Texas Hold'em Poker Probability/Statistics for Single Hand Pocket Cards
In this section we will be demonstating the possible outcomes for pocket card hands in Texas Hold'Em. We will run through the various possible scenarios the player may have.
Scenario 1
In this scenario we will be examining the best hand in Hold'Em.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Straight Flush | 0.0044% | 0.0001% | 0.0002% | 0.0002% | 0.0002% | 0.0051% | 0.0102% | 0.0102% |
| Four of a Kind | 0.8163% | 0.0022% | 0.0022% | 0.0022% | 0.0022% | 0.0174% | 0.8424% | 0.8526% |
| Full House | 6.4045% | 0.1786% | 0.1786% | 0.1786% | 0.1786% | 1.4288% | 8.5476% | 9.4002% |
| Flush | 1.8876% | 0.0311% | 0.0197% | 0.0118% | 0.0065% | 0.0049% | 1.9616% | 11.3618% |
| Straight | 0.469% | 0% | 0.0467% | 0.0467% | 0.0467% | 0.6092% | 1.2184% | 12.5803% |
| Three of a Kind | 11.7738% | 0% | 0% | 0% | 0% | 0% | 11.7738% | 24.3541% |
| Two Pairs | 39.6674% | 0% | 0% | 0% | 0% | 0% | 39.6674% | 64.0214% |
| Single Pair | 35.9786% | 0% | 0% | 0% | 0% | 0% | 35.9786% | 100% |
| High Card | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main points of interest in this scenario are:
1. Almost a 1 in 3 chance of having just a pair of aces at the end.
2. Almost a 1 in 4 chance of having three of a kind or better.
3. Almost a 1 in 10 chance of having a full house or better.
4. Less than 1% chance of having a four of a kind.
Scenario 2
In this scenario we will be examining a pocket pair of Jacks.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Straight Flush | 0.0044% | 0.0043% | 0.0043% | 0.0043% | 0.0001% | 0.0009% | 0.0185% | 0.0185% |
| Four of a Kind | 0.0022% | 0.0022% | 0.0022% | 0.8163% | 0.0022% | 0.0174% | 0.8424% | 0.8609% |
| Full House | 0.1952% | 0.1952% | 0.1952% | 6.3547% | 0.1786% | 1.4288% | 8.5476% | 9.4085% |
| Flush | 0.6649% | 0.477% | 0.3288% | 0.4712% | 0.0065% | 0.0049% | 1.9533% | 11.3618% |
| Straight | 0.469% | 0.4223% | 0.4223% | 0.4223% | 0% | 0.2336% | 1.9696% | 13.3315% |
| Three of a Kind | 0% | 0% | 0% | 11.726% | 0% | 0% | 11.726% | 25.0575% |
| Two Pairs | 3.6735% | 3.5877% | 3.5019% | 28.7616% | 0% | 0% | 39.5246% | 64.5821% |
| Single Pair | 0% | 0% | 0% | 35.4179% | 0% | 0% | 35.4179% | 100% |
| High Card | 0% | 0% | 0% | 0% | 0% | 0% | 0% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main point of interest in this scenario is:
1. Probabilties very similar to 2 Aces except tilted towards the Jack.
Scenario 3
In this scenario we will be examining a pocket Ace and King off-suit.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Straight Flush | 0.0044% | 0.0022% | 0.0001% | 0.0002% | 0.0002% | 0.003% | 0.0102% | 0.0102% |
| Four of a Kind | 0.051% | 0.051% | 0.0022% | 0.0022% | 0.0022% | 0.0174% | 0.1259% | 0.1361% |
| Full House | 0.8006% | 0.7819% | 0.0583% | 0.0583% | 0.0583% | 0.4667% | 2.2241% | 2.3602% |
| Flush | 1.2764% | 0.6423% | 0.0197% | 0.0118% | 0.0065% | 0.0049% | 1.9616% | 4.3219% |
| Straight | 2.599% | 0% | 0% | 0.0467% | 0.0467% | 0.6092% | 3.3016% | 7.6235% |
| Three of a Kind | 1.4707% | 1.4707% | 0.1329% | 0.1329% | 0.1329% | 1.0874% | 4.4275% | 12.051% |
| Two Pairs | 12.4163% | 6.8984% | 0.5981% | 0.5437% | 0.4893% | 1.7127% | 22.6585% | 34.7095% |
| Single Pair | 11.3325% | 11.3325% | 1.9981% | 1.9981% | 1.9981% | 16.9129% | 45.5723% | 80.2819% |
| High Card | 19.7181% | 0% | 0% | 0% | 0% | 0% | 19.7181% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main points of interest in this scenario are:
1. Just a 1 in 5 chance of ending on a high card (which has to be an Ace).
2. A 45.6% chance of ending with a single pair.
3. Just over a 1 in 3 chance of ending with a hand better than a single pair.
Scenario 4
This is the same scenario as above except with same-suit cards.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Straight Flush | 0.0512% | 0.0001% | 0.0001% | 0.0002% | 0.0002% | 0.003% | 0.0548% | 0.0548% |
| Four of a Kind | 0.051% | 0.051% | 0.0022% | 0.0022% | 0.0022% | 0.0174% | 0.1259% | 0.1808% |
| Full House | 0.8006% | 0.7819% | 0.0583% | 0.0583% | 0.0583% | 0.4667% | 2.2241% | 2.4049% |
| Flush | 6.4162% | 0.0466% | 0.0296% | 0.0177% | 0.0098% | 0.0074% | 6.5272% | 8.9321% |
| Straight | 2.4388% | 0% | 0% | 0.0432% | 0.0432% | 0.5667% | 3.0918% | 12.0239% |
| Three of a Kind | 1.4629% | 1.4629% | 0.1267% | 0.1267% | 0.1267% | 1.0365% | 4.3424% | 16.3663% |
| Two Pairs | 12.246% | 6.759% | 0.5607% | 0.5097% | 0.4588% | 1.6057% | 22.1399% | 38.5062% |
| Single Pair | 10.9992% | 10.9992% | 1.8554% | 1.8554% | 1.8554% | 15.7048% | 43.2695% | 81.7757% |
| High Card | 18.2243% | 0% | 0% | 0% | 0% | 0% | 18.2243% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main point of interest in this scenario is:
1. A better chance of obtaining a flush compared to the off-suit cards, there is now a 6.5% chance.
Scenario 5
In this scenario we will examine a matching pair lower down in the deck.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Straight Flush | 0.0023% | 0.049% | 0.049% | 0.049% | 0.049% | 0.0008% | 0.1991% | 0.1991% |
| Four of a Kind | 0.0022% | 0.0022% | 0.0022% | 0.0022% | 0.051% | 0.0662% | 0.1259% | 0.325% |
| Full House | 0.0595% | 0.0595% | 0.0595% | 0.0595% | 0.7983% | 1.188% | 2.2241% | 2.5492% |
| Flush | 1.8658% | 1.4132% | 1.0665% | 0.7736% | 1.2565% | 0.0074% | 6.3829% | 8.9321% |
| Straight | 0.4371% | 2.0017% | 2.0017% | 2.0017% | 2.0017% | 0.1296% | 8.5734% | 17.5055% |
| Three of a Kind | 0.1296% | 0.1267% | 0.1238% | 0.1209% | 1.4362% | 2.3258% | 4.2629% | 21.7684% |
| Two Pairs | 1.9625% | 1.8558% | 1.7556% | 1.6617% | 9.1753% | 5.3547% | 21.7657% | 43.5341% |
| Single Pair | 1.9217% | 1.8223% | 1.7229% | 1.6235% | 10.3139% | 23.1693% | 40.5735% | 84.1077% |
| High Card | 7.9462% | 4.1026% | 2.2025% | 1.0796% | 0.5614% | 0% | 15.8923% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main points of interest in this scenario are:
1. A slighly higher chance of getting a decent hand as the scenario above except with lower value cards.
2. A greater chance of obtaining a straight.
From this, the previous scenario and the mathimatical probabilites in cards we can ascertain that there is approximately a 1.5% chance of obtaining a flush in any pocket hand which is off suit and there is
approximately a 6.5% to 7% of obtaining a flush when the pocket cards are of a matching suit.
Scenario 6
In this scenario we will examine pocket cards which are spaced out but still able to make a straight.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Straight Flush | 0.0044% | 0.0043% | 0.0022% | 0.0023% | 0.0023% | 0.0009% | 0.0164% | 0.0164% |
| Four of a Kind | 0.0022% | 0.051% | 0.0022% | 0.0022% | 0.051% | 0.0174% | 0.1259% | 0.1423% |
| Full House | 0.0595% | 0.8% | 0.0589% | 0.0589% | 0.7802% | 0.4667% | 2.2241% | 2.3665% |
| Flush | 0.665% | 0.8652% | 0.1742% | 0.1135% | 0.1326% | 0.0049% | 1.9554% | 4.3219% |
| Straight | 2.599% | 2.1299% | 0% | 0.4223% | 0.4223% | 0.1869% | 5.7604% | 10.0823% |
| Three of a Kind | 0.1329% | 1.4617% | 0.1299% | 0.1299% | 1.4617% | 1.0844% | 4.4005% | 14.4828% |
| Two Pairs | 1.9857% | 11.6044% | 1.1544% | 1.1017% | 4.9717% | 1.7127% | 22.5306% | 37.0134% |
| Single Pair | 1.9981% | 11.05% | 1.8733% | 1.8554% | 11.05% | 16.6096% | 44.4366% | 81.45% |
| High Card | 8.3639% | 10.1861% | 0% | 0% | 0% | 0% | 18.55% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main points of interest in this scenario are:
1. There is a drop in the chance of obtaining a straight.
2. As expected, there is a drop in the probability of a flush.
Scenario 7
In this scenario we will examine pocket cards which are spaced out far enough that it isn't possible for both cards to be used in a straight.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Straight Flush | 0.0023% | 0.0023% | 0.0023% | 0.0022% | 0.0023% | 0.0071% | 0.0185% | 0.0185% |
| Four of a Kind | 0.0022% | 0.0022% | 0.051% | 0.0022% | 0.0022% | 0.0662% | 0.1259% | 0.1444% |
| Full House | 0.0595% | 0.0595% | 0.7994% | 0.0589% | 0.0589% | 1.188% | 2.2241% | 2.3685% |
| Flush | 0.6669% | 0.4789% | 0.5623% | 0.1134% | 0.0689% | 0.063% | 1.9534% | 4.3219% |
| Straight | 0.469% | 0.4223% | 0.4223% | 0% | 0.4223% | 1.3137% | 3.0497% | 7.3716% |
| Three of a Kind | 0.1359% | 0.1359% | 1.4796% | 0.1359% | 0.1359% | 2.4311% | 4.4545% | 11.8261% |
| Two Pairs | 2.0262% | 1.9548% | 10.9721% | 1.1354% | 1.0692% | 5.6287% | 22.7864% | 34.6125% |
| Single Pair | 2.123% | 2.1052% | 11.4031% | 2.0874% | 2.0695% | 26.0681% | 45.8563% | 80.4688% |
| High Card | 9.2049% | 5.4202% | 4.9062% | 0% | 0% | 0% | 19.5312% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main point of interest in this scenario is:
1. The probability of a straight takes a hit compared to the previous scenario while the other probabilities remain roughly the same.
Scenario 8
For interest sake, in this scenario we will examine the worst pocket cards in Hold'Em.
| Hand Name | Ace | King | Queen | Jack | 10 | Other | Total | Accum. |
| Four of a Kind | 0.0022% | 0.0022% | 0.0022% | 0.0022% | 0.0022% | 0.1151% | 0.1259% | 0.1423% |
| Full House | 0.0595% | 0.0595% | 0.0595% | 0.0595% | 0.0595% | 1.9268% | 2.2241% | 2.3664% |
| Flush | 0.667% | 0.4809% | 0.3326% | 0.217% | 0.1332% | 0.1247% | 1.9554% | 4.3219% |
| Straight | 0.0467% | 0.0467% | 0.0467% | 0.4223% | 0.4223% | 1.6893% | 2.6741% | 6.996% |
| Three of a Kind | 0.1359% | 0.1359% | 0.1359% | 0.1359% | 0.1359% | 3.7748% | 4.4545% | 11.4505% |
| Two Pairs | 2.0262% | 1.9548% | 1.8835% | 1.8121% | 1.7407% | 13.3691% | 22.7864% | 34.2369% |
| Single Pair | 2.123% | 2.1409% | 2.1409% | 2.123% | 2.1052% | 35.3652% | 45.9982% | 80.2351% |
| High Card | 9.2516% | 5.6071% | 3.0372% | 1.3083% | 0.4673% | 0.0935% | 19.7649% | 100% |
Total Possibilities |
2118760 | | | | | | | |
The main point of interest in this scenario is:
1. The probability of getting anything good is small.
You may now like to continue to the after the flop or after the turn scenarios:
After the Flop Scenarios
After the Turn Scenarios
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