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More analysis - same hand. No, I'm not in love with it.
Villain POV:
ATs on BTN is a playable hand - the tight aggro "Hero" fella on the right raises to 4bb and villain decides to play ATs in position.
Table has been very passive so this could be an out of position steal with air, but best probably to give him credit for a proper hand. Call it any pair (raised to disguise smaller pairs), any two broadways, any suited connector 87s+, any suited one-gapper J9s+ (Yep, same as villain range in version 2 above).
Preflop Equity:
AhTh: 51.46%
22+,ATs+,KTs+,QTs+,J9s+,T9s,98s,87s,ATo+,KTo+,QTo+ ,JTo: 48.54%
Hero didn't get a chance to 3bet, so AA etc is not removed from his range.
Flop Equity:
AhTh: 37.68%
22+,ATs+,KTs+,QTs+,J9s+,T9s,98s,87s,ATo+,KTo+,QTo+ ,JTo: 62.32%
Ok, flop hits the Hero's range better and he's donking it or c-betting or whatever you call it when he's second of three to act. Villain's gutshot looks like it has good implied odds on an aggro Hero and who knows - if a heart comes on the turn equity goes up. Worth a call for one more card certainly.
Unfortunately this Hero's been c-betting a lot before and we can't really say for sure that he would slow down and slowplay a set or boat. He's representing because the board is scary.
Ok, I've talked myself into a corner here. I can't view Hero in an unbiased manner, because it's me - and I probably would bet any two cards because the flop is so scary. Could someone please give me some Hero pocket holdings that he would not bet here? Any pocket pair I'd semi-bluff with as I can't know for sure if the other guy has a J until he looks me up. Any two broadways give something I'd bet in this way even if only a straight draw. J9s, T9s qualify. Only two hands I'm not sure about are 98s and 87s. Ok, let's rule those two out for a not much slimmer hand range.
Turn Equity
AhTh: 44.11%
22+,ATs+,KTs+,QTs+,J9s+,T9s,ATo+,KTo+,QTo+,JTo: 55.89%
Now, which hands would Hero make the turn bet with. Let's have a look at post turn bet equity. With the T on the board straight is much more likely and any hand threatened by the straight draw would bet to find out where it is at or price out any straight draws. Maybe this would be a good spot for Hero to slow down a KK, KJ, JJ, KT or TT hand. AQ now has the made straight, but could not slow down as the board has paired and a boat may be in the offing. Underpairs probably slow down. They're still made two-pair hands but they would rather check to a showdown than pay for it.
AhTh: 21.82%
AA,QQ,ATs+,KQs,QTs+,J9s+,T9s,ATo+,KQo,QTo+,JTo: 78.18%
Ok this is funny - and probably misleading. Is it fair to use that range for Hero's hand in this situation as villain?
River Equity (same range as the bet above):
AhTh: 72.14%
AA,QQ,ATs+,KQs,QTs+,J9s+,T9s,ATo+,KQo,QTo+,JTo: 27.86%
Ok, the river hits our villain well! Hero checks - which hands would Hero only check with in this situation? What's he afraid of? Is he trying to induce a bluff? We've already taken a lot of boats out of his range because we thought he'd slow down with them on the turn. So what would he bet at this point? All remaining kings just made their boat (AK and KQ) and might be making a value bet. Would an AQ straight dare go for a value bet with 2 pairs on the board? Doubtful. They'd likely call a smallish bet though. Any remaining Ts would probably also do a value bet. AT, QT, JT, T9s. So - because Hero checked we have the below:
AhTh: 100%
AA,QQ,ATs+,KQs,QTs+,J9s+,T9s,ATo+,KQo,QTo+,JTo: 0%
Villain really should have value bet the river.
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