What is my error ?
 

I played in a PS tournament and two players went all in on the flop against my top pair ace kicker.

They had 6 and nine outs. (Flush draw and open straight draw with the flush cards no good for the straight draw)

I think, the probability of me winning when they combined have 15 outs is 46% (32/47*31/46)

But if I try another way, I dont get the same result :

Probability of the 6 outs beating me 1-(41/47*40/46) = 24%

Probability of the 9 outs beating me when the 6 outs havent beated me (1-0,24)*(1-(38/47*37/46) = 27%

If I add those two I get 51%

You could say that it doesnt matter very much as I am getting around 1:1 odds with the pot laying 2:1, but it has been obsessing me.

By the way, I won this hand and later lucked out to win the tournament.

Kim

Re: What is my error ?
 

Your error is in the statement

"Probability of the 9 outs beating me when the 6 outs haven't beaten me (1-0.24)*(1-(38/47*37/46)) = 27%"

You know that the 6 outs are not among the cards if they haven't beaten you so,

Probability of the 9 outs beating you when the 6 outs haven't beaten you is <font color="green"> (1-0.24)*(1-(32/41*31/40)) = 30%. </font color>

The rest looks good [img]/forums/images/icons/grin.gif[/img]

Re: What is my error ?
 

It ignores the times when the both beat you.

Thank you very much, I feel enlightened