It's heads up. There's only a small blind and a big blind, no antes. Small blind always has the button.


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We're playing against a GTO bot. You cannot gain an edge vs this bot supposedly.

It just happens that we have a higher EV with 72 off by limping it from the sb than open folding it vs this GTO bot. This means we can limp 72 off suit and lose less than 0.5bb. (the cost of our small blind). So 72 off makes more chips than if it just open folds.

However, the GTO bot doesn't even play 72 off from the sb.



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Now then if the above is true, that means we are making chips from the small blind with 72 off, (Let's say we're doing 00.1 chips better than open folding it) but the bot is losing 0 chips with 72 off in the same position.

So we're doing 00.1 chips better than the bot with 72 off from the sb, compared to when the bot has 72 off in the sb.

But how can this be true, as it's impossible to gain an edge vs this GTO bot.

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I clearly have a fallacy here and am wrong about something, or just can't currently see why limping 72 off from the sb vs this bot is a mistake. The reason being that it's a GTO bot and it's impossible to gain an edge vs such a bot.

Is it simply that I'm wrong about it being profitable to limp 72 off and that I cannot profitably play 72 off from the sb against this bot.

Or is it that by playing 72 off, i'm weakening my range, and therefore I will lose (or gain less) chips with other hands as a result of playing 72 off?

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Let me know how i'm wrong, maybe it is just as simple as "72 off cannot actually have higher EV limped compared to folding vs this GTO bot".

If it is that simple, I'd like to know, and if it's not that simple, I'd like to know why.

Thanks.

The bot's EV (and yours) is averaged over all hands and all situations - I don't think it's a requirement that for every hand/position, the bot's EV is greater than or equal to yours.

I expected it was something along these lines.

Could you give an example of how the bot for example "makes up" for the fact that I do better than folding with 72 off and perhaps other hands that it doesn't even play in the sb. So clearly i'm making chips here from the sb with 72, where the bot is gaining 0 chips with the same hand in the same position.

But those "chips gained", that I gain by playing 72 off and perhaps other hands that the bot doesn't even play has to be "returned" to the bot somewhere, right?

Because it has to make up those chips somewhere for it to be unexploitable.

Also, assuming what you just said is true...

Then the statement that "If my opponent plays the same hand that I play, in the same position/scenario that I have that hand, and makes more money with that hand/loses less money with that hand than I do, then I'm being exploited" (assuming heads up)... is a false one?

This is not really my area of expertise. But I think some common sense can apply.

Your sentence there almost has to be false. Let's say your opponent completely owns you with 72, but open folds every other hand. Would you say this opponent is "exploiting" you? Could they beat you?

In order to describe he your opponent might make up for the discrepancy, I think you'd need to know why/how you make more than him with 72o. Snowie isn't perfect, but for example a lot of people make money off snowie in the short term by taking very unbalanced strategies. I expect that they will make money off Snowie folding a lot, and then lose money in other situations. So they're probably having +ev on some trash hands that snowie won't open, and losing money with decent hands where snowie beats them in other ways. I honestly don't know that I could say for sure, though.

I was thinking about this -

You make more/lose less chips than snowie does with the trash hands.

But you play exactly as snowie does in every other situation. With this line of thinking you'd have an edge on snowie.

However, I then thought about it ... that you couldn't actually play "exactly as snowie does in every OTHER situation" BECAUSE your range consists of those trash hands. So it wouldn't be possible.

So I think the because fact your range is weaker in every situation as a result of playing the trash, snowie gains back those chips, and possibly more as a result.

For example -

You can no longer "properly" defend against snowies triple barrel an adequate amount of the time, so by having those trash hands in your range, snowie barrels and makes you fold in spots where snowie could otherwise call an adequate amount of the time against such barrels when the roles are reversed because its range is stronger.


Would that sound like a solid reasoning for why it is you can gain chips with a hand that snowie doesn't, but still not have an edge on snowie?

Well, I think it's something like that. You end up seeing flops with trash hands when snowie calls. You can't play those the same as snowie, because snowie wouldn't play them

What do you mean by "it just happens"? If 72o was a profitable limp, the bot would also make that play. But it's not a profitable play, so the bot wouldn't limp, and nor should you.

Right, so the error was that 72o wasn't actually a profitable limp vs the bot, for the range as a whole.

But, that doesn't change the fact that 72o made slightly more than 0EV by playing it, 72o specifically made more 0EV by being played than being folded vs that bot.

But, the range as a whole suffered as as result of 72o being played.

Does that make sense or does it make no sense at all?

I think i'm onto something here, but I could be talking non-sense.

Would like more input on this, thanks.

Just to clear this up for everyone, because I think I can sum up what you're asking more clearly. Correct me if I'm wrong, but I believe this example shows what you're asking..

I can show a profit from the SB with 72o, by only limping a range of [TT+, AK, 72o], and folding everything else. So if I'm making money by limping with 72o (because of my fold equity from the other strong hands in this range), and the bot isn't making money with 72o (with his wider SB range), then he must be making more money elsewhere to make up for that, right?

Or did I totally misunderstand what you were asking lol?

Not quite like that.

In the example you gave, "only limping a range of [TT+, AK, 72o], and folding everything else."

Here's my response -

The 72o is not a profitable limp for our "overall for our strategy", but is a profitable limp SPECIFICALLY for the hand 72o, not because of the fact the range is made up of other stronger hands.

The 72o is making money because the bot doesn't iso raise enough, folds to limp c-bets enough or some other reason that makes 72o profitable.

However, my thoughts are that the 72o, while it is a profitable limp for that hand SPECIFICALLY, it will make the range as a whole suffer in some way at some stage of the game, for example because you're forced to fold too often to a check raise on the flop for example.

So the way i'm thinking about it is -

72o specifically may have a higher SPECIFIC hand profit by being limped.

However, the range as a whole will suffer so much as a result, that the range as a whole would be more +EV if the 72o was not in the range.

So the question is -

Is it possible for a hand to be a profitable hand to limp, but as a result, the range is weaker, thus resulting in less EV for the range as a whole?

For example if you looked in pokertracker over the course of an infinite amount of hands vs this bot, and in this hand sample, let's call it "Sample #1" and you checked out the EV of limping "72o", it shows that that hand was say 000.1 chip better than folding.



And now say you had another hand sample with an infinite amount of hands (Sample #2) vs this bot, and in this hand sample you didn't limp that 72o, and as a result your range as a whole was more profitable than the first hands sample where you did limp 72o. So much so that you had a higher EV by not playing 72o.

Could someone comment on this also -



10-9 suited is a profitable x2 open from the sb in heads up at 100bb.

Vs a "GTO" opponent it will be guaranteed to be +EV, assuming you also play "perfect gto".

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However, vs an opponent who shoves every single time you open, 10-9 suited will not be a profitable open. Why isn't it a profitable open? Because you fold every single time your opponent shoves when you have 10-9 suited.

So the EV vs this opponent with the SPECIFIC hand of 10-9 suited is -2 big blinds.

But because you're playing perfect "GTO play", it has to be impossible for any opponent to gain an edge against you.

And the reason they don't gain an edge vs you by shoving any two cards, is because your range as a whole consists of enough strong hands, that they cannot possibly do such a thing. So you lose 2x every single time you have 10-9 suited. However you gain the entirety of that lose and possibly more with your other stronger hands that do call the shove.

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If all the above seems straight forward and makes sense, look at what I've got to say next -


In the same way we can see how 10-9 suited is part of a profitable range AS A WHOLE.

Now add 72o to this range, 72o could be a profitable open vs a GTO opponent.

However, you now play against a non GTO opponent, you play against an opponent that shoves every hand, every time you open to x2.

Well now you're opening too many hands, and your opponent can actually profitably shove any 2 cards, you're being exploited.

So while 72o, the SPECIFIC hand "72o" is showing to be a +EV open, the range as a whole suffers because you cannot call an adequate amount of the time vs the guy who shoves any two cards every time.

So the range as a whole would be better off without 72o.

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I'm giving a bunch of examples trying to understand this better, if I'm wrong, i'd appreciate if someone could use examples to explain how i'm wrong.

Thanks

You keep saying this. Why?

No it can't, otherwise it would have been part of the GTO strategy to begin with.

You can have "72o is a profitable open vs a GTO opponent", while dubious, you can at least imagine a game scenario where that might be true. But you can't simultaneously claim that you are playing a GTO strategy, while also claiming that you can add a profitable hand to your range while playing against another GTO strategy. If you can deviate your strategy and gain value, players are not at an equilibrium.

The same goes if we were talking about a button range with 72o to begin with. Its true that its possible the button can be playing GTO, and the big blind can be playing GTO, and the 72o shows a profit. But it can't be true that the big blind could show more profit by shoving on top of every hand, because again it means that he gains EV by deviating, which means it wasn't an equilibrium in the first place.

I'd like to know that too. My only guess is that he's playing against a "GTO" bot like PokerSnowie, thinking it's playing perfectly GTO, and found a way to profit with 72o. And/or is profitable in general with 72o from the SB, but doesn't realize his sample size is too small to come to any conclusion. Or maybe he's just assuming it to be true without any evidence. Is any of that correct?

But NMcNasty summed it up very nicely.

The bot doesn't adjust to your play, does it? Assuming the bot doesn't adjust, the EV of other hands in your range will be unaffected by whatever you do with 72o. With that exact holding, though, I think you have a negative expectation, so by playing it all you're doing is lowering the EV of your overall strategy.

e.g. If there was a game where the only hands were AA, KK, QQ and 72, and AA-QQ were the only playable hands (with a total EV that broke even against an optimal opponent), adding 72 to your playable range would just be adding a losing hand to your strategy. It wouldn't make AA-QQ any more profitable. In the same way, if JTs was a breakeven hand UTG in a 6-max game, you couldn't increase its EV by playing T2s or J4o as well. You'd just be weakening your range.