Poker Probability

Poker is very much a math and statistics-based game. While winning isn’t always guaranteed, playing a strategy that follows correct poker probability and odds will undoubtedly increase your chances. In this article, we will break down the odds of poker and the probabilities associated with the game:


Poker Hands Probability

There are 2,598,960 distinct 5-card hands that can be made/dealt with in poker. Let’s take a closer look at how these combinations break down into the various ranks of hands that one can get in this poker probability chart:

Poker Hand Frequency (Distinct Hands) Probability (%) Odds (~)
Royal Flush 4 0.000154% 1 in 649,740
Straight Flush 36 0.00139% 1 in 72,193
4-of-a-Kind 624 0.0240% 1 in 4,165
Full House 3,744 0.1441% 1 in 694
Flush 5,108 0.1965% 1 in 509
Straight 10,200 0.3925% 1 in 255
3-of-a-Kind 54,912 2.1128% 1 in 47
Two Pair 123,552 4.7539% 1 in 21
One Pair 1,098,240 42.2569% 1 in 2.4
High Card 1,302, 540 50.1177% 1 in 2

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Common Odds & Probabilities in a Poker Game

The most common odds in a poker game are:

  • Odds of being dealt certain hole cards
  • Odds of flopping a made hand

Odds of Being Dealt Certain Hole Cards in Poker

If you take a hand like AK, you can multiply the 4 Aces by 4 Kings to see that there are 16 combinations of AK total, both suited and unsuited for example. Of these 16 combos, as there are 4 suits in poker, 4 of these AK combinations will be suited, leaving there to be 12 unsuited combinations of unpaired hands. (The same figures go for any non-paired poker hands). For pocket pairs, there will be 6 combinations of each value. Knowing the above information, we can then do some basic math to determine the likelihood of getting certain combinations of hole cards. For example, for Pocket Aces, we would divide 6 combinations by 1,326 total combinations to see that we’ll receive this hand every 1 in 221 hands, on average. For any specifically suited hand, because there are only 4 combos of each holding (instead of 6 like with the pocket pairs), you’ll receive suited non-paired hands (of specific values) less frequently than you will pocket pairs. Therefore, on average, you’ll be dealt a hand like AKs, specifically every 1 in 332 hands, meaning you’ll be dealt AA more frequently than you will AKs.

The Odds of Flopping a Made Hand

The above section dealt with the likelihood of getting certain combinations of hole cards. But what about poker odds on how those hole cards will improve (and to what degree) on specific flops? Here’s a chart of various poker hole card probabilities to sift through and get accustomed to regarding the chances of flopping a made hand (of varying strengths):

Your Hole Cards Flop (Your Hand) Probability (%) Odds
Unpaired Cards A Pair 29.0% 1 in 3.5
Pocket Pair A Set 11.8% 1 in 8.5
Connected Cards (JT thru 54) A Straight 1.3% 1 in 77
Suited Connectors A Flush 0.8% 1 in 119

Calculating the Probability of Poker Hands

One critical thing to note in poker is the difference in terms of equity spread when there is only one opponent versus multiple opponents in a poker hand with you. Against many players, the equity of everyone’s respective hands is going to be lower than if it was a heads-up because it’ll be divided and spread out among the other remaining players. Take Pocket Aces, for example. Against the following Villain range for your opponent(s) –

  • Any pocket pair
  • Any suited Ace
  • Any two Broadway cards
  • Suited connectors: 54s to T9s
  • One-gapped suited connectors: 86s to J9s
  • Q9s, K9s

Here are the equity percentages that Pocket Aces has against:

  • One opponent: 83.4%
  • Two opponents: 70.6%
  • Three opponents: 60.2%
  • Four opponents: 51.4%

Poker Probability – A Summary

To increase the probability of winning poker, you must become accustomed to the odds and probabilities that are presented to you in the game. Become familiar with outs and calculating your percentages of improvement and be able to quickly relate these to the pot odds you may be getting so that you can determine if you can call profitably or not. Remember also that you don’t always need to “just call” whenever you have a draw. Sometimes, it can be advantageous to bet or raise. This way, you can either win by improving later on to the best hand or getting your opponent to fold.

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