Yeah this is the key. It seems like you would want to be the small blind in either case, since you have positional advantage. Unless it's less than optimal to be raising 100% from the sb 20bb, then we should be the bb. But that I don't know so I'll just stay out of it.

thanks for the post Mers. Wonderful things to think about I can't continue the discussion till tomorrow, I'm excited to see what other people think about this.

I think that my answer, which is necessarily unique since it's what *I* would do and have to try my best at, and not some GTO computer, would still be option b) playing bb since I have something I can try to exploit and I'm good at that and at the same time I'm too confident to choose the cut your losses option of a) sb play nash push/fold.

But I think that if a GTO computer (that can maximally exploit its awareness of the other computer's minraise 100% strategy in b) ) were choosing an option, I'd be really interested in its choice. I really do not know and can not lean or think of a clever way of comparing the two in that situation.

i've played pretty much everyone who could be considered the best shortstackers headsup at either hypers or stars cap and noone has come even close to making a raise 100% strategy work as well as people have made a 75ish% work. Obviously this is far from conclusive evidence or whatever but how incredibly simple it seemingly becomes once anyone raises 100% is enough to make me think it's fairly impossible that it's GTO. That said i have more doubts about beating bot in scenario b than in scenario a, but my support of the notion that sb probably has an advantage at any stacksize is probably known to you

GTO post-flop is tough to think about. It's quite likely that it's very different than the way that we currently play. But thanks to Nash's thesis, we know that it exists.

HSNL actually had a long "debate" recently, that mostly consisted of durrrr saying there was no GTO solution to HU Cash, and people reminding him that if that were true, a thoroughly scrutinized, Nobel Prize winning piece of academic work that has been expanded on for 50 years, would be invalid.

To answer your specific question, yes, I think on the river, a GTO bot, if it determines that GTO your range is always bluffcatchers, would always try to bet an amount that made you indifferent between calling and folding (sometimes that bet would be more than all-in), but someone please correct me if I'm wrong.

whoops misread disregard

If it's that bad, why not want to play game B?

Can someone explain what GTO is?

isnt the answer game B from the bb im to dumb to work this stuff out but seems to me to be the most logical answer since raising 100% from the button is EXPLOITABLE and is the only thing we can gain an edge on, if we choose any other game the computer will play optimally and if we choose to be the sb in game b then we become exploitable so seems game B from the bb is the only game we can be +ev in.

i think sb should have quite an edge 20bb deep so what i would define as bad does not necessarily make it a losing strat just less than optimal

a strategy which, assuming equal playing fields you cannot do better than breakeven against

You said which games would you be +Ev assuming you play optimally. When you say optimally, you must mean playing like the bot.

Therefore your question is who has the advantage, SB or BB at 10bb and 20bb respectively, when a forced min raise is in place. As such, I think I would choose 10bb being OOP, since like r-q said, the 100% open is not optimal.





Just had a thought, maybe I am thinking about this whole scenario completely wrong.


Lets say 2 GTO bots played each other at HUNL 1000bb deep, 1 bot is always SB, the other BB. Does the bot who is SB have an advantage, or does position not matter when you are playing optimally? - i.e. is the function of position being an advantage a trait only accrued by humans, and not bots. Probably a naive question

Didn't really think about it too much yet but isn't the worst option SB in game B because you always have to min raise so it's exactly like being the BB in game A except the computer has the option to call and you can't shove over his call.

Worst option to Best option
SB game B, BB game A, SB game A, BB game B

one of the two will almost certainly have the advantage

what does GTO mean? isnt it kinda like nash, we have a set range of actions for one player and the other one optimizes against that ranges and then the other one does the same, going on until noone can improve?

if that is GTO, how do we even know it exists? and if that strategy is a fixed one, couldnt we easily exploit it, for example by minbetting every street or something, because it isn't used to respond to exploitative strategies?

sorry if those questions are trivial, GTO doesnt occur too often in my games :P

edit: sorry again, took some time to make that post and it seems mers already answered it.

sb is the net winner in deep hunl play -- it's not just a human thing.

the EV=0 thing is a misconception. (or, rather, its true in some games, but hunl isn't one of them.)

i don't know why you quoted my post but with even playing fields i meant equal sbs and bbs and stuff

as my reply to tgsm shows i didn't mean that it's always 0 EV, just that if you both got put into the same positions an equal amount of the time you could not outperform it ev wise

aha! one thing i just realized that makes it unlikely that 100% raise is GTO. A proof by contradiction with some critical unproven, but not baseless, assumptions:
So assume that raise 100% is GTO. If we choose to play nash push/fold 10bb as bb over the 100% sb minraiser then sb GTO computer should be have a calling range that is different from the nash calling range at 10bb.
Proof for this statment is where we have to make the following assumption: there exists some hand for which flatting (or even 3b non allin) is better than both jamming and folding. There is a lot of empirical evidence pointing that this is probably true, with for example near GTO solutions to HU limit where capping the action is of immense value, and so calling and capping the action, should have quite some value. Once we assume this to be true, then it becomes obvious from the definition of GTO that bb's GTO strategy should be different from nash push fold since it has to be a best response to a strategy that is non push fold, which means that sb's GTO strategy should be different from nash call at 10bbs because it must be GTO versus bb's GTO strategy.

But the nash calling range is the nash equilibrium for the push/fold sub game, which the bb is actually playing, and so that implies that by deviating from that calling range sb is going to be doing worse than the nash calling range. This also implies that, since sb was assumed to be playing GTO, the game value is going to be less than the game value of the restricted push fold game of the sb at 10bb.

So one last critical assumption: the game value for sb goes up with stack depth (again unproven claim but incredibly reasonable empirically, and almost definitely provable but involves quite a bit of work to actually prove).

This last assumption together with the previous analysis results in a contradiction, since we showed that if 100% minraising at 20bb is GTO then sb should have a game value less than that of a restricted game at 10bbs (to be pedantic I'd like to point out that restriction should clearly mean game value is less than or equal to unrestricted game, which is almost definitely proven in academic literature). So we have a contradiction. So at 20bbs raising 100% cannot be GTO if we assume that game value is increasing with stack depth (and decreasing with restriction) and that there exists a hand for which bb should flat or 3b non all in rather than playing push fold. This means that raising 100% is not GTO.

QEDish, yay. sleepy time now.

Oh and @Ohly John Nash proved that a Nash Equilibrium exists in all finite games, poker included, so this means that a GTO strategy exists. It follows from some deep math, but basically it's because you can use the argument "I pick strategy A, you take best strategy against it, call it B, now I pick strategy A' which is best against your strategy B, now you pick B' best against A', and deep math says that after a finite amount of repetition this process will end in strategies AGTO and BGTO after which BGTO is best response against AGTO and BGTO is best against AGTO (a fixed point).

This also defines the GTO strategies for the game as exactly AGTO and BGTO, so that's the definition of a GTO strategy for the other people who were asking.

Yea, my thoughts pretty much....so you are prolly wrong

actually the more i think about it the more im thinking game A from the sb,

in my head i keep thinking of the games in terms of both players will face the same situations so if u both play optimally there wnt be any edge instead of it being just one game,

GTO - game theory optimal

= a completely unexploitable strategy

In terms of poker (is used in other fields as well), this means playing every hand perfectly. The strategy is not fixed as playing optimally would involve doing all the things poker plays do (suboptimally), like constructing ranges, whilst considering previous history.

GTO is a (mixed) fixed strat actually

what do you mean?

it does not take previous history into account. if a GTO strat was discovered it could be in theory written down and given to you and you could still not beat it in a fair game

it doesn't have to be mixed. It just has to satisfy being the fixed point of the best response function on strategies (the sequence A B-> A' B'->...->AGTO BGTO I had at the end of my last post). Which means that it is fixed (but could be a mixed probabilistic strategy like I do one thing 50% of the time and another thing 50% of the time)

oh ok, didn't know what you meant by even playing fields. yea, on average over both positions players' evs will be 0 at the equilibrium. but in any one play of the game (i.e. one hand) one player will have an advantage at most stacks.

seems like i see people who mean it the other way pretty often though. like they'll even try to solve for optimal strategies by setting EV=0 and finding a strategy that makes it so.

gto is nash equilibrium. the nash equilibrium concept applies to lots of different games, not just nlhe shove/fold.

http://en.wikipedia.org/wiki/Nash_equilibrium

this is often the case but not always. e.g. suppose i'm polar, you have a bluffcatcher, but the nuts part of my polar range is >50% of my total range. then at equilibrium, if there's enough behind, i can bet large enough that you have to always fold (i.e. youre not indifferent between call/fold)