Probabilities in poker

 Poker probabilities

​If you play poker for a long time, you might notice sometimes the hands at the tables which seem to be far from reality and not being defined by the mathematical laws. In this article, we will tell you about various kinds of poker probabilities in details, so you can consider this article as guide of poker odds for dummies. 

The probability theory plays a huge role in poker. Poker is a game based on odds, probabilities and math. Neglecting poker math and not knowing it will eventually lead any luckless player to a financial crash. In a short period of time the luck can play an important role but the longer you play the more important poker mathematical probabilities become.

In most cases, you can determine your basic poker odds using basic arithmetic as well as using special poker calculators and supplementary programs. Understanding the poker probabilities will allow you to beat the players who blindly hope for luck more often.

Players don't play poker "in a vacuum", each player must proceed from his opponent's range and calculate his winning odds only against the particular opponent. In the table below we'll give you the winning probabilities versus different ranges of hands.

Probabilities of the certain preflop situations

HeroOpponentWinning probabilities
High pair (JJ, QQ, KK, AA)Two weak cards (76, 98, etc.)83%
High pairSmall pair (22 – 66)82%
Medium pair (7 7–10 10)High card with a small kicker (A 2 – A 6)71%
Two high cards (KQ, AJ, AQ, AK)Two small cards (10 9, 9 8)63%

Now let's look at the probability of various events occurring when playing different starting hands.

Hitting one pair on the flop32%2 to 1
Two suited cards will form a flush6,50%15 to 1
Two suited cards will hit a flush on the flop 0,85%118 to1
Odds of flopping a set with a pair12%8 to 1
Odds of flopping quads with a pair0,25%400 to 1

The novice players often overestimate the value of starting hands, for instance, suited cards. As you can see, suited cards don't form the flush often enough. Also, the pocket pairs hit a set only in 12% of cases, therefore it's not always profitable to play small pocket cards.

In this part of the article, we will tell you about the mathematical probabilities for forming various poker combinations. Get acquainted with poker odds table in order to be a winning player. 

Royal Flush1 to 649 740
Straight flush1 to 72 192
Quads 1 to 4 165
Full house1 to 694
Flush1 to 508
Straight1 to 254
Set1 to 46
Two pairs1 to 20
Pair1 to 1,4

As you can see royal flush is the rarest and the strongest poker combination. The probability of collecting royal flush in poker is 1 to 649 740. The odd to catch this combination on the flop with pocket broadway cards is equal to 0.0008%. If there is a potential royal flush on the board, the probability that it will be collected on the turn is 2%, and till the river  4%.

A cooler is a situation at the poker table when a player loses the hand not because of his own mistakes but because of an unfortunate coincidence of circumstances and a stronger opponent's hand. This is a classic poker term that professional poker players use in their lexicon.

Kings versus Aces

With Aces, you have nothing to fear before the flop but if you got pocket Kings, you can always be afraid of opponents' Aces. But do such coolers occur often enough? If you play heads-up, the odds of pocket aces for your opponent will be be equal to only 1 time out of 220 hands. But at a full-ring table facing 8 opponents the odds of someone getting Aces versus your pocket Kings are much higher. The probability of this event is 1 to 25.

Queens versus Kings (Aces)

Queens are a much more vulnerable hand than Kings. More often you will be ahead with them on the preflop but don't reject the probability that one of your opponents received Kings or Aces. At the full table the probability of this event is 1 to 12. Raise, re-raise and all-in before you – all these actions indicate that one of your opponents has got a monster and you had better muck your Queens.

Important probabilities for high pocket pairs

Getting pocket Aces on the flop0,4525%1 to 220
Heads-up. Both you and your opponent have pocket Aces0,0816%1 to 1 224
Full-ring. You and one of your opponents have pocket Aces0,6512%1 to 153
Heads-up. Getting pocket Kings versus Aces0,4898%1 to 203
Full-ring. Getting pocket Kings versus Aces3,8518%1 to 25
Heads-up. Getting pocket Queens versus Kings or Aces0,9796%1 to 101
Full-ring. Getting pocket Queens versus Kings or Aces7, 5732%1 to 12

The probability of getting a set versus the set

Now let's talk about postflop cooler situations. As you already know, the odds of flopping a set with a pocket pair is equal to 12% or 1 to 8. But an event, that many poker players are afraid of, is getting a set on the flop against the stronger set. If two players have a pocket pair, then the situation where both players make the set on the flop will occur once per 100 flops.

The probability of getting quads versus the quads

Let's move from the set to an even more powerful combination. The probability of collecting quads when you have a pocket pair and a set on the flop is 1 to 123.

If the probability of getting a set against the set is not too high, then the probability of a situation where two players will collect quads in one hand is 1 to 39,000 in heads-up and 1 to 313,000 at the full table. For most poker players this event will occur only once in their entire career.

Confident knowledge of poker odds and probabilities will help you to remodel your strategy and tactic profitably during the game, and the very understanding of mathematical principles will give you emotional stability to play your best game.

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I’ve been working in the Cardmates team since 2018. Started playing poker the same way most people usually do – socially, with friends and fellow students. I adored those exciting poker nights but never thought my life would be connected with this game, even tangentially.
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