Poker Probabilities

Here are some basic probabilities that you should know:

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, by the number of opponents. Note: this can be used for any card (because the chances of you being dealt an ace or a king is exactly the same).:
  1. 84.5%
  2. 70.9%
  3. 59.0%
  4. 48.6%
  5. 39.7%
  6. 32.1%
  7. 25.6%
  8. 20.1%
  9. 15.6%
• Probability someone else does not have an ace, assuming you do have an ace, by total number of opponents:
  1. 88.2%
  2. 77.5%
  3. 67.7%
  4. 58.6%
  5. 50.4%
  6. 43.0%
  7. 36.4%
  8. 30.5%
  9. 25.3%