AsKs vs TT
 

Hi all,

A friend of mine had a hand where he was dealt A [img]/images/graemlins/spade.gif[/img]K [img]/images/graemlins/spade.gif[/img]. The board came up 9 [img]/images/graemlins/spade.gif[/img]8 [img]/images/graemlins/spade.gif[/img]9 [img]/images/graemlins/heart.gif[/img]. The opponent had T [img]/images/graemlins/heart.gif[/img]T [img]/images/graemlins/diamond.gif[/img] and we thought he was the favorite because of his 14 outs (T [img]/images/graemlins/spade.gif[/img] not helping him).

Unfortunately we could not seem to figure out his chance of winning in a way that matched what twodimes said (48.38%).

My thought was 100%-(2 cards which don't help him)-(one card that helps him/one card that kills him(a ten))-(second card that helps him/first card kills him(ten)) or:

1-(31/45*30/44)-(2/45*14/44)-(14/45*2/44)=50.2%

Any idea where I am going wrong?

Thanks!

Re: AsKs vs TT
 

you have 4 cards that invalidate the flush not 2. The 2 nines also kill you...

Of course both nines hitting and you win. It is a bit more complicated [img]/images/graemlins/smile.gif[/img]

pokerscott

Re: AsKs vs TT
 

I ran it on PokerStove enumerating all boards and got the following results:

AsKs - 48.6869%
ThTd - 51.3131%

There are 45 unseen cards. Looking at it from AsKs point of view:

2 cards (T [img]/images/graemlins/club.gif[/img]T [img]/images/graemlins/spade.gif[/img]) leave you with 0 outs
2 cards (9 [img]/images/graemlins/club.gif[/img]9 [img]/images/graemlins/diamond.gif[/img]) leave you with 7 outs (any A, K or 9)
27 cards (the blanks for both players) leave you with 14 outs (A, K or non-T [img]/images/graemlins/spade.gif[/img]'s)
6 cards (any A or K) leave you with 42 safe river cards (no T)
8 cards (non-T [img]/images/graemlins/spade.gif[/img]'s) leave you with 40 safe river cards (no 9 or T)

So AsKs will win:

(2/45 * 0/44) + (2/45 * 7/44) + (27/45 * 14/44) + (6/45 * 42/44) + (8/45 * 40/44)
= 48.6869%

Lost Wages

Re: AsKs vs TT
 

Ahh, that's what we were missing. Thanks for the help!