Alright, so who wants to show off their math wizardry?

Emperor IX

Emperor IX

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PokerStars Game #16571135279: Tournament #83916013, $3.00+$0.40 HORSE (7 Card Stud Hi/Lo Limit) - Level X (400/800) - 2008/04/08 - 01:34:45 (ET)
Table '83916013 1' 8-max
Seat 2: Emperor XIX (2384 in chips)
Seat 3: JPS19 (3124 in chips)
Seat 6: ecalien (6492 in chips)
ecalien: posts the ante 80
Emperor XIX: posts the ante 80
JPS19: posts the ante 80
*** 3rd STREET ***
Dealt to Emperor XIX [Ac 8h As]
Dealt to JPS19 [Qs]
Dealt to ecalien [Jd]
Emperor XIX said, "all skill"
ecalien: brings in for 120
Emperor XIX: raises 280 to 400
JPS19: calls 400
ecalien: folds
*** 4th STREET ***
Dealt to Emperor XIX [Ac 8h As] [Ah]
Dealt to JPS19 [Qs] [3h]
Emperor XIX: bets 400
JPS19: calls 400
*** 5th STREET ***
Dealt to Emperor XIX [Ac 8h As Ah] [3c]
Dealt to JPS19 [Qs 3h] [4d]
Emperor XIX: bets 800
JPS19: calls 800
*** 6th STREET ***
Dealt to Emperor XIX [Ac 8h As Ah 3c] [5s]
Dealt to JPS19 [Qs 3h 4d] [2s]
Emperor XIX: bets 704 and is all-in
JPS19: calls 704
*** RIVER ***
Dealt to Emperor XIX [Ac 8h As Ah 3c 5s] [9s]
*** SHOW DOWN ***
Emperor XIX: shows [Ac 8h As Ah 3c 5s X]

JPS19: shows [Qc 3d Qs 3h 4d 2s X]

What are my odds of:
Scooping
Getting scooped
Splitting
Overall odds of surviving the hand

I'd offer a big reward to whomever does it right first, but right now I can only spare $0.24 :eek:
 
OzExorcist

OzExorcist

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Stud8 makes my head hurt!

I'm assuming you're talking figures on sixth street for the river?

First thing's first, villain can't make a low hand, or a straight, or a flush. And you've got them beat for high right now.

So the only way you can get beat for high is if he hits one of two remaining queens, or the case three, to make a boat on the river. That's the easy bit, to my mind - they're at three outs, or 6.52% to make their boat.

Which means, unimproved, you scoop 93.48% of the time.

After that I've gotta admit, my math is a little bit fluffy. So my answers are:

You scoop: 93.48%, + (15.22%* of 6.52% = 0.99%) = 94.47%+**
You get scooped: 6.52% - 0.99% - (30.45%*** of 6.52% = 1.98%) = 3.55%
You split: 1.98%
You survive: 96.45%+

* giving you seven outs (three eights, three fives and the case ace) to beat queens-full or threes-full)
** plus a little bit more for the times when he catches a queen and you get the case three
*** giving you 14 outs to make a low (three twos, three fours, four sixes and four sevens)
 
Dorkus Malorkus

Dorkus Malorkus

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lol you got scooped didn't you? :p

i might have a look at this in a bit if i'm feeling sufficiently un-lazy
 
Dorkus Malorkus

Dorkus Malorkus

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1 J is dead in addition to yours and villain's cards (folded on 3rd)

X1 = your river
X2 = villain's river

We get scooped if...

X1 = 9,T,J,Q,K
AND X2 = 3,Q

X1 = 4+4+3+2+4 = 17 cards
X2 = 1+2 = 3 cards

X1*X2 = 17/39 * 3/39 = 0.436 * 0.0769 = 0.0335 or about 1 in 30.

We split if...

X1 = 2,4,6,7
AND X2 = 3,Q

X1 = 3+3+4+4 = 14 cards
X2 = 1+2 = 3 cards

X1*X2 = 14/39 * 3/39 = 0.359 * 0.0769 = 0.0276 or about 1 in 36

We scoop if we don't split or get scooped, thus we scoop 1-0.0276-0.0335 = 0.9389, or about 93.89% of the time.

We 'survive' if we split or scoop, thus we survive 0.9389+0.0276 = 0.9665, or about 96.65% of the time.

edit: well whaddaya know, Oz was right (the discrepancy is probably just rounding errors). :)
 
OzExorcist

OzExorcist

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edit: well whaddaya know, Oz was right (the discrepancy is probably just rounding errors). :)

Woo!

My figures don't take into account the case where villain makes queens-full and we catch the last three, as working out how to not double-count that out was gonna be too much for my poor little brain to bear. Figured it would've made less than half a percent of difference to the outcome and had us erring on the conservative side though.

So - given that we blanked the river but this post still exists, I take it the villain hit his three-outer? Ouch.
 
Emperor IX

Emperor IX

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So - given that we blanked the river but this post still exists, I take it the villain hit his three-outer? Ouch.

Yeah, he caught the case three and I failed to improve with a J :(

knocked me out of the HORSE tourney in 3rd obviously. steep prizes in that. I got $4.80 for third, second gets $7.50 ish, and first gets $12
 
OzExorcist

OzExorcist

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Don't have one actually - Full Tilt is the only site I play at.

My online bankroll is so small that I figure it's probably best kept in the one pile :eek:
 
Emperor IX

Emperor IX

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Don't have one actually - Full Tilt is the only site I play at.

My online bankroll is so small that I figure it's probably best kept in the one pile :eek:

Damn, well you have 24c with your name on it! lol
 
Dorkus Malorkus

Dorkus Malorkus

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Woo!

My figures don't take into account the case where villain makes queens-full and we catch the last three, as working out how to not double-count that out was gonna be too much for my poor little brain to bear.

seeing as i used 1-P(get scooped)-P(split), i think mine does (it's early in the morning, forgive me), and that might be where the 0.2% difference comes from. pretty negligible, heh.
 
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