View Full Version : Basic flush question

10-28-2004, 03:50 PM
Stats make my brain hurt....

What are the odds of a board offering a flush possibility--i.e. how often will there be three cards of a suit on the board by the river?

10-28-2004, 05:07 PM
Taken from SSH, 35% chance the flush will come in by the river.

Lost Wages
10-28-2004, 05:47 PM
Depends on what you are holding but lets suppose that you are just watching...

Then there are C(52,5) = 2,598,960 possible boards

The board can come all in one suit 4*C(13,5) = 6435 ways.
P = 6435/2,598,960 = 0.248%

The board can come 4 to a suit 4*C(13,4)*39 = 111,540 ways.
P = 4.29%

The board can come 3 to a suit 4*C(13,3)*C(39,2) = 847,704 ways.
P = 32.6%

The probability of the board containing 3 or more of a suit is 0.248 + 4.29 + 32.6 = 37.1%

Lost Wages

10-29-2004, 12:32 PM
How do you increment the odds. For example, I hold two of the suit, two additional cards of that suit come on the flop. What are the odds of an additional card coming first from either the turn or the river and if missed on the turn then just the river. Sorry, if this is dumb but I am trying to implement some of the suggested math.