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Okay so here's my analysis.
1. I really don't like the threebet size and I think its definetely an issue that should be brought up. He's going to be calling much tighter and your building a pot with a weak range OOP.
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My first thought when I looked at this hand was vbet. Now I'm reconsidering. I considered both value calling range girth and raise/call range we lose. AA/KK are two hands im expecting that if we get called and lose this will be his hand, but it can also be AT, 77, but that's extremely unlikely. His value calling range is JJ, 88, 99. Now that's 3 hands versus 2, those are his [b]range girths[b], and assuming each hand is just as likely as the other (all are pp's so yes, I think it goes suited hands, pp's than unsuited hands as least to most likely), than this is an +EV value bet.
But there is some other things we need to consider. Is check/calling better? Well there's also the chance he has 66-22 and bluffs, or some random hand and bluffs. And there are only 2 hands that would bet and we would be losing AA/KK, + but also an unlikely AT or quad 77. 66-22 on the other hand is 5 hands, + there could be other ones.
The issues here are hand frequency. AA/KK we cant bet sure wont raise the flop, so thats a little less likely. 66-22 may not call preflop or on the flop, and may even not bluff, so that's even more unlikely. He's also unlikely to have any hand he would want to bluff. So there I think c/c would be a little -EV.
But we incorporate this concept into vbetting, we still are pretty convinced to vbet. JJ, 99,88 all seem to be very likely, moe likely than AA/KK, as we can reasonably expect flop calls sometimes from these hands or a fourbet preflop. Yet, if we get bluff raised randomly sometimes, AND most of all JJ-88 aren't always calling, in fact they probably aren't calling a majority of the time, besides JJ. In conclusion though, this seems slightly +EV to b/f.
If it was just on the -EV side though, we would have 2 -EV decisions. So in that scenario we would rather take the 0 EV option, c/f.
I thought this was interesting because the river range off opp was so wide.
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