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Analysis of the 3-bet - LONG
Introduction:
Okay if your lazy or you just don't care, this is going to be super long so either don't bother reading and learn nothing or get off your ass and try to understand so this will benefit you and me.
I hope I am wrong (and well I probably am somewhere in this post), since nothing is ever learnt from being right. I do however feel fairly comfortable with my analysis as I did it carefully, though I may have made numerous mistakes in both my assumptions and maths. Specifically, the part about the EV after villain calls our 3-bet. I basically don't know what to do here so I just went with what I felt was right, and am hoping someone will step in and correct that.
EDIT: Calculations have been fixed, total $EV was incorrect as the pot size was correct for postflop.
Assumptions:
-We hold AdKs
-Villain raises here with {77+, ATs+, KQs, AQo+}
-Blinds .50/1.00 for simplicity in calculations
-UTG folds 100% of limping range in this situation
-Villains continuing range to our 3-bet is {TT+, AKo, AQs+}
-Of villains continuing range, he 4-bets only {KK+}
-We 3-bet to $18, which is roughly 3.5x the raise (3.6 to be exact)
Now to disect villains raising range, taking into account our blockers:
Combo's of 77+ = (6*6)+(3*2) = 42
Combo's of ATs+ = (3*3)+(2*1) = 11
Combo's of KQs = (3*1) = 3
Combo's of AQo+ = (12*2) = 24
Therefore based on the assumed range, villain is raising a total of 80 combo's
Now to disect villains continuing range, taking into account our blockers:
Combo's of TT+ = (6*3)+(3*2) = 24
Combo's of AKo = (9*1) = 9
Combo's of AQs+ = (1*3) = 3
Therefore based on the assumed continuing range, villain continues with 36 combo's
Villain calls or 4-bets 36/80 combo's, = 45% of the time
Villain folds 44/80 combo's, = 55% of the time
Of the 45% continuation, villain 4-bets 6/36 combo's, = 17% of the time, thus calling 28% of the time he continues
Against villains continuing range:
equity win tie pots won pots tied
Hand 0: 52.251% 37.58% 14.67% 19305294 7535541.00 { QQ-TT, AQs+, AKo }
Hand 1: 47.749% 33.08% 14.67% 16992744 7535541.00 { AdKs }
Figuring out the expectation of 3-betting:
POT: $1 limp + $1 bb, + $0.50 sb, + $5 raise = $7.50 pot
We risk $17 to win $7.50
Case 1: Villain folds
EV = .55 (+$7.50) = $4.13
Case 2: Villain 4-bets KK+, and we fold
EV = .17 (-$17) = -$2.89
Case 3: Villain calls and we go see a flop with villain having about 52% equity. This is where I'm unsure of how to figure out the EV, because basically, we're assuming we win exactly 48% of the time and lose 52%. The problem with this is it does not take into account any postflop action, so it really depends on how villain plays postflop to determine whether we have an edge, what our implied odds are, and blah blah blah beyond this I'm stuck so I just did this (let me know if this is just fucked or whatever, but I'd really like to see some further analysis before anyone starts saying everything I've typed so far is wrong, which I think it probably is):
EV= .28(+$36.50*.48) + .28(-$36.50*.52)
= $4.9056 + (-$5.3144)
= -$0.4088
Total EV estimate:
$4.13 - $2.89 -$0.4088 = +$0.83
So according to my simplified scenerio, raising is slightly +EV. HOWEVER, this is based on many assumptions, and it also does not take into consideration at all how either villain or hero plays postflop. Because we are at a disadvantage being out of position, I would have to believe this number is actually quite generous. Figuring out anything beyond this is pretty ridiculous and I'd be surprised if anyone even though about it.
The assumption that we win 48% of the time postflop I believe is very flawed, but I'm really stumped on how many more assumptions we can make for this beyond preflop. Basically, it assumes no further betting postflop. Of course this won't really be the case :/
BASED ON FOLDING EQUITY ONLY: i.e, we give up on 100% of flops (another flawed assumption), 3-betting is -EV. We must squeeze out some value postflop for this to make us money.
Personally, I feel calling may yield a higher EV, even though 3-betting has been shown to be +EV. When making decions, we don't just want to take EV, we want to MAXIMIZE EV. I could do up the EV of just calling based on assumptions, but that's for another week, possibly month.
Blah blah blah, I'm done talking now. Please give me some feedback on this analyis if you feel like it or w/e. If somone could run the EV of just calling that'd be sick since we'd find out for sure whether calling>3-betting, though being out of position, I would never 3-bet here, as intuitively, I'm able to see that calling yields higher EV, for obvious reasons stated earlier.
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