Quote:
one thing you’re not factoring in is that AK has a lot more combos than AA KK.
16 vs. 12. Yes, I factored that in.
Quote:
Even if you just call and donk shove every flop with no A or K, you’d still make more money than going all in pre vs a range of JJ+ AK, providing villain never folds pre, and JJ calls as overpair always.
...do the math.
Well, I don't really agree that JJ is in that range, but let's run with it:
Note that I don't advocating going all-in pre but folding pre in this case - so that will be my baseline. Also note that if we plan on going all in post on a non-A/K flop then this is, IMO, worse than going all-in pre because he might call it off with AKs pre, but not post..., but I will try to show that call-shoving on a flop without an A or K is already worse than folding
Assumption:
- Stacks 300 effective before the hand started
- We call the 3-bet pre.
- Villain plays AK and JJ+ (16 combos AK, 6 combos AA, 6 combos KK, 1 combo QQ, 6 combos JJ...I'll omit the QQ in the calcs because that hand is +0 EV against ours. It has a tiny effect because of the antes. So the end result should be a few cents higher.)
- A flop without an A or K happens and we Donk-shove. Villain will call it off JJ+ but not with AK (omitting the fact that villain could flop the nut straight or the nut flush with AKs..which would skew the end result a tiny bit against us...also omitting that he calls with a flush- or straight-draw because he's not getting the right price to do so).
Probability we make a set or quads on the flop: 11.75% (actually it's a tiny bit higher because there are more boards that have 1 or 2 queens on them that don't have an A or K as compared to such boards without any queens. In the former case there are 2 (1) slot(s) that can have an A or K in the latter there are 3....so this is a point of contention. But as we shall see the difference is so large that I think this will not change a -EV play into a +EV one)
Villain Range distribution (omitting QQ):
AK 16/34 = 47.1%
JJ 6/34 = 17.6%
KK/AA 12/34 = 35.3%
...entire calloff range (JJ+): 17.6% + 35.3% = 52.9%
So we have 2 cases
i) We hit a set (or quads): 11.75%...in this case we are ahead of his entire range
ii) We remain unimproved: 88.25%...in this case we lose to AA and KK; AK folds and we win on the flop (+49$); against JJ we win his entire stack (except in a further 11.75% cases in which the villain improves to a set of jacks on the flop)
Baseline win/loss from just folding pre to the 3-bet:
-15$
Win/loss for villains range after calling and shoving a non-A/K board:
11.75% * (52.9% * 304$ + 47.1% * 49$) + 88.25% * (47.1% * 49$ - 11.75% * 17.6% * 300$ + 88.25 * 17.6% * 304$ - 42.9% * 300$)
=
21.6$ - 57$ = -35,4$
Please someone check my math, but if the above is correct then the fold pre at -15$ is +EV compared to the call/shove strategy on a non-A/K board at -35.4$
Note that redraws on turn or river are not factored in, as we have as many redraws to beat a villain with an overpair to our QQ when we're behind as he does when we hit a set. So that effect should cancel out somewhat (the JJ case is a bit more tricky because we or villain could have a reredraw to quads....but the probabilities for that are really low)
Last edited by antialias; 05-17-2018 at 11:02 AM.