Was reading Super System and didn't understand...

[Tobes]

In the limit Holdem section it states that if person A holds 8 /images/graemlins/spade.gif9 /images/graemlins/spade.gif he/she is actually the favorite against person B who holds 4 /images/graemlins/heart.gif5 /images/graemlins/heart.gif after the flop comes...
3 /images/graemlins/diamond.gif 6 /images/graemlins/spade.gif 7 /images/graemlins/spade.gif
It states that there are 14 cards that person A can catch to win the pot with two chances to do it. Thus person A is a 53% to win over person B (47%).
I don't understand how this conclusion was reached. If someone could help me to understand how 14/45 (and assuming person A doesn't catch one of those 14 cards on the turn), then 14/44 becomes 53%. Am I crazy or just overlooking something... /images/graemlins/confused.gif If someone could explain this to me I would very much appreciate it. Thanks!

P.S. I'm not sure if that is exactly how it was stated. But it's close enough to serve my query. If you want you can check it out in the Limit Holdem section of Super System. Thanks again.

[BruceZ]

[ QUOTE ]
In the limit Holdem section it states that if person A holds 8 /images/graemlins/spade.gif9 /images/graemlins/spade.gif he/she is actually the favorite against person B who holds 4 /images/graemlins/heart.gif5 /images/graemlins/heart.gif after the flop comes...
3 /images/graemlins/diamond.gif 6 /images/graemlins/spade.gif 7 /images/graemlins/spade.gif
It states that there are 14 cards that person A can catch to win the pot with two chances to do it. Thus person A is a 53% to win over person B (47%).
I don't understand how this conclusion was reached. If someone could help me to understand how 14/45 (and assuming person A doesn't catch one of those 14 cards on the turn), then 14/44 becomes 53%.

[/ QUOTE ]

14/45 + (1 - 14/45)*(14/44) = 53%.

[slickpoppa]

There are two way for A to win. He could catch one of his 14 outs or 2 of his 14 outs. The probability of either of these is:
(14/45)*(31/44)*2 + (14/45)*(13/44) = 53%

[Tobes]

Thanks fellas. I see how that conclusion was reached. However, I'm a little confused. If player A hits one of the 14 cards on the turn, wouldn't player B be drawing dead? Hense (14/45)(44/44) any of the remaining 44 cards in the deck could come at that point and Player B would not be able to win the pot. Still confused...

[slickpoppa]

Yes, if the first card is an out for player A, then the second card can be anything. But that is only one way that it could happen. You could also get a non-out on the turn and an out on the river. Hence:
(14/45)*(44/44) + (31/45)*(14/44) = 53%
This is the same formula that brucez used in his post, just written a little more explicitly.

[Tobes]

AHHH. I see. Thank you very much for your help. /images/graemlins/grin.gif