Poker Hand Odds Calculator
This calculator works out your exact chance of completing a drawing hand from your outs. Enter how many outs you have (the unseen cards that improve your hand), how many cards remain unseen, and how many cards are still to be dealt. It returns the probability of hitting on the very next card, the probability of hitting by the final card, and the odds against improving. The maths is exact combinatorics for drawing without replacement, the same calculation behind the familiar rule of four and two used at the table. No estimation is involved.
Poker outs formula
Let u = outs, c = unseen cards, t = cards to come
P(hit next card) = u / c
P(miss all) = product over i from 0 to t-1 of (c - u - i) / (c - i)
P(hit by end) = 1 - P(miss all)
Odds against = P(miss all) / P(hit by end)
Each factor in the miss product is the chance a given card avoids your outs, given the cards before it have already been dealt. Multiplying them gives the chance you miss on every remaining card.
Common drawing situations
- Flush draw after the flop: 9 outs, 47 unseen, 2 to come, about 34.97 percent to hit.
- Open-ended straight draw after the flop: 8 outs, about 31.45 percent with two cards to come.
- Gutshot straight draw: 4 outs, about 16.47 percent with two cards to come.
- Flush draw on the turn: 9 outs, 46 unseen, 1 to come, about 19.57 percent.
- The rule of four and two estimates these by multiplying outs by 4 (flop) or 2 (turn).
Poker hand odds: frequently asked questions
What are outs in poker?
Outs are the unseen cards that would complete or improve your hand to a likely winner. For example a four-card flush after the flop has 9 outs, the 9 remaining cards of that suit. Counting outs is the first step in working out your chance of improving.
How is the hit probability calculated?
If there are u outs among c unseen cards, the chance of missing on a single card is (c minus u) divided by c. Over the remaining draws, the chance of missing every time is the product of those falling fractions, and the hit probability is 1 minus that. This is exact combinatorics for drawing without replacement.
How many unseen cards are there in Texas hold'em?
After the flop you have seen your 2 hole cards plus the 3 community cards, so 5 of 52 cards are known and 47 remain unseen. After the turn, 6 are known and 46 remain. This calculator lets you set the unseen count and the cards still to come.
What does odds against mean for a draw?
Odds against express how many missing outcomes there are for each hit. If the hit probability is p, the odds against are (1 minus p) divided by p, shown as that number to 1. A flush draw on the flop with two cards to come is roughly 1.86 to 1 against.
What inputs should I enter?
Enter your number of outs, the number of unseen cards (47 after the flop, 46 after the turn in hold'em), and the number of cards still to be dealt (2 from the flop, 1 from the turn). The calculator returns the single-card and by-the-end hit probabilities and the odds against.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: Hypergeometric distribution.
- NIST Digital Library of Mathematical Functions: Combinatorial functions.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.