Poker Odds Calculator: Outs to Odds
Turn your outs into exact odds. A flush draw hits 34.97% of the time by the river, an open-ender 31.45%, a gutshot 16.47% — computed exactly, not approximated.
From outs to a percentage
An out is any unseen card that turns your hand into the winner. Once you know your out count, the odds follow from arithmetic. After the flop you have seen five cards — your two plus the three on the board — leaving 47 unknown. Note that this is 47 and not 45: your opponent's two cards are unknown to you, so from your point of view they are still part of the pool, and treating them as removed would bias every number you compute.
With N outs and 47 unseen cards, the turn brings one of them N/47 of the time. To get the chance of hitting across both the turn and the river, it is easier to compute the miss twice and subtract: 1 − ((47 − N)/47 × (46 − N)/46). If you are already on the turn with one card to come, the river hits N/46.
Working that through for the draws you actually hold:
- Flush draw (9 outs) — 19.15% on the turn, 34.97% by the river.
- Open-ended straight draw (8 outs) — 17.02% on the turn, 31.45% by the river.
- Gutshot (4 outs) — 8.51% on the turn, 16.47% by the river.
- Set to full house or quads (roughly 7 outs) — about 27.8% by the river.
- Pocket pair to a set (2 outs) — 4.26% on the turn, 8.42% by the river.
Is the rule of 2 and 4 good enough?
The shortcut — multiply outs by 2 for one card, by 4 for two — is a decent mental approximation and a poor calculator. For a flush draw it gives 36% against a true 34.97%, close enough to act on. But the error grows with the out count: at 15 outs the rule claims 60% when the real figure is 54.1%, an overstatement of nearly six points that can flip a marginal call.
Use the rule of 4 at the table and the exact number when you are studying. This calculator shows the exact figure by default so that the numbers you commit to memory are the correct ones.
One important caveat on the rule of 4: it only applies when you will actually see both cards, which usually means you are all in on the flop. If you call a flop bet expecting to face another bet on the turn, you are paying for one card, not two — price that call with the turn-only number.
Counting outs honestly
The arithmetic is the easy part; counting outs is where money is lost. Discount any out that completes your hand while making someone else a better one — a straight card that puts a third suit on board, or a card pairing the board when a full house is live. Overcards to a paired board are frequently not outs at all. It is better to count six good outs than nine optimistic ones, because every inflated out makes a losing call look profitable.
Once you have a trustworthy percentage, compare it with the price you are being laid using the pot odds calculator. If your equity clears the threshold the call is profitable on raw odds alone; if it falls just short, implied odds have to make up the difference. For exact equity against a specific hand or range rather than a raw out count, use the equity calculator, and check ICM before flipping for your tournament life.