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Texas Hold’em Poker Hand Probabilities

December 30, 2009

I have searched around the net and some of the poker books that i have read for some good statistics on probabilities of hitting some big hands. Although it is all mathematics to most, it is this very jargon that can separate the losers from the winners.

Flush Probabilities

Probability of being dealt suited cards 23.5%
Probability of flopping a flush when holding two suited cards 0.8%
Probability of flopping a flush draw when holding two suited cards 10.9%
Probability of hitting a flush draw (both turn/river, needing one card to hit) 35%

Straight Probabilities

Probability of hitting an open-ended straight draw (i.e. 4 straight cards, need one on either end to hit on turn or river) 31.5%
Probability of hitting a gutshot draw (inside straight draw) on turn or river 16.5%

Pocket Pair Probabilities

Probability of being dealt a pocket pair 5.9%
Probability of hitting a three of a kind or quads at the flop when you hold a pocket pair 11.8%
Probability of being dealt AA 0.45%

Unpaired Hole Cards Probabilities

Probability of making a pair with one of your hole cards (example: hitting an ace or a king if you hold AK) 32.4%
Probability of hitting two pair on the flop with each of your hole cards (example: hitting both an ace and a king on the flop, when holding AK) 2%

Ace Probabilities

Probability that at least one of your hole cards is an ace 14.9%

Probability of no one holding an ace, assuming you do not have an ace. Note: this can be used for any card (because the chances of you being dealt an ace or a king is exactly the same).

# Players Probability
2 84.5%
3 70.9%
4 59%
5 48.6%
6 39.7%
7 32.1%
8 25.6%
9 20.1%
10 15.6%

Probability someone else does not have an ace, assuming you do have an ace, by total number of players:

# Players Probability
2 88.2%
3 77.5%
4 67.6%
5 58.6%
6 50.4%
7 43%
8 36.4%
9 30.5%
10 25.3%

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Mathematic Skills Know your percentages in most common situations. For instance, if you are dealt a pocket pair, that the most common percentage of hitting a set will be 1 to 8. Get to know your common percentages and gain an edge over novices. Get to know how outs work and what your outs are in any hand.  Outs imply then number of cards that will help the best hand. Count your outs, multiply the outs by two,  add one, and that's roughly the percentage you have at hitting. If you dont have a basic understanding of the above pronciples then rather dont play high stakes poker. Understand Reward vs. Skill The best poker players in the world  will understand that they need to be more risk-averse with their overall bankroll than their stack at the table. When you play a poker game,  value every chip equally at the table. You should only care about making correct plays. But play within your bankroll but play with calculated risks outside the poker room. Discipline and Patience Good poker players demand an advantage. What separates a winning poker player from a fish is that a fish does not expect to win, while a poker player does. A disciplined player knows when to play and when to quit. Recognize when you are on tilt. Game awareness and picking your moment to move in is key to success in poker. Psychological Fitness Understand your opponents and play according to what they may be thinking buy taking factors into account ie. stack size, betting patterns, position and tells etc. The poker pro always tries to have an answer to these questions: What does my opponent have? What does my opponent think I have? What does my opponent think that I think he has? Master this skill and start manipulating the tables but remember to have respect for all poker players. Enjoy the Game If you get to a stage where playing poker is more of a chore than fun...then stop playing. Take a break until the hunger returns.