Point noted about the blockers, AE. I wasn't sure how to do the math correctly to take account of blockers, because, as you've said, we not only block part of his 5-betting range, but also we block some of his 3-betting range as well.

Regarding 4-bet/calling small PP vs a 5betting range of QQ+,AK; I don't see how we can call the ship at all here, according to Stove, 33 is 35% against a range of QQ+,AKs,AKo, so we definitely are not getting odds to call the shove after we 4bet. Unless, that is, we 4bet to a size such that the pot odds we are getting for calling the jam are 1.85-1 or better. Which would mean we had 4bet to around 30bbs, which is a pretty bad size for a 4bet imo. If we had instead 4bet to something around 22bb, we'd be getting just a bit over 1.5-1 odds to call his 5bet. And we'd need 39% equity, which 33 doesn't have, and AK... hmmn ... it's closer than I thought, it looks like AKo might barely have enough equity to call the shove, with 38.8% vs QQ+,AKo,AKs. But anyway it is much closer to a call than 33 is. Nevertheless, 4-bet/calling 33 IS profitable vs that opponent compared with folding to his 3bet, due to his tendencies of folding to a 4bet way too often, yet 4-bet/folding 33 is more profitable still. So we can surely 4bet ATC vs this guy. Even in the other example I gave where the guy is shipping it in with 99+,AJs+,AJo+, 33 seems to not have quite as much equity as needed to call the ship - It has about 38% equity against that range. But 66 has enough equity to call the ship.

Regarding flatting AK, I think you are right that flatting AK can be correct in some circumstances. I realize we would rather play AK against an 11% range than a 2.6% range - by 4-betting it we only play huge pots when we're in bad shape, and otherwise win small pots; whereas by calling the 3bet we play medium-big pots where we have good equity and often dominate our opponent. Perhaps I didn't make my example sufficiently straightforward; I was positing a situation wherein we didn't know how our opponent reacted to 4bets, or what his postflop tendencies were, so I was trying to come up with a good "default" line with AK which would be ok either against a narrow 5-betting range, or a wider one, assuming that we know only his 3bet% in this spot. Which is why I made up the 2 "sub-examples" with the different jamming ranges for opponent. Also, I think flatting a 3bet with AK is more sensitive to opponent's postflop tendencies than flatting something like JJ or TT, due to the fact that we will have no-pair on the flop 2/3 of the time, yet will often still have the best hand. So against players whom we don't know much about their postflop game, I'm inclined to put more action in preflop than try to play post with AK.

As I said, I was lazy when I wrote that post. You are obv correct that 4-bet/folding>4-bet/calling. I just did the quick math with 35% equity compared to 39% and it was still +EV. But as you point out 4-bet/folding is better.

As for the math with blockers I think the easiest way is to use something like the ev++ poker tools and have them count combos.

So using your range [TT+,AJs+,A8s-A6s,KQs,K9s-K8s,J9s,T8s,87s,76s,65s,AJo+,A9o-A8o] villain have 146 combos. Adding in Ah Kc as dead cards he now has 113 combos out of which 21 is QQ+,AK.

21/113 = 18.6% so the math is (.814 x $2.90) + (.186 x -$4.85) = $1.46 which is 40% more than in your calculations.

As for flatting, I don't think it matter all that much what we know of villains postflop game. It is of course something we would like to know but we can't really guard ourselves against playing against unknowns. I think IP vs OOP are much more relevant factors. So if it were CO vs BTN I'm much more inclined to 4-bet AK than in BTN vs SB.

Basically, in BTN vs blind battles I don't want to weaken my 3-bet calling range to much. I'm on BTN and I'm going to take advantage of it so I'll be opening very wide. In order to do that I need to be able to defend vs 3-bets. I could react with only 4-bets or fold but I think it is really hard to construct such ranges. I would much rather have a calling range and a 4-betting range and neither of them being completely unbalanced. So in my calling range I want to play my big broadways, including AK, as I'll often be dominating him postflop. I don't want it to be 99-JJ,AQ or something like that as it is too capped. And in my 4-betting range I'll have a lot of bluffs because his range is so weak. I will of course still have valuehands and I will 4-bet AK from time to time but as a default I'll flat.

Compared to when I'm OOP and BTN is 3-betting me a lot. The response here will be to tighten up from CO, rarely, if ever call, and have a wide 4-betting range (both value and bluffs).

That being said, the approach of putting more money in when against an unknown isn't bad, I just prefer to be able to combat people who 3-bet a lot OOP by playing pots against them IP.

Thanks for the feedback AE. I will remember about ev++ poker tools for when I need to count combos in future.

You are totally correct about the disadvantages of having a capped range to call a 3bet. Against some players, who both 3bet too much and love to barrel their stack away postflop, I think it might be correct to not even have a 4bet range, or to have a very small 4bet range. They may be putting in so much money bad postflop in 3bet pots, that you do better by flatting and taking advantage of their aggression with your entire range rather than getting them to fold against the top of your range by 4betting, and letting them have better equity against your weaker range to call a 3bet.

Quick challenge update:

Hands: 2,757/4,000 (68.9%)
Big bet profit/loss: +95.58 (94.58 more than the 1BB minimum)
$ profit/loss: +$78.91

Don't have a complete graph atm due to Bovada's 24 hour rule. I feel like I've adjusted to the madness of this game. Coming from nlhe, things can be very counter-intuitive at first.. esp adjusting to how wide ranges can be.. but Mike and Schu have really helped me out, at least enough so that I don't feel like a complete fish.

hmmmm..... We are making these challenges too EZ it appears or teh IceW0lf has enlisted some high powered coaching...hmmm.

Good thing we hand picked a very tough super secret stalking horse. I have great confidence in our stalking horse.

Bovada, +13.38BB in 735 hands



Merge, +41.7BB in 2450 hands



3185 hands
+55.08BB
815 hands to go