Hold 'em Board Win Probability

The board is the winning hand if its five cards are a higher ranked hand than each of the players' hands. Consider the case of 2 players. The board wins with a pair if the following holds:

Board Pair Wins Case. Both players are not dealt a pair and do not straighten or flush. The board has a pair and the ranks of the 3 other board cards are higher than the player card ranks.

This means that the board pair must be > 33 and the board’s lowest ranked card for a win is a 4. With a 4, the two players must each have 32.

Example: P1- 32o. P2- 67s Board- 8 T T J A. Both players play the board.

I have not seen the metric of board win probability and there’s no way I can do it either analytically or by simulation. I would guess it’s less than 1%.

Does anybody have data on board win probability?