Texas Hold'em Poker Probability/Statistics for Single Hand After the Flop
In this section we will be demonstrating the possible outcomes of a hand in Texas Hold'Em after the flop. We will run through the various possible scenarios the player may have.
Scenario 1
In this scenario we will be examining the possible outcomes when a player already has a pair.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Four of a Kind  0.0925%  0%  0%  0%  0%  0%  0.0925%  0.0925% 
Full House  1.6651%  0%  0%  0%  0%  0.8326%  2.4977%  2.5902% 
Flush  0%  0%  0%  0%  0%  0%  0%  2.5902% 
Straight  0%  0%  0%  0%  0%  1.4801%  1.4801%  4.0703% 
Three of a Kind  6.6605%  0%  0%  0%  0%  0%  6.6605%  10.7308% 
Two Pairs  37.4653%  0%  0%  0%  0%  0%  37.4653%  48.1961% 
Single Pair  51.8039%  0%  0%  0%  0%  0%  51.8039%  100% 
High Card  0%  0%  0%  0%  0%  0%  0%  100% 
Total Possibilities  1081        
The main points of interest in this scenario are:
1. Almost a 1 in 2 chance of having two pairs or better at the end.
2. About a 1 in 10 chance of having three of a kind or better.
3. Almost a 1 in 25 chance of having a full house.
Scenario 2
In this scenario we will be examining the possible outcomes when a player already has 3 of a kind.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Four of a Kind  4.2553%  0%  0%  0%  0%  0%  4.2553%  4.2553% 
Full House  29.1397%  0%  0%  0%  0%  0%  29.1397%  33.395% 
Flush  0%  0%  0%  0%  0%  0%  0%  33.395% 
Straight  0%  0%  0%  0%  0%  0%  0%  33.395% 
Three of a Kind  66.605%  0%  0%  0%  0%  0%  66.605%  100% 
Two Pairs  0%  0%  0%  0%  0%  0%  0%  100% 
Single Pair  0%  0%  0%  0%  0%  0%  0%  100% 
High Card  0%  0%  0%  0%  0%  0%  0%  100% 
Total Possibilities  1081        
The main points of interest in this scenario are:
1. There is a 4.3% chance of getting 4 of a kind.
2. There is about a 1 in 3 chance of getting a full house or better.
Scenario 3
In this scenario we already have two pairs, we will examine the chance of getting a full house.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Four of a Kind  0%  0.0925%  0%  0.0925%  0%  0%  0.185%  0.185% 
Full House  0%  8.3256%  0%  7.9556%  0%  0.2775%  16.5587%  16.7438% 
Flush  0%  0%  0%  0%  0%  0%  0%  16.7438% 
Straight  0%  0%  0%  0%  0%  0%  0%  16.7438% 
Three of a Kind  0%  0%  0%  0%  0%  0%  0%  16.7438% 
Two Pairs  0.555%  82.7012%  0%  0%  0%  0%  83.2562%  100% 
Single Pair  0%  0%  0%  0%  0%  0%  0%  100% 
High Card  0%  0%  0%  0%  0%  0%  0%  100% 
Total Possibilities  1081        
The main point of interest in this scenario is:
1. There is a 16.6% chance of getting a full house.
Scenario 4
This scenario is similar to the one above except this time we have a flush and straight possibility as well.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0.0925%  0.0925%  0%  0%  0%  0%  0.185%  0.185% 
Four of a Kind  0%  0.0925%  0%  0.0925%  0%  0%  0.185%  0.37% 
Full House  0%  8.3256%  0%  7.9556%  0.2775%  0%  16.5587%  16.9288% 
Flush  0.7401%  3.2377%  0%  0%  0%  0%  3.9778%  20.9066% 
Straight  1.3876%  1.3876%  0%  0%  0%  0%  2.7752%  23.6818% 
Three of a Kind  0%  0%  0%  0%  0%  0%  0%  23.6818% 
Two Pairs  0.555%  75.7632%  0%  0%  0%  0%  76.3182%  100% 
Single Pair  0%  0%  0%  0%  0%  0%  0%  100% 
High Card  0%  0%  0%  0%  0%  0%  0%  100% 
Total Possibilities  1081        
The main point of interest in this scenario is:
1. We have a 23.7% chance of improving our hand, compared to a 16.7% in the previous scenario.
Scenario 5
In this scenario we are waiting for a King to make a straight (we have an inside straight draw).
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Four of a Kind  0%  0%  0%  0%  0%  0%  0%  0% 
Full House  0%  0%  0%  0%  0%  0%  0%  0% 
Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Straight  16.4662%  0%  1.4801%  0%  0%  0%  17.9463%  17.9463% 
Three of a Kind  0.2775%  0%  0.2775%  0.2775%  0.2775%  0.2775%  1.3876%  19.334% 
Two Pairs  3.3302%  0%  2.4977%  1.6651%  0.8326%  0%  8.3256%  27.6596% 
Single Pair  7.7706%  0%  7.7706%  7.7706%  7.7706%  11.6559%  42.7382%  70.3978% 
High Card  29.6022%  0%  0%  0%  0%  0%  29.6022%  100% 
Total Possibilities  1081        
The main points of interest in this scenario are:
1. There is a 16.5% chance of getting the King we need, with another 1.5% chance of getting a 9 and a 8 to make a Queen high straight.
2. There is a 8.3% chance getting 2 pairs and a 5.8% chance of getting 2 pairs using at least one of our pocket cards.
3. There is a 42.7% chance getting a single pair and a 15.5% chance of getting a single pair using one of our pocket cards.
Scenario 6
In this scenario we are waiting for a Ace or 9 to make a straight (we have an open ended straight draw).
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Four of a Kind  0%  0%  0%  0%  0%  0%  0%  0% 
Full House  0%  0%  0%  0%  0%  0%  0%  0% 
Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Straight  16.4662%  14.9861%  0%  0%  0%  0%  31.4524%  31.4524% 
Three of a Kind  0%  0.2775%  0.2775%  0.2775%  0.2775%  0.2775%  1.3876%  32.84% 
Two Pairs  0%  3.3302%  2.4977%  1.6651%  0.8326%  0%  8.3256%  41.1656% 
Single Pair  0%  6.6605%  6.6605%  6.6605%  6.6605%  9.9907%  36.6327%  77.7983% 
High Card  0%  22.2017%  0%  0%  0%  0%  22.2017%  100% 
Total Possibilities  1081        
The main points of interest in this scenario are:
1. There is a 16.5% chance of getting the Ace we need to get an high straight, with another 15% chance of getting the 9 to make a King high straight.
2. Based on the point above, we have a 31.5% chance of making a straight.
Scenario 7
In this scenario we are waiting for a spade to make a flush.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Four of a Kind  0%  0%  0%  0%  0%  0%  0%  0% 
Full House  0%  0%  0%  0%  0%  0%  0%  0% 
Flush  34.9676%  0%  0%  0%  0%  0%  34.9676%  34.9676% 
Straight  0%  0%  0%  0%  0%  0.8326%  0.8326%  35.8002% 
Three of a Kind  0.2775%  0%  0%  0.2775%  0%  0.6475%  1.2026%  37.0028% 
Two Pairs  3.0527%  0%  0%  2.2202%  0%  1.9426%  7.2155%  44.2183% 
Single Pair  6.6605%  0.2775%  0.2775%  6.6605%  0.2775%  19.1489%  33.3025%  77.5208% 
High Card  22.4792%  0%  0%  0%  0%  0%  22.4792%  100% 
Total Possibilities  1081        
The main point of interest in this scenario is:
1. There is a little over a 1 in 3 chance of getting a flush.
Scenario 8
In this scenario we have a chance for a straightflush, flush and an inside straight draw.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  4.2553%  0%  0%  0%  0%  0%  4.2553%  4.2553% 
Four of a Kind  0%  0%  0%  0%  0%  0%  0%  4.2553% 
Full House  0%  0%  0%  0%  0%  0%  0%  4.2553% 
Flush  30.7123%  0%  0%  0%  0%  0%  30.7123%  34.9676% 
Straight  9.9907%  0%  0%  0%  0%  0%  9.9907%  44.9584% 
Three of a Kind  0.2775%  0.2775%  0%  0.2775%  0.2775%  0.0925%  1.2026%  46.161% 
Two Pairs  3.0527%  2.2202%  0%  1.3876%  0.555%  0%  7.2155%  53.3765% 
Single Pair  5.8279%  5.8279%  0%  5.8279%  5.8279%  5.8279%  29.1397%  82.5162% 
High Card  17.4838%  0%  0%  0%  0%  0%  17.4838%  100% 
Total Possibilities  1081        
The main points of interest in this scenario are:
1. There is a 4.3% chance of getting a straight flush.
2. There is a 30.7% chance of getting a flush.
3. There is a 10% chance of getting a straight.
4. There is a 45% chance of getting a straight or better.
Scenario 9
This scenario is similar to the one above except with a open ended straight draw.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  4.2553%  4.1628%  0%  0%  0%  0%  8.4181%  8.4181% 
Four of a Kind  0%  0%  0%  0%  0%  0%  0%  8.4181% 
Full House  0%  0%  0%  0%  0%  0%  0%  8.4181% 
Flush  0%  26.5495%  0%  0%  0%  0%  26.5495%  34.9676% 
Straight  9.9907%  9.1582%  0%  0%  0%  0%  19.1489%  54.1166% 
Three of a Kind  0%  0.2775%  0.2775%  0.2775%  0.2775%  0.0925%  1.2026%  55.3191% 
Two Pairs  0%  3.0527%  2.2202%  1.3876%  0.555%  0%  7.2155%  62.5347% 
Single Pair  0%  4.9954%  4.9954%  4.9954%  4.9954%  4.9954%  24.9769%  87.5116% 
High Card  0%  12.4884%  0%  0%  0%  0%  12.4884%  100% 
Total Possibilities  1081        
The main points of interest in this scenario are:
1. There is a 8.4% chance of getting a straight flush.
2. There is a 26.5% chance of getting a flush. This is lower than the previous scenario because of the greater probability of a straightflush.
3. There is a 19.1% chance of getting a straight.
4. There is a 54.1% chance of getting a straight or better. This is higher than previously because of the extra possibilites of a straight.
Scenario 10
In this scenario we basically have nothing going, there is just an outside chance of a straight.
Hand Name  Ace  King  Queen  Jack  10  Other  Total  Accum. 
Straight Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Four of a Kind  0%  0%  0%  0%  0%  0%  0%  0% 
Full House  0%  0%  0%  0%  0%  0%  0%  0% 
Flush  0%  0%  0%  0%  0%  0%  0%  0% 
Straight  0%  1.4801%  0%  0%  0%  0%  1.4801%  1.4801% 
Three of a Kind  0%  0.2775%  0%  0.2775%  0%  0.8326%  1.3876%  2.8677% 
Two Pairs  0%  3.3302%  0%  2.4977%  0%  2.4977%  8.3256%  11.1933% 
Single Pair  0.555%  8.8807%  0.555%  8.8807%  0.555%  29.4172%  48.8437%  60.037% 
High Card  10.3608%  29.6022%  0%  0%  0%  0%  39.963%  100% 
Total Possibilities  1081        
The main points of interest in this scenario are:
1. There is just a 11.2% chance of getting two pairs or higher.
2. There is just a 7.9% chance of getting two pairs or higher while using at least one of the pocket cards.
3. There is a 17.7% chance of getting a pair while using one of the pocket cards.
You may now like to continue to the after the turn scenarios:
After the Turn Scenarios
