dgi and Avaritia I agree with most of your analysis, but I also think you're oversimplifying the situation a little bit. CallMeVernon basically sums up what I was thinking here:
The operative question we need to be asking is "does the extra money we make from V1 by flatting outweigh the money we lose from V2 due to the fact that he is more likely to fold postflop than preflop?". I think it's a pretty legitimate question, and you can make arguments for either side, but if you aren't weighing both sides of the question against each other then your analysis is incomplete.

If V1 almost always folds even when we flat then we aren't making much more money from him by doing so, and therefore it's probably better to shove and maximize what we can win from V2. By the same token but conversely, if V2 almost always stacks off on any flop, then we're not losing a lot of value against him by flatting, so it's probably better to take that route and try to win extra money from V1.

It all comes down to reads at this point. If both players were confirmed regs then I prefer a shove, because both V2's cold-4bet and our flat should look strong enough to get V1 to fold all but the top of his range, and our flat should also scare V2 into playing cautious postflop, while shoving is the best way to rep AK. However, given that we're essentially readless on V1 and thus must consider the fact that he could be less than stellar, and that we know V2 to stack off too lightly postflop, I think flatting is the better play. But it's certainly closer than dgi and Avaritia suggest, and as I hopefully made clear it can easily change to a shove if our reads change.

fwiw I definitely agree that "protecting our aces" or worrying about getting drawn out on or outplayed postflop should not really enter into the equation here.

this. To be clear we are stacking off on every flop even if it comes kqj monotone with none of our suit. The only reason to 5bet is if the 4bettor is certainly stacking off and if other villain will fold everything but kk+ or maybe qq+ even if u flat 4bet. Yes flatting increases variance but this is the one time flatting is perfect. Even if both have pocket pairs thy only have 24% chance of hitting a set on flop combined. The point is u will still have the best hand on the flop 76+% of the time regardless of their hands and u could be an even bigger favorite if they have ace high or other non pocket pair hands

Btw aa is the one hand I'd flat here. With kk just 5bet pre, u want to charge an ace to outdraw u and u could be left guessing if an ace flops and ur up against two villains wih a pot sized bet left

I think stacking off on kqj monotone not our suit is equivalent to writing the villains a big juicy cheque.

I like the discussion very much, because I really wasn't sure what to do - good to see, that there really are more opinions on how to play it (still don't know though what is the best).

But my thinking was though...if I flat, I can make villain 1 call - I think he will put me on JJ+/AK here, but will think I could play AA this way too. Villain 2 is not even thinking in terms of ranges I would say and will not put me on AA often here. He will think I have 1010+, AQs+ probably.

So I tried to think about it quickly when I saw the 4bet, and came to this: If I flat, villain 1 will flat JJ+/AK, and shove KK sometimes and flat sometimes I think - this could not be right maybe and he would also call with 99/1010 but at the time, I didn't think so. I also didn't think he shoves with AK with only 60 invested against 4bet and call from tag in UTG+1. So I guess he flats almost always if he has the goods.

On the flop with pot around 480 I would bet my last 410 unless I flop trip aces and better and no draws possible there. I thought about check/calling on flop, but thought that donking is better here - but didn't really know why (I would think about it differently now and have plan to check/call if flop is not with FD or with some gutshots...).

So I would bet if I flat pre and on...

dry small flop
- Villain 1 could look me up sometimes with JJ/QQ, calls always with KK and "hopes" that villain (and me too) has AK or worse pair than he has. Also Villain 2 will overcall with overpair here everytime and folds AK/AQ.
- Villain 1 folds his unpaired hands and sometimes JJ/QQ and Villain 2 looks me up with every overpair and folds AK/AQ

On A or K high flop
- Villain 1 looks me up with AK and folds rest
- Villain 2 looks me up with AK and folds rest

What I didn't like was, that I take two outs to AK, so AK will not hit the flop a lot of times and will be able to fold on the flop. So when the situation is something like one has AK and other has JJ+ and I get small flop, I get still only one of them to call at most. If both have JJ-KK, I can get both to call on small flops only sometimes. If both have AK, they both fold on majority of the flops (they have only 2 outs).

Results:

The results don't confirm it's the best play at all. ROT much?

I think you can come up with a mathematical relationship for this exact situation.

Hero opens with raise, V1 3-bets, V2 4-bets, Hero???

V1's 3-betting range = X
V1's 4-bet calling range = W
V1's 5-bet calling range = Z
V1's preflop stack-off range = Z
V1's post flop stack-off range = X or W or Z > flop

V2's 4-betting range = Y
V2's 5-bet calling range & preflop stack off range = Y
V2's postflop stack off range = Y > flop

Lets look at the case of Hero flatting the 4-bet

In this case

X*p1 = W
p1 = variable for percentage of range. if p1 = 90% then that means that V1's 4-bet calling range is 90% of his 3-betting range. if p1 = 100% then that means that V1's 3-betting range is equal to his 4-bet calling range.

A = percentage that V1's range is ahead of the flop
B = percentage that V2's range is ahead of the flop

If Hero flats, then the math would involve V1's 4-bet calling range and then the percentage that this calling range is greater than the flop PLUS V2's 4-betting range and the percentage his 4-bet range is greater than the flop.

flatting scenario
(W x A x V1's stack + Y x B x V2's stack) x Hero's equity = EV

Conversely, if we shove preflop then
X*p2 = Z

p2 = variable for percentage of range. if p2 = 20% then that means that V1's 5-bet calling range is 20% of his 3-betting range.

(Z x V1's stack + Y x V2's stack) x Hero's equity = EV


So, what all of the above translates to is: If V1's 3-betting range is fairly snug, JJ+, AK and if V2's 4-betting range is also very snug like QQ+, AK and both ranges are likely to be ahead of most flops, then flatting is going to yield you more money.

However, if V1's 3-betting range is just a touch wider like TT+, AK, AQ and if V2's 4-betting range is just a little looser, 99+, AK, AQ, AJ but at the same time V2's 4-betting range is equal to his preflop stack off range, then shoving is going to yield you more money.

My above math formulas might not be exact, but they conceptual make the point.

I will circle back and tighten up the formula, but after thinking this through here is my conclusion.

If we have AA and are facing 2 villains with heavy preflop action and we know with near 100% certainty that one of the villains will definitely stack off preflop AND this same villain has a fairly wide preflop stack off range but post flop will only stack off if ahead of the board, then the most optimal EV line is going to be to shove preflop.

I'm going to try to come up with an analytical model and equations for this exact scenario to identify the exact cut off points. This is a sliding scale depending on villain ranges. It will probably take me a couple of days and I will post it in the poker theory section and then I'll bump this thread and put a link to the new thread I start in poker theory...

a lot of good talk in this thread, but this basically summed it up in a nutshell IMO.

totally agree with you. This was my point all along. we have a fish ready to stack off with a dominated hand, why risk letting him fold on the flop? Plus it would have been hard to get V1's money post flop no matter what line we would have took.