board pairing

[ZEN MASTER]

is the board in holdem favored to pair or not. If it is? by how much. Wopuld You please wlk me thrugh Your calculations. Thank You

[BruceZ]

The board is a slight favorite to be unpaired in 5 cards. The number of unpaired boards counting every order the cards can occur in is 52*48*44*40*36. The number of total boards is 52*51*50*49*48. The ratio is 50.7% unpaired boards.

[morgan]

If the flop is unpaired then the chance the board will remain unpaired at the river is 61.2%. The calculation is the same as Bruce's, just with the last two numbers: 40*36 / 49*48

Morgan