Four of a kind | 4.3 |
| Two pair | Full house | 17.0 |
| A pair | Four of a kind | 0.09 |
| A pair | Three of a kind | 8.4 |
8. The probabilities of the Table Flop.
| The Table Flops | Percentage (%) |
| Three of a kind | 0.24 |
| A pair | 17.0 |
| Three suited cards | 5.2 |
| Two suited cards | 55.0 |
| No suited cards | 40.0 |
| Three cards to a straight | 3.5 |
| Two cards to a straight | 40.0 |
| No straight cards | 56.0 |
