Poker Hand Probability Table

• Royal Flush
• Four Of A Kind
• Poker Hand Probability Table Worksheet
• Poker Hand Probability Table Example
• Probability Of Poker Hands

The poker hand probability chart shows the odds of making a specific hand type by the showdown. It is valid for any 7-card poker variant, including Texas Holdem and 7 Card Stud.

The probability of a player having Ay, where y is a rank such that x hand. The following table shows the probability that before the flop another player has an ace with a larger kicker in the hand. The following table lists, for each hand, the number and probability of a given hand. Five-Card Stud (Natural) Probabilities Hand Number Probability Straight Flush 2 40 0.00002 Four-of-a-Kind 624 0.00024 Full House 3744 0.00144 Flush 5108 0.00197 Straight 10,200 0.00393 Three-of-a-Kind 54,912 0.02113 Two Pair 123,552 0.04754.

The chart assumes that you have a random hole cards. Some hole cards (for example pocket pairs), are more likely to make a good hand by the river. This is why playing tight is such important in poker.

The cumulative odds column displays odds to make a particular hand or better. For example, the probability for making four of a kind or straight flush or royal flush is 0.0311%.

In Texas Hold'em, poker odds are THE probability tool you need as a poker player. In fact, you should always be thinking about poker odds - yours and your opponents' - when making decisions. In short, poker odds is the probability of you winning that hand, or the price it offers (pot odds). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. Three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise. Poker Math & Probabilities (Texas Hold'em) The following tables provide various probabilities and odds for many of the common events in a game of Texas hold 'em. Odds% Example Win% 330-to-1 0.30% JJ v 77 80% v 20% 220-to-1 0.45% 55 v AQ 55% v 45% 110-to-1 0.90% 55 v AQs 50% v 50% 82-to-1 1.21% JJ v 75 85% v 15% 82-to-1 1.21% JJ v 75s 80% v 20%.

The total number of unique 7-card hands is 133,784,560. Suits have no relative value in poker, so by ignoring them the total number ot unique 7-card hands drops to 6,009,159.

Since in poker you can use only 5 cards out of 7 to make the best hand, there is a further reduction in possible combinations, making the total of 4,824 unique poker hands.

An interesting fact is that you are more likely to make a pair than a high card by the showdown in 7-card variants. This is a bit against the poker hand ranking, which was originally built with the assumption that the less frequent hand beats the more frequent one.

The ranking was correct for 5-card poker variants, which were dominant at the times the ranking was created. Maybe people that invented 7-card variants forgot to update the ranking, who knows?

Poker hand probability chart

More articles on poker probability:

Poker odds calculator
Poker outs and odds
Pot odds and expected value
Sklansky bucks
Implied odds
Reverse implied odds
Common preflop odds chart
Common flop odds chart
Pocket pairs - flopping overcards odds

Go back to the Online Poker Strategy.

Brian Alspach

13 January 2000

Abstract:

The types of 3-card poker hands are

• straight flush
• 3-of-a-kind
• straight
• flush
• a pair
• high card

The total number of 3-card poker hands is .

A straight flush is completely determined once the smallest card in thestraight flush is known. There are 48 cards eligible to be the smallestcard in a straight flush. Hence, there are 48 straight flushes.

In forming a 3-of-a-kind hand, there are 13 choices for the rank and4 choices for the 3 cards of the given rank. This implies there are3-of-a-kind hands.

The ranks of the cards in a straight have the form x,x+1,x+2, wherex can be any of 12 ranks. There are then 4 choices for each card ofthe given ranks. This yields total choices. However,this count includes the straight flushes. Removing the 48 straightflushes leaves us with 720 straights.

Royal Flush

To count the number of flushes, we obtain choicesfor 3 cards in the same suit. Of these, 12 are straight flushes whoseremoval leaves 274 flushes of a given suit. Multiplying by 4 produces1,096 flushes.

Four Of A Kind

Now we count the number of hands with a pair. There are 13 choices forthe rank of the pair, and pairs of the chosen rank.The non-pair card can be any of the remaining 48. Thus, thereare 3-card hands with a single pair.

We could determine the number of high card hands by removing the handswhich have already been counted in one of the previous categories.Instead, let us count them independently and see if the numbers sumto 22,100 which will serve as a check on our arithmetic.

A high card hand has 3 distinct ranks, but does not allow ranks of theform x,x+1,x+2 as that would constitute a straight. Thus, there arepossible sets of ranks from which we remove the12 sets of the form .This leaves 274 sets of ranks.For a given set of ranks, there are 4 choices for each cardexcept we cannot choose all in the same suit. Hence, there are274(4³-4) = 16,440 high card hands.

Poker Hand Probability Table Worksheet

If we sum the preceding numbers, we obtain 22,100 and we can be confidentthe numbers are correct.

Here is a table summarizing the number of 3-card poker hands. Theprobability is the probability of having the hand dealt to you whendealt 3 cards.

Poker Hand Probability Table Example

Probability Of Poker Hands