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he probably has some random suited bullshit in his range depending what hands he likes to 3bet (i.e suited bways or scs) so by checking we give him the opportunity to bluff these hands.
it seems unlikely we get 3 streets from much worse, people flat TT and JJ often preflop too when they arent sure about whether they can get it in vs a 4bet range so I think we can even discount those hands. we could make an arguement for discounting AA as well since sometimes people will 5bet it.
keeping villains range wide here is ideal, and we shouldnt really care much about a ace or king turning/rivering. thats 6 outs, and we could peel club turns on a card that will likely get bluffed enough for us to get away with it, so effectively less.
against a get it in range on the flop (included all combos of JJ but no TT) our equity is only 40%. I kept all JJ and AA in because I think they are both equally as likely - sometimes JJ will not 3bet preflop, and sometimes AA will flat our 4bet. we just need to approximate anyway, knowing how our hand stacks up vs different parts of villains range is the focus here:
Board: 8c 3c 8h
Hand 0: 59.284% 57.21% 02.08% 78159 2835.00 { JJ+, AcKc, AcJc, AcTc, Ac3c, Ac2c }
Hand 1: 40.716% 38.64% 02.08% 52791 2835.00 { QQ }
while we would be priced to get it in I think, or at least damn close if we take a c/r line and bloat the pot with dead money, we are narrowing villains range to him basically never getting it in w/ worse. there must be a more profitable line.
our equity against a range of some hands that would bluff (AK may bet but should pretty much always check imo) but if he never checks it:
Board: 8c 3c 8h
Hand 0: 23.601% 23.60% 00.00% 43458 0.00 { AKs, AJs-ATs, A3s-A2s, AKo }
Hand 1: 76.399% 76.40% 00.00% 140682 0.00 { QQ }
I chose some random suited Ax for this range, though perhaps some more middling gapped broadways and fewer Ax would be approriate (keep in mind that just about everyone flats 4bets ip with various suited shit at 100bb, so this deep its a given)
Board: 8c 3c 8h
Hand 0: 22.730% 22.73% 00.00% 45900 6.00 { AKs, A5s, KJs-K9s, QTs, AKo }
Hand 1: 77.270% 77.27% 00.00% 156048 6.00 { QQ }
you can see here that we have really awesome equity vs any potential bluff hands in villains range. you can add or subtract hands as you see fit depending on how you think his range is composed. if you think he only has AK:
Board: 8c 3c 8h
Hand 0: 26.386% 26.39% 00.00% 25077 0.00 { AKs, AKo }
Hand 1: 73.614% 73.61% 00.00% 69963 0.00 { QQ }
There are 16 combos of AK which we beat. We can stack maybe 6 combos of JJ or worse which we are way ahead of, though that would be very optimistic. We want AK to put money in the pot. With 26% equity against us, we aren't really worried about giving a free card when we would win checking to showdown 73% of the time. And if villain has worse hands than AK that start betting... he is making an even bigger mistake.
This is a classic way ahead way behind scenario where we have little to no incentive to worry about betting to protect our hand, which makes check calling flop the optimal line.
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