Poker probability is unusual among casino maths because none of it is about a house edge. It is about whether a specific call is profitable, and the answer is always a comparison between two numbers you can compute.
Where to start
- Pot odds — the one division that decides most calls, at every common bet size.
- Outs and equity — exact equity for every draw, and how far the rule of 4 and 2 drifts.
- Preflop matchups — equities from enumerating all 1,712,304 boards.
- Starting hands — 1,326 combinations, 169 hands, and the arithmetic behind ranges.
- Flop odds — how often the flop brings what you were hoping for.
Three numbers worth memorising
A flush draw is 35% from flop to river and 20% with one card to come. Almost every drawing decision is a variation on this.
A pot-sized bet needs 33.3% equity to call, and a half-pot bet needs 25%. Those two cover most of the bets you will face.
A pocket pair flops a set 11.8% of the time. Everything about playing small pairs follows from that one figure.
What this section does differently
Published equities are quoted per hand class, as though AK against AQ were a single number. It is not: the value moves by several percentage points with the suits, and this section names the exact cards for every figure it gives.
The equities here enumerate every board rather than sampling, so they are exact for the cards shown rather than accurate to within a simulation's error.
For the games where the house does have a fixed edge, see our blackjack, baccarat and craps sections.
Frequently Asked Questions
- What equity do I need to call a pot-sized bet?
- 33.3%. You risk one unit to win three including your own call.
- What is a flush draw worth?
- 34.97% from the flop to the river, 19.57% with one card to come.
- Is AK against QQ a coinflip?
- Close: 45.88% for AK, so the pair is a slight favourite.
- How accurate is the rule of 4 and 2?
- Good to half a point up to eight outs, and it overstates a 15-out draw by nearly six percentage points.
- Are these numbers simulated?
- No. Equities enumerate all 1,712,304 possible boards and the rest is exact combinatorics.
Equities on this page are computed by enumerating every one of the 1,712,304 boards that can follow the two hands shown, not by simulation, so they are exact for those specific cards. Draw and flop probabilities are exact combinatorics. The hand evaluator is checked against known orderings and the equities against published ranges before publication. Note that published figures usually quote one number per hand class while the real value moves with the suits, which is why this section names the exact cards.