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% before rounding. 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
With the example flop known, how often a random hand contains the specified cards. The three flop cards are removed before the hand is dealt.
| A random hand… | NLHE | PLO4 | PLO5 | PLO6 | 7-card PLO | 8-card PLO | 6+ |
|---|---|---|---|---|---|---|---|
| Two off-board ranksJ and T on Kd9s6h | 1.5% | 7.0% | 11.0% | 15.5% | 20.5% | 25.5% | 3.0% |
| Board-rank pocket pairtwo 9s on Kd9s6h | 0.5% | 1.5% | 2.5% | 3.5% | 5.0% | 6.5% | 0.5% |
| Paired-rank carda K on KdKs9h | 8.0% | 16.0% | 19.5% | 23.0% | 27.0% | 30.5% | 12.0% |
| Off-board pocket pairtwo aces on Kd9s6h | 0.5% | 3.0% | 4.5% | 7.0% | 9.0% | 12.0% | 1.0% |
| Two board-rank matchesa K and a 9 on Kd9s6h | 1.0% | 4.0% | 6.5% | 9.5% | 13.0% | 16.5% | 1.5% |
| Board-rank carda 9 on Kd9s6h | 12.0% | 23.0% | 28.0% | 33.0% | 37.5% | 42.0% | 17.5% |
| Two of the two-tone suittwo spades on Ks9s6h | 4.5% | 21.5% | 31.0% | 41.0% | 50.0% | 58.5% | 4.0% |
| Two of the monotone suittwo spades on Ks9s6s | 4.0% | 18.0% | 26.5% | 35.5% | 44.0% | 52.5% | 3.0% |
| Three off-board ranksJ, T and 8 on Kd9s6h | — | 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.
Loading PLO4 probabilities…
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 for the cards in each example. The denominator is every possible hand from the deck after the three example flop cards are removed: C(49, K) for K-card hands, or C(33, 2) in 6+. These rows count card holdings; a hand with three specified ranks need not have a wrap.
- 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 PLO4 hand rows under each Board texture average every flop in the selected class. They use exact one-flop hand enumerations, with rates stored to 1/65,535 before averaging. The rows headed "Best hand" are exclusive; a hand can have a made hand and a draw.
- Hands on one flop: the exact ranks change the hand mix, so this panel reads a figure per flop rather than an average over a 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. 7-card and 8-card PLO are high-only games here. Their universes are 85,900,584 and 450,978,066 hands per flop, so each of their 74 distinct one-flop rows uses 25,000,000 random hands. The largest per-bucket 95% sampling half-width is about 0.02 percentage point. A value near a rounding boundary can change by 0.1 point in the printed display.
- 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 a two-rank draw (including a double gutshot), three or more is a wrap. Counting cards instead put 2-3-5 on A-A-4 in the two-rank row, even though only the wheel window is available there.
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.