50NL; KhQh on 8hJhAs board gets raised

[Sean Fraley]

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You guys are probably misunderestimitating the times villian has A[img]/images/graemlins/heart.gif[/img] X[img]/images/graemlins/heart.gif[/img]

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You're right. I reran it with all A[img]/images/graemlins/heart.gif[/img]X[img]/images/graemlins/heart.gif[/img] hands in villains range and that knocks Hero's equity down to 35% which is still profitable assuming that we have at least 20% fold equity.

[Dumle]

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Ok, I crunched some numbers and we need some FE, but I got it at about 3%, assuming 40% equity if called. Here's the math:

x = FE

31x + (1 - x)*(0.4*59 - 0.6*41) = 0
31x + 23.6 - 23.6x - 24.6 + 24.6x = 0
32x = 1
x = 1/32 = 0.031

Did you calculate with another equity Sean?

Dumle


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I put it in PokerStove with villain on a range of AJo+, AJs+ AA, JJ, 88, A8s, and A8o. The great thing about PokerStove is that it also makes sure you factor in the times that villain has a better draw or fills up by showdown. As far as fold equity, if you use Dan Harrington's rule that anytime a player makes a decent raise there is at least a 10% chance that they are bluffing, and add to this another 10% chance that villain will not be willing to call all-in with his hand, we have more than the 13% fold equity I estimate we need to turn a profit by shoving here.

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And with that range on villain, we have about 40% equity. And according to my math above, we only need him to fold 3% in order for an all-in to be profitable. How did you get 13%?

Dumle

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If if did my math correctly we are putting in 47% of the pot, which means that we need another 7% fold equity over our chance of winning to break even in an unraked pot. The other 5% is put there to represent what we need to win in this hand to keep ahead of the rake, and makes a necessary 12% to break even. The additional 1% added to make 13% is simply there to represent turning a minimal profit.

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Alright, I am confused. [img]/images/graemlins/confused.gif[/img] First off, did you discount the money that was raised preflop and on the flop? Because I get 41/100 = 41% (100 = 48 + 48 + 2 + 2) and (41 = 48 - 5 - 2). Secondly, this doesn't add up to my numbers, but makes more sense to me. Don't ask, I'll go through it all again.

Dumle

[Jouster777]

I used this range: JJ, 88, AQs-AJs, AhTh, Ah9h, A8s, Ah7h, Ah6h, Ah5h, Ah4h, Ah3h, Ah2h, AQo-AJo, A8o

However, the EV equation needs to be run against the calling part of this range not the entire range:
Board: As Jh 8h
Hand 0: 69.015% 69.02% 00.00% 21864 0.00 { JJ, 88, AhQh, AJs, AhTh, Ah9h, A8s, Ah7h, Ah6h, Ah5h, Ah4h, Ah3h, Ah2h, AJo, A8o }
Hand 1: 30.985% 30.98% 00.00% 9816 0.00 { KhQh }

That calling range means all AQ hands folded...9 of 42 combos or a FE of 21.5% making the EV equation:
31(.215) + (.785)*(0.3*59 - 0.7*41) = -$1.98

Admittedly using all A[img]/images/graemlins/heart.gif[/img]x[img]/images/graemlins/heart.gif[/img] may overestimate them and bluffs are not considered but I still like a fold.

[Lego05]

You guys did a lot of work on this while I was gone. I'm still gonna try to do the math myself tomorrow. Just real quick to emphasize something Jouster said:

When doing this equation you only stove the calling range. So if you're assuming he's going to fold his AQ no heart hands or somethig like that then you can't include AQ in his range when calculating hero's equity once called so that makes hero's equity lower.

Just going intuitively I don't think hero needs too much fold equity here to profitable....but I think hero actually has less than he needs. I don't really see a fold like Jouster suggests though. I would think a call is good.


Again I'll try to run my own math tomorrow.

[Dumle]

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You guys did a lot of work on this while I was gone. I'm still gonna try to do the math myself tomorrow. Just real quick to emphasize something Jouster said:

When doing this equation you only stove the calling range. So if you're assuming he's going to fold his AQ no heart hands or somethig like that then you can't include AQ in his range when calculating hero's equity once called so that makes hero's equity lower.

Just going intuitively I don't think hero needs too much fold equity here to profitable....but I think hero actually has less than he needs. I don't really see a fold like Jouster suggests though. I would think a call is good.


Again I'll try to run my own math tomorrow.

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Of course, only his calling range should be included. However, for some reason I did forget to include [img]/images/graemlins/heart.gif[/img]-draws in his range, though. Pokerstove gives:

Text results appended to pokerstove.txt

43,560 games 0.015 secs 2,904,000 games/sec

Board: 8h Jh As
Dead:

equity win tie pots won pots tied
Hand 0: 35.945% 35.75% 00.20% 15572 85.50 { KhQh }
Hand 1: 64.055% 63.86% 00.20% 27817 85.50 { AcAs, JJ, 88, AJs+, AhTh, Ah9h, A8s, Ah7h, Ah6h, Ah5h, Ah4h, Ah3h, Ah2h, Th9h, AJo+ }


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This is probably close. I am pretty sure we have some FE here, but don't know if we have this much.

Dumle

[Dumle]

Opps, just realized I must have deleted my math. Alright, here goes:

31x + (1 - x)*(0.36*59 - 0.64*41) = 0
31x + 21.24 - 21.24x - 26.24 + 26.24x = 0
36x = 5
x = 5/36 = 0.139 = 13.9%

Dumle