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Strategy: Others

Probabilities in Texas Hold'em

by Indy1701e

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Introduction

An understanding of basic probabilities will give your poker game a stronger foundation, for all game types. This article discusses all the important, and interesting, probabilities that you should be aware of.

Probabilities in poker

Probability means the degree of certainty that a possible event will occur. The classic definition is: "The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible." The probability of flipping heads in a coin toss is therefore 1 to 2, or 50%.

For poker players, stochastics is the most interesting part of studying probability. Stochatics deals with frequence-based probabilities. Combinatorics (card combinations), statistics (sample size) and other subdisciplines are all a part of stochastics.

Probabilities are always a number between 0 and 1 and are usually expressed as a percentage. Probability can also be given as odds, which tells how often one event will occur in relation to the number of times another event will take place (1:2).

In the following sections you will get an overview of many useful probabilities that will help you improve your game. You can see the calculations used to arrive at these results on the second page of this article.
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Article Contents

  • page 1
    • Introduction
    • Probabilities in poker
    • Probability of being dealt a given starting hand
    • Probability of facing a higher pocket pair when you have a pocket pair
    • Probability of facing more than one higher pocket pair when you have a pocket pair
    • Probability of facing a better A when you have an Ax hand
    • Probability that no overcard will show up on the flop
    • Probability of making a specific hand (5 out of 52)
    • Probability of making a specific hand (7 out of 52)
    • Probability of improving on the flop
    • Probability of improving on the turn
    • Probability of improving on the river
    • Probability of improving from flop to river
    • Probability of seeing a specific board on the flop
  • page 2
    • Deriving the probabilities
    • 1. Probability of being dealt a specific starting hand
    • 2. Probability of facing a higher pocket pair when you have a pocket pair
    • 3. Probability of facing several higher pocket pairs
    • 4. Probability of facing a better A
    • 5. Probability that no overcard will come when you have a pocket pair
    • 6. Probability of being dealt a specific hand
    • 7. Probability of improving on the flop
    • 8. Probability of improving on the turn
    • 9. Probability of improving on the river
    • 10. Probability of improving from flop to river
    • 11. Probability of seeing a specific flop
    • Note

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