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I'm not sure exactly how villain will play certian hands such as sets/draws/pairs etc however I'm going to attempt to put him on a betting range on the river and then calculate the EV of just calling VS raising.
So villain check/calls two streets then leads the river for what looks alot like a blocking bet. Assuming he has at least a pair I'll give him this range. Feel free to add or eliminate hands as appropriate. I don't know if a 30/5 really knows what a blocking bet is, so I think he probably still has strong hands in his range here like sets as well as marginal ones such as KJ.
Villains range: Any 2 pair hand, Pair+busted draw, straight, sets, 1 pair, maybe as worse as 88. Let's assume he'll 3-bet AA/KK preflop so the only overpair he may have is QQ. He is fairly loose so I threw in a couple trash Jx hands that make 2 pair. Perhaps we could eliminate a few hands based on his betting tendencies, maybe QQ never takes this line on this flop for him. I decided just to include it anyway since after the analysis the range can be tweaked to whatever seems most appropriate.
Putting the following assumed range into Pokerstove we get:
Board: Jc Th 9s 5s 4c
equity win tie pots won pots tied
Hand 0: 54.545% 54.55% 00.00% 42 0.00 { KhKs }
Hand 1: 45.455% 45.45% 00.00% 35 0.00 { QQ-88, AJs, KJs+, J8s+, AJo, KJo+, J8o+ }
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So we're ahead of villains donking range, and of course we have equity to call here.
To show this: Equity Needed To Break Even = Amount We’re Calling/Total Pot After We Call - - - therefore: $11/($25.25+$11) = 30% aprox. to break even. So we're +EV calling.
Is raising more profitable?
Feel free to correct my math here as I may have made some mistakes. I'm going to show the average gain/loss of calling and raising to determine which will be more profitable based on the range I came up with.
NOTE: All calculations are approximations. Some decimals may have been ignored.
EV of Calling:
EV=P(win)($x)-P(lose)($x)
EV=.545(36.25)-.455(11)
EV=$14.70
Therefore, we expect to earn $14.70 if we made this exact call 100 times.
Let's assume he will fold a couple of the hands we beat if we raise, such as J8 and 88, but he will still call with top pair or better. Also assume we cannot get better hands than ours to fold, thus our equity vs his raise calling range is:
Board: Jc Th 9s 5s 4c
equity win tie pots won pots tied
Hand 0: 47.059% 47.06% 00.00% 24 0.00 { KhKs }
Hand 1: 52.941% 52.94% 00.00% 27 0.00 { QQ-99, AJs, KJs, J9s+, AJo, KJo, J9o+ }
EV of raising:
EV=P(win)($x)-P(lose)($x)
EV=.47(102.75)-.53(38.75) *
EV=$27.76
*Hero shove makes it $27.75ish for villain to call to win a $102.75 or so pot. We lose $38.75 this time because we matched villains bet of $11 and raised $27.75 more.
So in this case, according to the assigned calling range of villain, its better to shove. However, if we assign villain a tighter range, this may not be the case. To figure that out we'd have to run the math on a new calling range. If villain will lay down his hand (assuming he doesnt have the nuts), then we may have some fold equity, so either way I would think raising is more profitable than calling.
EDIT: I forgot to add T9o and T9s into the ranges, seeing as this would be likely in his range as well, although I don't think it will make too big of a difference equity wise. We're still looking at some EV here.
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