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Old 05-28-2005, 09:41 PM
pzhon pzhon is offline
Join Date: Mar 2004
Posts: 66
Default Re: Probability to make boat/quads from flopped set?

flopped a set

6:1 to make boat/quad on turn (7 outs)
4:1 to make boat/quad on river (10 outs)

if i went all in on flop, what are the odds to make a boat/quad by showdown?

[/ QUOTE ]
If you have no information about what anyone else has, you will fill up 7/47 + (40/47)(10/46) = 33.4%.

If you know your opponent has a flush, you will fill up 7/45 + (6/45)(9/44)+(32/45)(10/44) = 341/990 = 34.4%. The middle term comes from when the turn would pair your opponent, giving you only 9 outs on the river. It is slightly more likely that you fill up if you know your opponent is not blocking the board from pairing.
Board: 9[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/heart.gif[/img]
cards win %win lose %lose tie %tie EV
A[img]/images/graemlins/heart.gif[/img] 2[img]/images/graemlins/heart.gif[/img] 649 65.56 341 34.44 0 0.00 0.656
7[img]/images/graemlins/spade.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 341 34.44 649 65.56 0 0.00 0.344

If you know your opponent has a straight or a baby flush, you get the same probability to fill up, but you also have outs to tie.
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