Board & Hand Probabilities
Study poker probabilities that help you gauge range frequencies and how often boards come.
Flop textures at a glance
Exact frequencies over all 22,100 distinct flops. Percentages are of all flops dealt. The first two blocks each sort every flop into exactly one row, so each sums to 100%. The last three are runouts, so they don't.
| Flop texture | How often |
|---|---|
| Unpaired | 82.82% |
| Paired | 16.94% |
| Trips | 0.24% |
| Rainbow (three suits) | 39.77% |
| Two-tone | 55.06% |
| Monotone | 5.18% |
| A flush becomes possible by the river, from a rainbow flop | 16.84% |
| A flush becomes possible by the river, from a two-tone flop | 45.83% |
| Board pairs by the river, from an unpaired flop | 38.78% |
Hands
How often a player dealt a random hand holds particular cards.
| A random hand… | NLHE | PLO4 | PLO5 | PLO6 | PLO7 | PLO8 | 6+ |
|---|---|---|---|---|---|---|---|
| Straighttwo specific ranks not matching the board | 1.5% | 7.0% | 11.0% | 15.5% | 20.5% | 25.5% | 3.0% |
| Seta specific pair, rank on the board | 0.5% | 1.5% | 2.5% | 3.5% | 5.0% | 6.5% | 0.5% |
| Tripsa card matching the paired rank (paired board) | 8.0% | 16.0% | 19.5% | 23.0% | 27.0% | 30.5% | 12.0% |
| Pocket paira specific pair, rank not on board | 0.5% | 3.0% | 4.5% | 7.0% | 9.0% | 12.0% | 1.0% |
| Two paira card matching each of two given board ranks | 1.0% | 4.0% | 6.5% | 9.5% | 13.0% | 16.5% | 1.5% |
| Paira card matching one given board rank | 12.0% | 23.0% | 28.0% | 33.0% | 37.5% | 42.0% | 17.5% |
| Flush drawtwo of a suit (two-tone board) | 4.5% | 21.5% | 31.0% | 41.0% | 50.0% | 58.5% | 4.0% |
| Flushtwo of a suit (monotone board) | 4.0% | 18.0% | 26.5% | 35.5% | 44.0% | 52.5% | 3.0% |
| Wrapthree specific ranks not matching the board | — | 1.5% | 3.0% | 5.0% | 8.0% | 11.5% | — |
Hands on one flop
What a random hand has on the exact flop you pick.
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Board
How often each flop texture comes, and how it then runs out by the turn and river. Pick the drill order and which levels to show, then expand a texture to see its runouts. The straight classes count gaps between the board cards. Straight means three of them already sit inside one straight, so two hole cards make it now. Straight draw means only two do, so two hole cards can draw at it.
Pick a flop texture - pairs, then suits, then straights
Methodology
- Hands: exact closed-form combinatorics. Every figure is for one specific holding, so the exact ranks never change it.
- Board: texture frequencies and runouts enumerated over all 22,100 flops and every turn and river. Nothing is simulated. Frequencies are a share of all flops. Runout odds are for the flop texture they sit under, with two kinds of indented rows: the "…on the turn" / "…on the river" pairs sum to their parent row, and the "…completes" rows are conditional on the turn row above them.
- The "a random hand here holds" rows are the only approximations: read off one representative flop per texture (one per pairing and straight class, since a paired flop draws with two live ranks and an unpaired one with three).
- Hands on one flop: the only panel where the exact ranks change the answer, so it is the only one that needs a figure per flop rather than per texture. Those are precomputed. Relabelling suits doesn't change anything, which collapses the 22,100 flops to 1,755 (short deck's 7,140 to 573), and the answers collapse again to about 74 distinct rows, because two flops with the same straight-window structure give the same split: K-8-7 and Q-7-6 are identical, while A-2-3 and 9-8-7 are not, since the wheel touches one window and 9-8-7 touches three. A whole game is a few KB, fetched when you pick it.
- Every figure through PLO6, and for 6+, is an exact walk of every hand the remaining deck can deal: 1,176 in NLHE up to 13,983,816 in PLO6. PLO7 and PLO8 are the two exceptions on this page: their universes are 86 and 451 million hands per flop, so they are sampled at 4 million hands each, which holds the 95% error under 0.05 percentage points. That is half the last digit shown, so nothing you can read here turns on it.
- Value uses the same board-relative categories as the rest of the site: Set is a pocket pair matching a board rank, Trips a card matching the paired rank, and None is a hand that contributes nothing of its own, which on a paired board still plays the board's pair. The draws are the ones the Board panel counts, and a hand that already made the hand is not also drawing to it: a made flush is never a flush draw and a made straight is never a wrap. The three straight draws are told apart by how many ranks fill the straight, not by how many cards: one rank is a gutshot, two is an open-ender, three or more is a wrap. Counting cards instead put 2-3-5 on A-A-4 in the open-ender row, and the wheel is the bottom straight, so nothing on that board can be open-ended at all.
Everything on this page is for a random hand. Real preflop ranges fold their low cards and keep their suited aces, which bends every one of these numbers. That's the next page: Range Frequencies: dealt vs opened vs 3-bet. And for how the solver actually bets each of these textures, see C-bet frequencies across all 1,755 flops.