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Poker Hand Probability Calculator

Select a poker hand to see its exact probability, odds against, and how it ranks among all 2,598,960 possible 5-card deals.
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Luis GonzalezCreated by Luis GonzalezLast updated:

How to Use This Calculator

  1. 1

    Select Poker Hand Type

    Choose the specific 5-card poker hand (e.g., Royal Flush, Full House) for which you want to calculate probabilities.

  2. 2

    Review Your Results

    The calculator will display the exact probability, odds against, number of ways to make the hand, and its percentile rank among all possible hands.

Example Calculation

A poker enthusiast wants to know the exact probability of being dealt a Royal Flush in a standard 5-card draw game.

Poker Hand Type

royal-flush

Results

0.000001539

Tips

Understand Odds vs. Probability

Probability is a fraction or percentage (e.g., 1 in 649,740). Odds Against is expressed as a ratio (e.g., 649,739 to 1). Both convey the same information but are used differently in betting contexts.

Memorize Key Hand Probabilities

For common hands like Two Pair or One Pair, knowing approximate probabilities can help you make better decisions about whether to draw more cards or fold in games like 5-card draw.

Contextualize with Pot Odds

In real poker games, hand probability is combined with 'pot odds' (the ratio of money in the pot to the cost of a call). If your pot odds are better than your hand odds, it's often a mathematically correct call.

Mastering the Odds: The Poker Hand Probability Calculator

The Poker Hand Probability Calculator is an indispensable tool for understanding the statistical backbone of poker, revealing the exact likelihood of being dealt any 5-card hand.

By selecting a hand type, users can instantly see its probability, odds against, and the number of ways it can be formed from a standard 52-card deck.

For instance, the probability of being dealt a Royal Flush is an incredibly rare 0.000001539, or roughly 1 in 649,740, highlighting the challenge and excitement of achieving such a premium hand.

Strategic Decision-Making in Card Games

Understanding poker hand probabilities is the bedrock of strategic decision-making in card games.

Players use these probabilities to calculate their "outs" (cards that will improve their hand), assess "pot odds" (the ratio of money in the pot to the cost of a call), and determine whether a bet is mathematically sound.

For example, if you have four cards to a flush, you know there are 9 remaining cards of that suit.

Knowing the odds against hitting that flush on the next card, and comparing it to the pot odds, guides whether you should call, raise, or fold.

This blend of combinatorics and betting theory transforms poker from a game of chance into a game of skill, where informed decisions consistently outperform gut feelings.

The Combinatorics Behind Poker Hand Probabilities

The Poker Hand Probability Calculator relies on combinatorial mathematics to determine the likelihood of each hand.

The total number of possible 5-card hands from a 52-card deck is given by the combination formula C(n, k) = n! / (k!(n-k)!), which for 52 cards and 5 selected cards is C(52, 5) = 2,598,960.

The probability for any specific hand is then calculated by:

Probability = (Number of Ways to Make the Hand) / (Total Possible 5-Card Hands)

For example, to calculate the probability of a Royal Flush:

  • There are 4 suits, so 4 ways to get a Royal Flush (one for each suit).
  • Probability = 4 / 2,598,960 ≈ 0.000001539.

This fundamental approach is applied to every hand type, from the strongest to the weakest.

💡 To translate betting lines into implied probabilities, essential for comparing with your own calculated hand odds, our Moneyline to Probability Converter can be a valuable companion.

Calculating Royal Flush Probability: A Classic Example

Let's calculate the probability of being dealt the most coveted hand in poker: a Royal Flush.

Here's the selected input:

  1. Poker Hand Type: Royal Flush

The calculation proceeds as follows:

  • Total Possible 5-Card Hands: From a standard 52-card deck, there are C(52, 5) = 2,598,960 unique 5-card combinations.
  • Ways to Make a Royal Flush: A Royal Flush consists of the Ace, King, Queen, Jack, and Ten, all of the same suit. Since there are four suits (clubs, diamonds, hearts, spades), there are only 4 distinct ways to form a Royal Flush.
  • Probability: 4 / 2,598,960 ≈ 0.000001539.
  • Odds Against: This translates to odds of (2,598,960 - 4) to 4, or 649,739 to 1.

The primary result, the probability for a Royal Flush, is 0.000001539.

This incredibly low probability underscores why it is such a rare and exciting hand in poker.

💡 For another classic probability puzzle that challenges intuition, explore our Monty Hall Problem Calculator to understand conditional probabilities.

Formula Variants for Different Poker Games

While the standard 5-card draw probabilities are foundational, poker hand probabilities shift significantly for different game variants.

  • Texas Hold'em (7-card probability): In Texas Hold'em, players are dealt two hole cards and share five community cards. The probability of making a hand is calculated from these 7 cards (best 5 out of 7). For example, the probability of hitting a Royal Flush in Texas Hold'em is much higher than in 5-card draw (around 1 in 30,940 for a single player by the river) because players have more cards to work with.
  • Omaha (9-card probability): Omaha players receive four hole cards and use two of them, plus three community cards, to make their best 5-card hand. This 9-card pool further increases probabilities for strong hands, making it a game known for bigger hands and more frequent straights and flushes compared to Hold'em.
  • Seven Card Stud (7-card probability): In Stud, players are dealt up to seven cards individually (some face up, some face down) and make the best 5-card hand. Like Hold'em, the larger pool of cards available to each player makes high-ranking hands more common than in 5-card draw.

These variations mean that a strong hand in one game (e.g., Two Pair in 5-card draw) might be a relatively weak hand in another (e.g., Two Pair in Omaha), profoundly influencing strategy and hand valuation.

Frequently Asked Questions

What is a 5-card poker hand probability?

A 5-card poker hand probability calculates the likelihood of being dealt a specific type of poker hand (e.g., a straight, a flush) from a standard 52-card deck. It's determined by dividing the number of unique ways to form that hand by the total number of possible 5-card hands, which is 2,598,960.

How many possible 5-card poker hands are there?

There are exactly 2,598,960 unique combinations of 5 cards that can be dealt from a standard 52-card deck. This total number forms the denominator for all 5-card poker hand probability calculations, from the rarest Royal Flush to the most common High Card hand.

What is the rarest 5-card poker hand?

The rarest 5-card poker hand is the Royal Flush, which consists of the A, K, Q, J, 10 of the same suit. There are only 4 ways to form a Royal Flush (one for each suit), giving it a probability of 1 in 649,740, or approximately 0.00015%.

How does hand probability influence poker strategy?

Understanding hand probability is fundamental to sound poker strategy as it informs decisions about betting, drawing, and folding. Players use probabilities to estimate their chances of improving their hand (e.g., hitting a flush or straight) versus the odds offered by the pot, enabling them to make mathematically favorable choices over the long term.