Poker Probability Calculator

In Texas Hold'em poker, knowing the probability of completing a drawing hand is one of the fundamental skills that separates recreational players from those who apply mathematical reasoning to their decisions. This calculator uses the standard combinatorial formula to compute exactly how likely you are to hit at least one of your outs given the number of unseen cards remaining in the deck.

What Are Outs?

An 'out' is any card in the remaining deck that, if dealt, would improve your hand to likely the best hand. For example, if you hold two hearts and two more hearts appear on the flop, any of the nine remaining hearts in the deck would complete your flush. Those nine cards are your outs.

Common drawing situations and their out counts include: a gutshot (inside) straight draw with 4 outs, two overcards that would pair the board with 6 outs, an open-ended straight draw needing either of two ranks with 8 outs, a flush draw with 9 outs, and combined flush plus open-ended straight draw with up to 15 outs.

The Exact Probability Formula

For a single street (one card to come), the probability of hitting at least one out is simply: outs divided by the number of unseen cards. After the flop in a standard game, there are 47 unseen cards (52 minus 2 hole cards minus 3 flop cards). A flush draw with 9 outs gives 9 / 47 ≈ 19.1%.

For two streets (two cards to come, flop to river), the exact formula accounts for the possibility of hitting on either the turn or the river. The miss probability is the number of ways to draw two non-out cards divided by the total ways to draw two cards: C(miss, 2) / C(total, 2). Subtracting from 1 gives the hit probability. For a flush draw this yields 1 − C(38, 2) / C(47, 2) ≈ 35.0%.

Odds Against and Pot Odds

Odds against hitting is the ratio of miss probability to hit probability. If you have a 20% chance of hitting, you miss 80% of the time, so the odds against are 80 / 20 = 4.0 : 1. This is expressed as '4 to 1 against.'

Pot odds represent the ratio of the current pot size to the cost of a call. To determine whether a call is mathematically profitable, compare your pot odds to the odds against hitting your draw. If the pot offers you 5 : 1 and your draw is 4 : 1 against, the call has a positive expected value. The 'pot odds needed' figure this calculator displays is the break-even percentage: if the pot is offering you at least that fraction of the total pot, calling is mathematically justified.

For example, with a flush draw (9 outs, one street), you need pot odds of at least 19.1%. If the pot is 100 and your opponent bets 25, the total pot becomes 125 and you must call 25. Your pot odds are 25 / 125 = 20%, which exceeds the required 19.1%, making a call mathematically sound in this scenario.

The Rule of 2 and 4

The Rule of 2 and 4 is a well-known mental shortcut used by poker players to quickly estimate draw probabilities without performing division at the table. Multiply your outs by 2 when one card is to come (turn or river), or by 4 when two cards remain (flop to river). For 9 outs this gives approximately 18% for one street and 36% for two streets — very close to the exact values of 19.1% and 35.0%.

This approximation becomes less accurate for very large or very small out counts but remains a useful heuristic for the typical 4–15 out range encountered in common drawing situations.

Important Caveats

These probability figures assume that your opponent's hole cards and any discarded cards are unknown — that is, the 'unseen cards' pool is treated as uniformly random. In reality, some of your outs may be in opponents' hands and therefore unavailable. This is why actual implied odds and reverse implied odds — the money you may win or lose on later streets given your draw — also factor into a complete decision.

Additionally, completing a draw does not guarantee winning the pot. An opponent may hold a higher flush, or the board may pair in a way that gives someone a full house. These strategic considerations go beyond simple probability and require experience and game-specific judgment. Results from this calculator reflect mathematical probabilities only.

Cards Remaining

After the flop in a standard 52-card game, 47 cards remain unseen from your perspective (assuming you do not know any opponent's hole cards). After the turn, 46 cards remain. The default value in this calculator is 47, appropriate for flop-to-turn calculations. You may adjust this figure if you have additional information, such as knowing cards that have been mucked in a live game.