Poker Hand Probability Calculator

How rare is a royal flush, really? What are the actual odds of being dealt pocket aces? This educational tool reveals the fascinating mathematics behind poker hands. Understanding these probabilities is what separates casual players from those who truly comprehend the game's underlying structure.

Texas Hold'em Outs Calculator

Calculate your odds of improving your hand on the turn or river.

Pre-Flop Starting Hand Odds

Before the community cards are dealt, your starting hand is determined purely by probability. The mathematics are precise and unchangeable. According to PokerNews, understanding starting hand probabilities is the foundation of sound poker strategy.

Probability of Being Dealt Specific Starting Hands

Pocket Aces (AA)
0.45%
1 in 221
Any Pocket Pair
5.88%
1 in 17
Suited Cards
23.5%
~1 in 4
AK (Big Slick)
1.21%
1 in 83
Curious Fact: If you played 1,000 hands of Texas Hold'em, you'd expect to be dealt pocket aces only about 4-5 times. Yet many players overvalue these hands when they finally arrive, not accounting for the community cards that can still defeat them.

Complete Poker Hand Probabilities

The odds of being dealt specific 5-card poker hands are calculated using combinatorics. There are exactly 2,598,960 possible 5-card combinations from a standard 52-card deck. These calculations, first formalized by mathematicians in the 18th century, form the basis of poker hand rankings. The Mathematics Is Fun probability guide explains the underlying combinatorial principles.

Royal Flush

A K Q J 10
0.000154%
1 in 649,740
The rarest hand in poker. Only 4 possible combinations exist.

Straight Flush

9 8 7 6 5
0.00139%
1 in 72,193
36 possible combinations (excluding royal flushes).

Four of a Kind

K K K K 7
0.024%
1 in 4,165
624 possible combinations across all ranks.

Full House

Q Q Q 8 8
0.144%
1 in 694
3,744 possible combinations (three of a kind + pair).

Flush

A J 8 4 2
0.197%
1 in 509
5,108 possible combinations (excluding straight flushes).

Straight

10 9 8 7 6
0.392%
1 in 255
10,200 combinations (excluding straight flushes).

Three of a Kind

7 7 7 K 2
2.11%
1 in 47
54,912 possible combinations.

Two Pair

J J 4 4 A
4.75%
1 in 21
123,552 possible combinations.
Did You Know? The probability of being dealt a royal flush is so low that if you played 20 hands of poker every day, you'd statistically expect to see one approximately once every 89 years. This rarity is why royal flush jackpot disputes can involve life-changing sums of money.

Complete Probability Reference Table

This comprehensive table shows every standard poker hand ranking with precise mathematical probabilities. These figures are based on the total number of possible 5-card combinations (2,598,960) from a standard 52-card deck, as documented by the Encyclopedia Britannica.

Hand Combinations Probability Odds (1 in X)
Royal Flush 4 0.000154% 649,740
Straight Flush 36 0.00139% 72,193
Four of a Kind 624 0.024% 4,165
Full House 3,744 0.144% 694
Flush 5,108 0.197% 509
Straight 10,200 0.392% 255
Three of a Kind 54,912 2.11% 47
Two Pair 123,552 4.75% 21
One Pair 1,098,240 42.26% 2.4
High Card 1,302,540 50.12% 2.0
Key Insight: Over 92% of all 5-card poker hands are either one pair or high card. This means most poker hands are quite ordinary, which is precisely why the rare hands command such high value. Understanding this distribution is fundamental to poker strategy.

Texas Hold'em: The 7-Card Advantage

Texas Hold'em changes these probabilities significantly because players choose the best 5 cards from 7 (2 hole cards + 5 community cards). This dramatically increases the chances of making strong hands. Research from the Carnegie Mellon University AI research program has extensively analyzed these probabilities in their poker AI systems.

7-Card Hand Probabilities (Texas Hold'em)

Royal Flush
0.0032%
1 in 30,940
Straight Flush
0.028%
1 in 3,590
Four of a Kind
0.168%
1 in 595
Full House
2.60%
1 in 38

Note: These 7-card probabilities are about 20x higher for royal flushes compared to 5-card draw, which is why Hold'em produces more dramatic showdowns.

Understanding Outs and Drawing Odds

In Texas Hold'em, "outs" are the cards that will improve your hand. Knowing how many outs you have and the probability of hitting them is essential for making mathematically sound decisions. The Card Player magazine provides extensive resources on calculating outs in various situations.

Common Drawing Situations

Draw Type Outs Turn % River % Both Cards %
Pocket pair to set 2 4.3% 4.3% 8.4%
Gutshot straight 4 8.5% 8.7% 16.5%
Two overcards 6 12.8% 13.0% 24.1%
Open-ended straight 8 17.0% 17.4% 31.5%
Flush draw 9 19.1% 19.6% 35.0%
Flush + gutshot 12 25.5% 26.1% 45.0%
Flush + open-ended 15 31.9% 32.6% 54.1%
The Rule of 2 and 4: Professional players use a quick approximation: multiply your outs by 2 to get the percentage of hitting on the next card, or by 4 for both remaining cards. For example, 9 outs for a flush draw gives roughly 18% (turn) or 36% (both), which is close to the actual 19.1% and 35%.

When Probability Meets Reality

Understanding poker probability helps explain some of the most dramatic stories in gambling history. The same mathematical principles that govern poker hands also underlie how casinos track player behavior and identify statistical anomalies.

The MIT Blackjack Team succeeded by exploiting probability in blackjack, and similar mathematical advantages exist in poker. Unlike blackjack, where the house always has an edge, poker is a game where skilled players can have positive expected value because they're playing against other players, not the house.

This is why the biggest wins in gambling history often involve games with player-vs-player elements or progressive jackpots where the mathematics occasionally favor the player. Understanding these probabilities doesn't guarantee winning, but it does explain why certain outcomes are remarkable and others are routine.

Did You Know? In 2008, at the World Series of Poker, four players at the same table all made straight flushes in a single hand. The probability of this occurring is so astronomically low that statisticians estimated it might happen once in several billion hands.

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