[BruceZ]

[ QUOTE ]
Assume a good flop comes for you, you see you have 17 outs to make a flush or filling an open ended straight, but you have still not made a hand. There are 47 unseen cards giving you ~ 36.2% (17/47) chance on the next card to make a hand. How can you infer your probability of making your hand by the river, post flop?

[/ QUOTE ]

Assuming 17 outs, even though you only have 15:

probability of hitting on the turn + probability of missing on the turn AND hitting on the river:

17/47 + (30/47 * 17/46) =~ 59.8%.


or 1 - probability of missing on both:

1 - (30/47)*(29/46) =~ 59.8%


or probability of hitting on the turn + probability of hitting on the river - probability of hitting on both:

17/47 + 17/47 - (17/47 * 16/46) =~ 59.8%


For 15 outs, substitute 15 for 17, 32 for 30, 31 for 29, and 14 for 16.