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Alright, so first of all let's try and get a rough idea for what hands he could be holding on the river.
Preflop: So he's raising 22% of hands, but probably a much tighter range from UTG+1, let's say something like: {AJ+, KQ, QJs, 66+)
Flop: If he's a run-of-the-mill reg like you suspect then he could easily be c-betting his entire range here, so it remains unchanged.
Turn: When he checks here I think we can say that he very rarely has hearts, or he'd be firing a second barrel. He's also not betting TT or 99 on the flop and then checking this turn I don't think.
So his range seems now to be: {AJ+, KQ, QJs, 66, 88, JJ+, but with no suited hearts} - I'm not sure how he plays JJ+ here, but I could maaaybe conceive he fired a cbet with them and is now scared you have a T, so I'm keeping them in there.
River: Maybe the flush coming in scared him, or the paired board, so I don't really want to eliminate KQ from his range based solely on his check. I think he's betting JJ however. In any event his range now consists of a bunch of missed hands that aren't calling anything (and that we beat if we check behind) so are largely irrelevant and this subrange, from which we could get value: {AJ, KQ, QJs, 88, QQ+}
And this is where I just sorta break down into even rougher guesswork, and start spouting stuff like this:
Hands he's calling 1/2 PSB with: {AJ, KQ, QJs, 88, QQ+} (All of the subrange that I decided we could get value from. 52 combinations, 100%) $2.5 * 100% = $2.5
Hands he's calling a PSB with: {KQ, 88, QQ+} (37 combinations, 71% ) $5 * 71% = $3.55
Hands he's calling a shove with: {KQ} (16 combinations, 31%) $24 * 31% = $7.20
So according to that a shove is best, but if I'm being honest I think it's marginal that he's actually calling a shove with the straight. Also a lot of you probably disagree that he never has hearts. In any event, this wasn't supposed to be definitive just some practice analysing I guess. Comments welcome!
Oh, and Surviva:
-Mark
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