I try solving it with mathematics. (To make it not to complicated I don't calculate with the outs we or he has. Feel free to calculate it if you want so.)
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Line: Donk/call flop, check/call turn, donk/call river.
Hand counts for:
- AK: 6
- QQ: 6
- AA: 1
- KK: 3
Now let's see what we gain with the above line:
- 12 times 3BB (AK, QQ)
- 1 time 0BB (AA)
- 3 times -4BB (KK)
= 24BB/16 = 1,5BB each time.
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Line: Check/raise flop, bet/3-bet/calldown turn, bet/call river.
Now lets say we play the standard valueline with check/raise flop, bet turn and bet river.
If he 3-bets the flop we check/raise the turn and calldown to a 3-bet.
If he raises the turn we 3-bet and calldown to a cap.
if he raises the river we just call.
I think he will call our check/raise and raise the turn with AA, KK and AK.
The more difficult part is how he plays with QQ. Maybe he folds the QQ to our check/raise, at the turn, at the river or even calls it down. I think if we calculate with the middle we have a good approximation.
He will cap with KK on the turn.
- 6 times 5BB (AK: 1BB flop, 3BB turn, 1BB river)
- 1 time 0BB (AA: split)
- 6 times 1,5BB (QQ: 1BB flop, 1BB turn, 1BB river divided by 2)
- 3 times -6BB (KK: - 1BB flop, - 4BB turn, - 1BB river)
= 21BB/16 = 1,3125BB each time.
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Line: Check/raise flop, bet/calldown turn, bet/call river.
Now let's consider fdwarriors line:
"if he call or raise flop donk with QQ, he would definitely cd it after c/r, so the best line here is to c/r flop, bet/cd turn because i think villain would raise turn only with
KK - 3 combos
AA - 1 combo
AK - 6 combos ( not 10 ciRith ) with weight of 0.5"
- 3 times -4BB (KK: 1 BB flop, 2 BB turn, 1 BB river)
- 1 time 0BB (AA: split)
- 6 times 3BB (QQ: 1BB flop, 1BB turn, 1BB river)
- 6 times 3,5BB (AK: 1BB flop, 1,5BB turn (he will raise the turn 50$ of the time), 1BB river)
= 27BB/16 = 1,6875BB each time.
So we got the same result and we are indifferent in which line we play.
EDIT1: Corrected a mistake and added fdwarriors line.
EDIT2: Changed the played line by Classicals note. (It's even lower because of my mistake pointed out at EDIT1.)
"Minor point: against KK we lose 4BB, as villain will raise the river. We won't fold to a river raise, will we? This makes 1,8BB EV"
EDIT3: Added the "line-headers".