hey bogdan!
Originally posted by BogdanPS
Playing is key to your progress. Studying a lot and playing little won't be very helpful.
You want to be able to put in practice the things you are learning before you forget about them and learn the next thing.
still struggling with this 
anyway, i thought i'd ask you this because you are good with numbers ♦ ...
was doing a bit of reading about EV and i decided to see what's going on with AK allin preflop since it's a spot i've always hated. ended up with a few more questions than i started...
1) does this look correct? (please bear in mind that i am not very good at maths but i'm trying to get better at poker maths so this might be a little off.) i know there are 2 ways of calculating EV that give the same result, so i was just using the way that i've seen the most often:
Spoiler
BTN: $12.03
SB: $14.34
BB: $10.52
UTG: $11.96
MP: $10.06
Hero (CO): $10
Pre Flop: ($0.15) Hero is MP with A
K 
2 folds, Hero raises to $0.30, 1 fold, SB raises to $1, 1 fold, Hero raises to $2.30…
--------------------------------
Assumptions:
Villain is an unknown but we assume he has some sort of 3bet bluffing range from the SB. We assume that he 3bets with the following strategy:
- Total range (total, T) = {QQ+, AKs, A7s-A2s, K9s-K7s, AKo, ATo, KJo} [7.09%]
- Value (continues, C) = {QQ+, AK} [2.56%]
- Bluff (folds, F) = {A7s-A2s, K9s-K7s, ATo, KJo} [4.52%]
We also assume that he will never call our 4bet; he only folds or jams.
Calculation:
Since we assume he continues with his value portion and folds his bluff portion…
FE = 1 – (C / T)
FE = 1 – (.256 / .709)
FE = 0.63
The probability of him calling is 1 - 0.63 = 37%.
We have a chance to win the pot when he folds 63% of the time, or win 38.82% (our equity vs. his C range) of the time when he jams and we are forced to call.
When he jams we our given the odds 77 / (124+77) = 38.308%, and therefore we have to call. If we account for our fold equity, then…
EV = P(villain folds) * (pot) + P(villain jams and we call) * (P(win) * (amount won) – P(lose) * (amount lost))
EV = 0.63 * 11 + ((0.3882 * 124) – (0.6118 * 77))
EV = 7.310433bb
If we assume 0% FE then…
EV = (P(win) * (amount won) – P(lose) * (amount lost))
EV = (0.3882 * 124) – (0.6118 * 77)
EV = 1.02819bb
2) so if that is right, then it tells us something not very new - that we can profitably 4bet/call AK vs a range of QQ+, AK and it is still +EV even when we have 0%FE. that's great for my peace of mind, but i want to know your opinion about the effect that rake has on this at nl25 and below... seems like if we remove 6bb from the amount that we can win we are left with 118bb (to account for ~5% rake) then, if we 4bet and then face a jam from our villain whose range is QQ+ and AK, our EV is then -1.301! which is only a really small difference, but it's still -EV. im just wondering if you have any comments about the effect that rake has and whether or not we should be slightly adjusting our strategy to account for this?
seems like overall if our villain is 3bet bluffing quite a lot, then the overall EV of the 4bet/call is fine simply because of the FE from our 4bet. but if they are 3betting a pretty narrow range it means our FE is going to be reduced and thus our EV drops...
i'm starting to see just how complicated EV can get when you start to account for future streets
soo what's your opinion about crEV? worth the $? i quite like doing this sort of work off of the table even if i get it wrong, but im just thinking if i plan on looking into the EV of some hands it might be much less tedious to just have the software to do it for me.
sorry this turned into an essay ♦