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big. we are pretty damn deep on the flop with a huge hand against a villain who sucks. and it was only min-raised pre. we need to be able to get our stack into the pot. villain's calling range is basically "hands which will call a raise here and likely pay us at least another street" (Ax, flush draws, sets, aces up), and "hands which are pretty damn weak, which will struggle to catch up, and rarely pay us off when they do" (underpairs, missed broadways). so we clearly need to maximise our expectation vs the first range, seeing as we hardly lose value against the second one (by taking an aggressive line on the flop) because it rarely, if ever, gives us another street of $ anyway. also, i think the money we win on average when we raise it up and get another couple of streets from Ax or flush draws considerably outweighs the money we make on average by taking some other line designed to have the parts of his range continue which will rarely make a decent hand with which to pay us off anyway.
convoluted sentences aside,
given that villain is a very weak player who probably cant fold top pair or any 8+out draw, and may see us as aggressive if he's paid attention to history, i don't mind being completely un-balanced with our sizing here and just bumping it up to ~$4.75. bearing in mind that we can get the money in over:
1 street with an SPR of 1
2 streets with an SPR of 4
3 streets with an SPR of 13
(assuming pot-sized bets)
we need the pot to be at least ~$10 going onto the turn if we are to get the money in by the river without over-betting. i doubt this guy's calling range changes significantly vs any raise size between $2 total and $5 total. so the absolute minimum i make it here would be $4, and i may go as high as $5.25 or $5.5 if the table dynamic has been particularly aggro and gambooly (ie high avg. pot), or if i have some reason to believe this guy is tilted in general, or pissed off at me specifically. in this case, i think $4.5 or $4.75 would be my size.
and on the turn i'm planning to bet at least 4/5 pot on most cards when checked to, or raise slightly more than required to get the money on the river when called, if he leads into us.
edit: now i think about it, i prefer something like $5 or $5.25 due to the logic outlined above. lets get the money in.
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