well, the tricky thing is you almost never fold AK hands (after you raised first) ) I mean, you need very obvious reasons for that. Playing with a short stack you fold more in wa/wb situations, for instance, with TT on a A 9 4 flop. There a 2/3 pot bet will normally make non-Ace hands fold and if we got reraised, we will be willing to safe our entire stack, since we have only 2 outs to improve in case we are behind (opponnet has an Ace).
With AK it is a different story. Basically, almost on any flop and against any range of hands we will have enough equity to call, meaning that we are pot commited. Lets play example hand:
We have AK.
Stack: 20BB
We raise 4BB from MP, BU calls.
Flop: Qh 7s 2c
Pot: 9,5BB
Stack: 16BB
According to the strategy we have to make a cbet of 7BB and fold to reraise. That kind of play will be likely correct in "TT on the ace flop" example, but it is not really the best play here.
We bet 7BB, our opponent reraises all-in.
Pot: 9,5BB + 7BB + 16BB = 32,5BB we have 9BB left -> pot odds: 32,5:9 = 3.6:1 -> we need to win in 21% of the time
If we assume that he makes a reraise only when he hit something strong, lets say with a range 77-TT, 22, AQs, KQs, AQo, KQo - we have 17% of equity (missing only 4%)
BUT! If we add at least one marginal hand, like AJ, our equity raises to 32% ! Therefore, unless we are up against VERY passive player, we are mathematically forced to make a call. (against unknown call will be also profitable in the long run, especially on the lower limits, since in reality players will have way looser range)
Now after we have figured out that in most cases we will have to play our hand till the end, we need to figure out what line has more EV: cbet/call or push first in?
Assumptions:
- flop, cards, pot and bets are the same
- we are up against moderatly agressive opponent:
Option 1: we cbet/call
Opp's pushing Range: 77-TT, 22, AQs-AJs, KQs, AQo-AJo, KQo
Our equity: 30%
Our fold equity: 40%
1) EV = 0.4*9.5 + 0.6*(0.3*25,5 - 0.7*16) = 3.8 + 0,6* (7,65 - 11,2) = 3.8 - 2.1 = +1,7 BB
Option 2: push
Opp's calling Range: 77, 22, AQs, KQs, AQo, KQo
Our equity: 10%
Our Fold equity: 70%
2) EV = 0.7*9.5 + 0.3*(0.1*25,5 - 0.9*16)= 6.65 - 3,55 = + 3,1 BB
This is just a simple example to illustrate why we are interested in maximizing the fold equity... Of course our FE will differ from situation and will depend on the opponent, but the general idea is the same:
Since we are commited after a cbet and have to call, it is reasonable to push directly to maximize our fold equity, which results in higher EV.
Can you please clarify it to me more detailed. Thanks a lot..
Statistically you are absolutelly correct...