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What are your stats? That is really a huge indicator of how you can play spots like this. If you have a tight image (don't steal a lot), you can tend to give Villains a bit more credit.
Regardless of the answer to that question, I think Hand 1 here is pretty standard 4bet/call. Make it like $8.50 and call it off. Villain seems pretty aggressive and is probably going to reraise wide in the BB against an SB open raise. I think your range is too tight for him; in particular you can't reference his overall BB stats (where he's usually OOP) when you're in a BvB spot.
Hand 2 isn't really a similar spot at all. For starters, there is a huge difference between a 21/19 and a 13/10. I think your range for this guy is a little more accurate, though. I really hate this spot, but let's consider our options:
1. Fold - We have AK BvB at 6max. We have blockers to the strongest part of his range. If we are raise/folding AK, we are almost always raise/folding the SB. And we are getting 2:1 just to call. Folding seems pretty bad.
2. Raise/call or raise/fold - We 4bet to about $7.25 and BB shoves. Now we only need 38% equity to call. If he's shoving exactly QQ+/AK, then it doesn't matter if we call or fold. If he's not always shoving QQ and AK, we need to be folding. If he's ever shoving JJ and especially AQ, we have to call. So 4betting kind of sucks because it leaves us with a terrible guessing game. And when he flats, he's probably not putting in much more when an A or K comes unless he has us beat (I guess he could sometimes have AQs or AJs?).
3. Jamming - This could be the best option, but I think it depends a lot on gameflow... if I had lost a big pot or been raise/folding a lot, a shove here is cool because it looks tilty and AQ might even call us. Obviously if we shove AA/KK in this spot (not the worst play against a tight reraiser) then we definitely should shove AK as well for balancing/fold equity reasons.
On the other hand, if we have 4bet small and gone to showdown with a big pair, a shove kind of sucks because it looks exactly like AK and he is going to play perfectly against us. But our equity combined with even a little fold equity (AQ and whatever else) might cause the shove to still be profitable.
As a sidenote I would raise/call AK in Hand #1 the same way that I would TT, so the decision to jam in Hand #2 is more because Villain is tighter and raise/fold and raise/call can both turn out pretty awful given the way the odds work out.
4. Call - I don't think calling in Hand #2 is all that bad with AK. We're getting 2:1 and that's pretty close to our chances of flopping a pair. We keep his range wide so that when he has AQ and the A comes, we can win a nice pot. In general if the flop comes A- or K-high he might make a bad cbet, so checking to him on the flop would be optimal. If he checks it back, we can lead like half pot turn and river expecting him to call us down with KK or QQ or a pot-controlling AQ/AJ. In fact, maybe calling could be the best play in this spot. It also balances our calling range a bit so that we can be strong on just about any flop.
As for 4-bet sizes, I heard a pretty good rule of thumb from a GrinderSchool video. Take the amount that Villain reraised you, double it, and raise that much more. So:
Hand 1: 3.25 - 1 = 2.25 * 2 = 4.5 (raise to 3.25 + 4.5 = 7.75)
Hand 2: 3 - 1 = 2 * 2 = 4 (raise to 3 + 4 = 7)
I like to add another BB when I'm out of position, and even a little bit more when we're deeper than 100 BBs, which is how I arrived at the totals indicated above.
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