Yup, correct

Thanks a lot, I've got it now. Helped tremendously

Never is a long time.

I mean I generally don't think its a good idea to purposefully sacrifice EV as part of our strategy but we shouldn't be mathematically or theoretically ruling it out. Against human opponents, who adjust to what they see, sacrificing EV may be perfectly reasonable. We shouldn't treat each hand as if its played in a vacuum when poker simply isn't played in a vacuum.

Most realistic example I can come up with when to sacrifice EV is just making more marginal semibluffs, especially early on in a session. A call with some marginal draw might have an EV of $4.00 where a semibluff raise for stacks might have an EV of $3.95. We sacrifice a nickle to build our image so when we have a trips or two pair vs their one pair we have a much higher chance of getting paid off.

Again, just to stress that's for human opponents, though I would argue that when we respond to poker theory posts we should assume our opponents are in fact human. With fixed strategies (GTO bots or whatever), there's no incentive to sacrifice.

Yeah, I agree that there are some rare spots vs humans, where it may be optimal to "sacrifice" some EV. But as I understood, OP was asking mainly about GTO solutions.

It would make sense to sacrifice some short term EV vs an opponent that is folding 80%+ vs 3b, by not 3betting him every single hand, so that he doesn't realize that we're exploiting him.

Also, if we're playing vs a fish that will stop playing when he doubles up, or loses stack. We may not want to call his preflop all-in with a certain hand, even though it may be slightly +EV, since keeping him in the game a bit longer would be worth much more.

I'm sure there are other examples like these, but I wouldn't really focus on them too much, especially in online play.

Imagine you're a robot and you have a pre-computed solution to poker, and it's basically just a database of combos and frequencies, so it effectively tells you how to play every possible hand. If someone asks you "What do you do if you get 22 on the next hand?", you just look at your database and find the answer. Perhaps the answer is "Shove 100% of the time". That's simple enough. If someone asks "What do you do with aces?" perhaps the database says "Raise 23% of the time, limp 77% of the time, because both actions have the same EV". Where the mixed frequencies appear, you need to use a random number generator to make sure you pick the action at the right frequency in the theoretical long run. Although you're only playing one hand in a vacuum (so you're either limping or raising in this single instance), if you kept playing this game forever the use of the RNG would mean you end up picking the actions at optimal frequencies. If your RNG malfunctioned and you limped 100% of the time, an opponent could gain EV by adjusting his strategy, because he'd know you don't have AA in your raising range. Since your raising range would no longer contain AA, the other hands in the raising range could lose a little bit of EV, if villain could 'exploit' your mistake.

Really enjoyed reading this thread. It seems every question the op had was answered in spades. Just to make sure I have not missed the original point, when the op is talking about shove ranges blind vs blind with 9BB, those are solved nash ranges, right? Therefore they include all the hands where limping is equal to shoving, right?
If limping is equal to shoving, then nash is to shove, since a flop would require another calculation, which is more complex for humans, and any time a human can place an indifference all in bet, the human should do so. As for hands where limp is better than fold or shove, what might those be, in a specific bvb 9BB scenario? All of those would be likely calls if the BB shoved, anyway?

That is to say, a "value limp" range would be capped below nash shove range and easily exploited. So would have to be balanced with above nash hands, hence you are back to the nash ranges but choosing to vary from equilibrium.

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The "Nash" push-fold ranges are only a "solution" to a game where the only options are push or fold. As soon as you start limping some hands, that alters the EV of the rest of the strategy. e.g. Part of the reason why it's profitable to jam T5s is that villain believes you also jam QQ+. In effect, he has to "respect" your jams, because you play the strongest stuff the same way as the weak hands. T5s benefits greatly from the fold equity generated by the threat of you having a monster. If you arbitrarily take QQ+ out of your jamming range (and villain knows this), he can call your shoves a little bit more often, because he's not going to run into a monster. This will mean that the bottom of the original shoving range will no longer be profitable. Indeed, your shoving range will be a fair bit weaker if you've taken out all the big hands.
In the real world, this is often the case in low stake MTTs. If someone jams 15bb and you have JJ, it's a snap-call, because you can be pretty sure that villain doesn't have QQ+, because he would have minraised to injuce. Many players look at a push chart and jam everything on it apart from monsters, but this means they are jamming a weak range and minraising a strong one, meaning both ranges are unbalanced. A stronger strategy would be to have a raise-fold strategy with some weak hands that are used to balance the raise-calls with monsters. The remainder of the hands can be shoved, as they will still have the roughly the same average strength as the original push-fold strat.
The same applies to limping. If you want to limp aces to induce, you also need to limp-fold some weak hands. Villain isn't going shove over your limp if you always have aces, but if you're balanced, your "threat" of aces means some weak hands get to see a cheap flop. i.e. You limp some weak hands that do better by potentially seeing a cheap flop than they do by jamming.

To use an abstract example, imagine a one-card game, where your playable range is A to 2, with A being value and 2 being a bluff. You could just shove all hands, but it might be more profitable instead to limp-call A, K, Q and balance by limp-folding with 3 and 2, leaving J-4 as shoves. A real NLH strategy is much more complicated than this, because different hands have different amounts of post-flop playability, but hopefully you get the gist of the idea of balancing the ranges for each action.

Unless its a satellite bubble hand, would not all decisions with a 9BB stack be all in or fold?
I understand what the nash charts are for, or maybe I don't?


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I think in a satty, a shove is more likely, because of the fold equity. (On many satty bubbles, the SB jams ATC, because of the ICM pressure. Limping would often be bad, because when you get shoved on, you can't call with many hands, due to that same ICM pressure. Indeed, in satties, it's often a case of trying to be the first player to jam all in, because it's seldom correct to call a shove).
Various people with solvers have computed near-perfect strategies for 9bb in HUSNGs. I believe there is some limping even at that small stack size. From memory, it's only at sub 7bb that the entire strat is push or fold.

Thanks for clearing that up for me.


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