Prob from WSOP question

[shutupndeal]

Hi
read this and then I will have my question,

Stu Ungar raised preflop with the A /images/graemlins/heart.gif Q /images/graemlins/heart.gif, and Perry Green called with the 10 /images/graemlins/club.gif 9 /images/graemlins/diamond.gif. Ungar's hand, almost a 2-to-1 favorite preflop, became stronger as the hand progressed. On the flop, Green had an open-end straight draw, but Ungar had the nut-flush draw and two overcards; Flop came: 4/images/graemlins/heart.gif 7/images/graemlins/diamond.gif8/images/graemlins/heart.gif Ungar was now a 2.5-to-1 favorite. When the 4 /images/graemlins/spade.gif came on the turn, Ungar improved to almost a 3.5-to-1 favorite. A queen/images/graemlins/diamond.gif on the river gave Ungar his second consecutive world championship.

Ok now I just dont see these numbers?? I calculated it by the outs and yes I know to allow for the turn card and to multiply the outs divided by the total cards in the deck so what am I missing? Is there math off, would someone like to prove this mathematically real fast as I just was feeling comfy with these damned odds and now I feel lost again, to be fair to me it IS the full moon and I get concentration loss or impairment on the full moon! Lol, I know U dont believe it right, well I didnt either and you know "Hutchinsons Omaha point system" well ole Ed is trying to tell me <Hutch's first name, sorry> that the effects of the moon have never been proven, I said ask any policeman what happens during the full moon and ask him if its real or not! lol, I know this because I lived in Vegas long enough to watch the maniacs! : ) In all seriousness and not trying to go off-topic here but I do have a problem with this equation, anyone wanna take a crack at it please?

[bigpooch]

Greetings, shutupndeal!

I am not going to even attempt to calculate the odds before
the flop but will simply defer to the twodimes hand
analyzer:


1) Before the flop, Stu was almost a 2-1 favorite.

http://twodimes.net/h/?z=198938
pokenum -h ah qh - tc 9d
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ah Qh 1113389 65.02 592046 34.58 6869 0.40 0.652
Tc 9d 592046 34.58 1113389 65.02 6869 0.40 0.348

1/0.348 - 1.0 = 1.87 to 1 which isn't THAT close to 2-1 !

2) After the flop:

This calculation most people ought to be able to compute
but not necessarily in the heat of the moment! There are
going to be C(45,2) = 990 possible combinations of two cards
that will hit the board. Perry can win only if he makes his
hand: either a straight or a pair (or better).

Straight by hitting BOTH ends and no flush: 3x3=9
Straight by hitting one end twice: 2xC(3,2) = 6
Straight by hitting one end with no flush: 6x(45-9-6) = 180

Trips with no flush: 1+1 = 2
Pairing up on T and 9 with no flush: 2x2 = 4
Pairing up once with no flush, without an A, Q, J, 6, and
without an extra T or 9: 4x(6x3+2) = 80

The (6x3+2) expression comes from the 3 other suits for
ranks other than 7 and the 7 on the table is a diamond so
there are only two "safe" sevens. The ranks to be concerned
with are the ones other than A, Q, J, 6, T and 9.

Altogether, there are 281 combinations and as a double check
I include a twodimes output:

http://twodimes.net/h/?z=203983
pokenum -h ah qh - tc 9d -- 8h 7d 4h
Holdem Hi: 990 enumerated boards containing 7d 8h 4h
cards win %win lose %lose tie %tie EV
Ah Qh 709 71.62 281 28.38 0 0.00 0.716
Tc 9d 281 28.38 709 71.62 0 0.00 0.284

1/0.284 - 1.0 = 2.52112 > 2.5 so Stu is better than a 2.5 to
1 money favorite.

3) After the turn: Here, anyone can just count cards and
there are only 44 possibilities. There are six cards that
complete the straight without making a flush and only four
cards that give the T9o a pair without giving a flush. So,
Stu is a 34-10 or 3.4 to 1 favorite here.

To be consistent, I just include the twodimes result here:

http://twodimes.net/h/?z=203984
pokenum -h ah qh - tc 9d -- 8h 7d 4h 4s
Holdem Hi: 44 enumerated boards containing 4s 7d 8h 4h
cards win %win lose %lose tie %tie EV
Ah Qh 34 77.27 10 22.73 0 0.00 0.773
Tc 9d 10 22.73 34 77.27 0 0.00 0.227

As far as the numbers given, everything seems fine except
most nits would think being a 2-1 favorite before the flop
is being a bit generous to Stu.

All clear on the Western Front?


Cheers,

bigpooch

[BruceZ]

It's all correct.

On the river, 10c 9d has 10 outs with 44 cards remaining, so 34:10 = 3.4:1.

On the flop, 10c 9d can catch one of 6 straight outs on the turn which don't make Ah Qh a flush, followed by one of 35 cards on the river which don't make a flush. This probability is 6/45 * 35/44. He can also catch 4 which pair him without making his opponent a flush, followed by one of 29 cards on the river which don't make a flush. This probability is 4/45 * 29/44. He can also catch any of these two cards in the opposite order, but if we just double these probabilities, we would double count the times he catches outs on both the turn and the river, which has probability 10/45 * 9/44, so we have to subtract this off:

(6/45 * 35/44 + 4/45 * 29/44 )*2 - 10/45 * 9/44 = 1 in 3.52 or 2.52:1.

You can get the preflop odds from www.twodimes.net/poker (http://www.twodimes.net/poker) as 1.96:1 (using EVs to ignore ties), and you can use this program to verify the above probabilities as well.