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

 

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