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…NLHEPLO4PLO5PLO6PLO7PLO86+
Straighttwo specific ranks not matching the board1.5%7.0%11.0%15.5%20.5%25.5%3.0%
Seta specific pair, rank on the board0.5%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 board0.5%3.0%4.5%7.0%9.0%12.0%1.0%
Two paira card matching each of two given board ranks1.0%4.0%6.5%9.5%13.0%16.5%1.5%
Paira card matching one given board rank12.0%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 board1.5%3.0%5.0%8.0%11.5%

Board

Order
Levels

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

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. Gold frequencies are a share of all flops. Teal 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.

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. And for how the solver actually bets each of these textures, see C-bet frequencies across all 1,755 flops.