Quote:
Originally Posted by 6bet me
Poker Maths regarding DLuo's ATs shove
Without blockers:
All suited broadways = 40 combos
AJo+/KQo = 64 combos
A2s-A9s = 32 combos
TT-AA = 30 combos
T9s = 4 combos
Total squeezing range = 170 combos
{QQ+, AK} = 34 combos
Defending range = 34/170 combos = 20%
With ATs blockers:
All suited broadways = 32 combos
AJo+/KQo = 52 combos
A2s-A9s = 24 combos
TT-AA = 24 combos
T9s = 3 combos
Total squeezing range = 135 combos
{QQ+, AK} = 27 combos
Defending range = 27/135 combos = 20%
Analysis:
So with or without the ATs blockers, I'm only defending 20% of hands against a 4bet jam. If we assume that the other players are always folding, and we deduct $15 for rake, then DLuo picks up $127 uncontested 80% of the time, and if ATs has 29.2% equity against a range of {QQ+, AK} when a $1177 pot is brewed, then he loses $(1177*0.292 - 570) = $226 in EV when called.
Conclusion:
(Wins $127 in EV 80% of time) + (Loses $226 in EV 20% of time) = EV gain of $56 by jamming ATs here. This means that it was a very profitable shove for DLuo, under these assumptions.
Yeah this isn't right. Bear with me here as these EV calculations while not difficult are quite tedious. Skip to the end if you can't follow it. I do have a degree in mathematics and checked over this carefully for errors, but it's always possible something got by.
TL;dr - The shove is actually really bad.
I'll walk through why, starting with simpler calculations and adding variables and adjusting ranges as we go on.
Let's assume the guys in the middle always fold. They don't and it affects the EV calculation drastically but let's assume it, why not. Let's also assume you 100% squeeze an UTG raise from MP the hands you listed like AJo and T9s and A6s, which if you actually did is pretty absurd, but let's assume it.
Your combinatorics work is incorrect. You squeeze 123 combos. You defend 27. Therefore you call 27/123 - .2195 and fold 96/123 = .7805. When you defend, the equities are
*******Equity*****Win*****Tie
UTG****29.31%**28.18%***1.13%*{ AsTs }
UTG+1**70.69%**69.56%***1.13%*{ QQ+, AKs, AKo }
There are four outcomes if the middle guys always fold, which again, they don't.
A) You fold and DL wins (15 + 15 + 15 + 90) - 15 = 125
B) You call and DL wins (15 + 15 + 15 + 570) - 15 = 600
C) You call and DL loses 570
D) You call and you both tie, and DL wins (15 + 15 + 15)/2 - 15 = 7.50
A happens with frequency .7805
B happens with frequency .2195*.2818 = .06185
C happens with frequency .2195*.6956 = .1526
D happens with frequency .2195*(.0113+.0113) = .004961
So the EV of the shove in fantasy land where you squeeze 10% from MP and middle guys always fold is
EV(shove) = .7805*125 + .06185*600 - .1526*570 + .004961*7.50
EV(shove) = 47.73
Not 56. I've also neglected tipping in all scenarios, which may or may not be relevant as I don't know if in Australian games you are expected to tip, but if you are the EV is a couple dollars less.
So under your assumptions the shove is okay, though calling in position with a hand that plays well multiway vs an aggrotard (you) who will triple barrel most of his range is almost certainly more +EV, and we can assume the other players usually call once the whale calls. I won't attempt an EV calculation 5+-ways at this juncture as there are too many variables but if DL flats and it goes 5+ ways he is playing ATs in position vs you (vs everyone if CO and BTN fold which they usually will) in a 450+ pot where 5 ways, given your squeezing range and some typical ranges for the other guys he has about 20% raw equity in position vs. some very bad players. If DL flats and the others fold, even better, as he now has 48% raw equity with a hand with good robust equity, in position, vs. an aggrotard (you).
If we come back to planet earth and put your squeezing range at more like 7% (still too wide, but probably about what you play), say, these 87 combos: JJ+,ATs+,KQs,KhJh,KsJs,KcJc,QhJh,QsJs,QcJc,KhTh,Ks Ts,KcTc,QhTh,QsTs,QcTc,JhTh,JsTs,JcTc,Ac9c,Tc9c,Ac 8c,Ac7c,Ac6c,Ac5c,Ac4c,Ac3c,Ac2c,AQo+,AdJh,AdJs,Ad Jc,AhJd,AsJd,AcJd,KdQh,KdQs,KdQc,KhQd,KsQd,KcQd
Now we have the EV(shove) = (60/87)*125 + (27/87*.2818)*600 - (27/87*.6956)*570 + (27/87*.004961)*7.50 = 15.64
We are still assuming everyone else always folds, which again, they do not.
Another question is, if you think DL is correct so shove this wide, why the **** would you only continue with QQ+ AK? You're only ~100BB deep, are you really folding JJ? TT? AQs? You 3-bet A7s but fold JJ? Getting (570 + 15 + 15 + 15 + 90) : 480 = 1.46875:1? I'm skeptical. You only need to win 40.5%. If you guess DL is shipping something like TT+,ATs+,KQs,AQo+, TT has 42.66% equity and AQs has 43.34%. Let's suppose you call TT+, AQs+, AK. Now you have 39 combos to call and
EV(shove) = (48/87)*125 + (39/87*.2968)*600 - (39/87*.6315)*570 + (39/87*.0718)*7.50 = -12.32
We are STILL assuming UTG never calls which is ridiculous. He's probably raising something like 99+,ATs+,KQs,AQo+,KQo, and open limping hands like 88 and QTo. Maybe not, "whale" is such a meaningless term but I'm just taking it to mean a typical bad LP player. He could be much tighter or much looser. But if he is tighter he has more premiums to call the 4 bet with and if he is looser he calls the 4 bet lighter, so let's just guess it's these 76 combos. And let's assume he calls JJ+ AK. That's 33/76 = .4342, so clearly this guy has a large effect on the EV of a 4 bet. I'm going to ignore the other guys flatting KK+ to trap, which happens from time to time but is too complicated to calculate and doesn't have a huge effect on the result like ignoring UTG does.
So let's see what happens if UTG calls sometimes. Back to your original scenario where we had the four outcomes A through D. I'm going to ignore ties for the 3-way calculation as it is complex enough already. Now we have outcome A, both fold, B, you call and DL wins, C, you call and DL loses, D, whale calls and you fold and DL wins, E, whale calls and you fold and DL loses, F, whale calls and you call and DL wins, and G, whale calls and you call and DL loses. I'm ignoring side pot considerations because that makes this mess even more complicated. Assuming effective stacks of 570.
A happens with frequency (43/76)(96/123) fold fold
B happens with frequency (43/76)(27/123)(.2818) fold call DL win
C happens with frequency (43/76)(27/123)(.7182) fold call DL lose
D happens with frequency (33/76)(96/123)(.2887) call fold DL win
E happens with frequency (33/76)(96/123)(.7113) call fold DL lose
F happens with frequency (33/76)(27/123)(.1852) call call DL win
G happens with frequency (33/76)(27/123)(.8148) call call DL lose
(43/76)(96/123) + (43/76)(27/123)(.2818) + (43/76)(27/123)(.7182) + (33/76)(96/123)(.2887) + (33/76)(96/123)(.7113) + (33/76)(27/123)(.1852) + (33/76)(27/123)(.8148) = 1 as expected
EV(shove) = (43/76)(96/123)*125 + (43/76)(27/123)(.2818)*600 - (43/76)(27/123)(.7182)*570 + (33/76)(96/123)(.2887)*600 - (33/76)(96/123)(.7113)*570 + (33/76)(27/123)(.1852)*1155 - (33/76)(27/123)(.8148)*570
EV(shove) = -77.72
This is the conservative case where OP is squeezing 10% and defending only QQ+ AK.
In the case where OP squeezes 7% and defends JJ+ AQs+ AK we have
EV(shove) = (43/76)(51/87)*125 + (43/76)(36/87)(.2870)*600 - (43/76)(36/87)(.7130)*570 + (33/76)(51/87)(.2887)*600 - (33/76)(51/87)(.7113)*570 + (33/76)(36/87)(.1860)*1155 - (33/76)(36/87)(.8140)*570
EV(shove) = -117.25
We can see how easy it is to manipulate the math to convince ourselves some sketchy move is "fine" but if we remove the simplifications it's actually very not fine. This shove is pure spew once we account for the possibility UTG calls, even if we use OP's ridiculous MP 10% squeeze 2.2% defend ranges. If he squeezes even slightly less and/or defends just a little wider we are torching money.
And again it's worth noting it isn't enough just to be +EV, we need a shove to be better than flat calling.
I'm not pointing all this out to make anyone feel bad. People make mistakes playing poker. The real mistake is when looking at the hand doing a biased and unrealistic analysis to justify our bad play as correct rather than looking at the situation objectively, realizing you made a mistake, and not repeating it in the future.
EDIT: Left out the blinds which makes a small difference, add a couple bucks to each result. But I also neglected tipping, so remove a couple bucks for each result.
Last edited by Shai Hulud; 12-10-2018 at 01:01 AM.
Reason: correction