Board & Hand Probabilities
Study poker probabilities that help you gauge range frequencies and how often boards come.
Hands
How often a player dealt a random hand holds particular cards.
| A random hand… | NLHE | PLO4 | PLO5 | PLO6 | PLO7 | PLO8 |
|---|---|---|---|---|---|---|
| Straighttwo specific ranks not matching the board | 1.5% | 7.0% | 11.0% | 15.5% | 20.5% | 25.5% |
| Seta pocket pair matching the board | 0.5% | 1.5% | 2.5% | 3.5% | 5.0% | 6.5% |
| Tripsa card matching the paired rank (paired board) | 8.0% | 16.0% | 19.5% | 23.0% | 27.0% | 30.5% |
| Pocket paira specific pair, rank not on board | 0.5% | 3.0% | 4.5% | 7.0% | 9.0% | 12.0% |
| Two paira card matching each of two board ranks | 1.0% | 4.0% | 6.5% | 9.5% | 13.0% | 16.5% |
| Paira card matching a board rank | 12.0% | 23.0% | 28.0% | 33.0% | 37.5% | 42.0% |
| Any specific rankdealt preflop, no board yet | 15.0% | 28.0% | 34.0% | 39.5% | 45.0% | 50.0% |
| Non-board ranka rank not on the board, after the flop | 16.0% | 29.5% | 36.0% | 42.0% | 47.0% | 52.0% |
| Flush drawtwo of a suit (two-tone board) | 4.5% | 21.5% | 31.0% | 41.0% | 50.0% | 58.5% |
| Flushtwo of a suit (monotone board) | 4.0% | 18.0% | 26.5% | 35.5% | 44.0% | 52.5% |
| Wrapthree specific ranks not matching the board | — | 1.5% | 3.0% | 5.0% | 8.0% | 11.5% |
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; expand a texture to see its runouts.
Pick a flop texture — pairs, then suits, then straights
Grouped shows each figure as a share of the row above it; Cumulative shows it out of all flops. The "a random hand here holds" rows are different: they're per-hand connection odds for that texture (from representative flops), never scaled by the flop share.
How to study with this page
Everything above is exact: every Board figure is enumerated over all 22,100 flops (7,140 in the 36-card deck) and their runouts, and every Hands figure is closed-form combinatorics. Nothing is simulated, and there's nothing to enter — these are the constants worth knowing cold.
Hands answers "how often does a player hold it?". Every figure is for one specific holding, so the exact ranks never matter — the ~7% straight-combo figure is the same for 6-4 on a 7-5-3 board as for Q-J on K-T-3. These are the raw inputs behind every "how often does he have it?" estimate.
Board answers "how often does this texture come, and what does it turn into?" — pick the drill order, expand a texture, and read how it runs out: how often the flush completes, the board pairs, or a bigger straight arrives by the river.
- Memorize the Hands table with Round ½ on (the default). Rough numbers are the point: in game you're testing whether you're beat ~15% or ~35%, not whether 18% beats 20%.
- Use the Board tree for intuition, not recall. Reorder the drill (Suits first vs Pairs first) to cut the same flops different ways, and lean on the two metrics: Grouped reads as a share of the row above — for reasoning once a flop is out; Cumulative reads out of all flops — for planning ranges before it.
- Connect the numbers to decisions. The highest-value use of the Hands figures is "how often am I beat?": work down from the strongest hand class, sum as you go, and count chops as half. Then test the sum against the ~20% benchmark — a pot-sized river value bet wants you beat no more than about 20% of the range you're betting into. The opponent folds roughly half against a pot bet, so at 20% beat you still win comfortably more than half the times you're called, with margin left for getting raised and for blocker effects. The Board runouts are the other half of the picture: they're the base rates for how textures shift by the river, which is what your flop ranges have to be built to survive.
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: PLO Range Frequencies — dealt vs opened vs 3-bet.