Skip to Universal Law
Flawless Poker

Universal Law 10

TERRAIN MAPS

How the board is built

These flops are dealt from the full deck. Your two cards are not removed yet, so the count is 22,100, not the 19,600 left after you have looked.

A flop texture is a property of the three board cards alone. There are 52 × 51 × 50 ÷ 6 of them, which is 22,100. The rows are different descriptions of the same flops, so they are not added together.

Flop textures from all 22,100 three-card boards.
Flop typeChancePlain English
Rainbow, three different suits39.76%1 in 2.5
Two-tone, two cards of one suit55.06%1 in 1.8
Monotone, all one suit5.18%1 in 19
Paired, exactly one pair16.94%1 in 5.9
Trips on the board0.24%1 in 425
Contains at least one ace21.74%1 in 4.6
Three to a straight: three different ranks inside a five-rank window, wheel included18.53%1 in 5.4
All three cards ten or higher5.16%1 in 19
All three cards nine or lower22.44%1 in 4.5

By the river.

Five community cards are C(52, 5), which is 2,598,960 boards. The pairing rows that start from an unpaired flop ignore hole cards and use the 49 cards still in the stub.

Five-card boards, and the chance an unpaired flop pairs later. The pairing rows ignore hole cards.
EventChancePlain English
The five-card board contains a pair or better49.29%1 in 2.0
The board shows four or more of one suit4.49%1 in 22
The board is five of one suit0.20%1 in 505
An unpaired flop pairs on the turn18.37%1 in 5.4
An unpaired flop pairs by the river37.07%1 in 2.7

Almost half of all final boards are paired. More than half of flops are two-tone, and another 5% are monotone, so a flush is still possible on most boards.

These counts are for study and post-session review. Where a row comes from a simulation, the caption names how many deals were run. Where a stack or a pot is made up, the caption says so. None of these figures is an instruction for a live pot.