A GTO strategy is guaranteed to be profitable vs every strategy except another GTO strategy where it will break even. It will beat "any random strategy" except if this random strategy somehow happens to be GTO.

It's pretty trivial to show that going all-in every time you have action isn't GTO. Since it isn't GTO then a true GTO strategy is going to be profitable vs it. In fact it will be extremely profitable because the 100% all-in strategy is deviating so far from GTO (I think).

Same goes for the min-raise 100% strategy, although I speculate that it might not be deviating as much and therefore not be in as bad a shape as the 100% push.

Not true. By definition, our GTO strategy can't lose vs any other strategy and will in fact be +EV vs every other strategy except GTO ones (where it will break even). We don't need to know the specifics of the strategy. All we need to know is whether it is GTO or not.

I have no idea why you think that clicking it back in every spot is even remotely close to being GTO. It's trivial to show that it isn't. And if it isn't GTO then it's going to lose money to our GTO strategy.

im a huge dog vs the bot tomorrow- I'm rly bad at hulhe... so like i told sauce- it needs to be a bet like this; 200k hands where we play anywhere between 3/600 and 2k4k (my choice). the higher i play the more ev i giveup obv vs ur bot thats solved the game- so this is good for u. u and kanu n sauce can all pool $$ or w/e. no buyouts fk that

u must watch a lotta fox news

This example I posted (see link below) demonstrates that GTO strategies are only guaranteed to be at least neutral EV. They are not guaranteed to be +EV.

http://forumserver.twoplustwo.com/sh...&postcount=440

^^^ Simple example where GTO is never more than neutral EV.

Of course, GTO poker might be +EV against all non-GTO strategies, but we do not have a proof of that. Currently we can only say it will be at least 0EV.

You fail to understand:

(1) Winning is not equivalent to not losing (see definition of "tie").
(2) Without seeing the GTO solution, we can't determine how GTO will preform against all the various strategies, including open shoving every hand (other than to say GTO will be at least neutral EV. That is, GTO won't lose to open shoving every hand, but GTO might be +EV against someone who always open shoves).

This is my exact question. Is the scale of the prop weighted more on Durrrr's perceived skill in HULHE or in the invincibility of the bot?

Real ngz do real things

Here's an example of a game where we can easily find a GTO strategy that is +EV vs any non-GTO strategy and zeroEV vs itself.

You sit down with your opponent at a blackjack table with a continuous shuffle machine and you crossbook your losses (times some factor) vs your opponent.

The GTO solution to this game is to play the well documented perfect strategy for this blackjack game according to all the house rules. If both players do so, they will be zero EV. If one player deviates, he will be -EV to the other player and therefore the other player will be +EV.

I would have bet on durrrr, if I had the moniez...

You are claiming to have found a game where GTO is more than neutral EV against any other strategy. But:

(1) Not all games have that property. See rock, paper, scissor:

http://forumserver.twoplustwo.com/sh...&postcount=440

(2) We do not know if poker is like the game you presented, or if it is like rock, paper, scissor.

Again we know GTO poker will be at least neutral EV against open shoving, but we expect GTO to be +EV against open shoving. That is really all we can say.

I see what you are saying now.

So let me counter with this:
Let A be the strategy of folding preflop 100% in a hu poker game with blinds. Every other strategy will be +EV against this strategy, including GTO. Therefore it's impossible for a GTO solution to poker to be 0-EV vs all strategies.

Does that make sense?

I believe the bots are better than any human, but I doubt it is provable. Based on the fact that they were closely matched 4 years ago and have gotten a ton better though I think it's a safe assumption.

epic thread... i had no idea GTO was so heavily misunderstood. make me feel super solid about my game.

durrr vs slumbot will be epic, also i'm amazed he took the bet o.0

I dont understand why people keep using this as an example. Folding preflop 100% should not even be considered playing. Find a different example

given that there are situations in poker like shortstacked push/fold play in which gto is always +ev against random strategies, it is at least a stretch to conclude a random strategy can be ev-neutral against gto overall.

Yes, folding every hand will be -EV against GTO. It will also be -EV to raise/fold every hand against GTO.

And yes, it's impossible for a GTO solution to poker to be 0-EV vs all strategies.

But these two statements are not equivalent:

(1) It's impossible for a GTO solution to poker to be 0-EV vs all strategies.
(2) GTO more than neutral EV vs. all strategies.
(3) GTO is at least neutral EV vs. all strategies.

The first is true, the second might be true, and the third is true.

Finding a few numbers with property A doesn't prove that all numbers have property A.

We know GTO will be at least neutral EV against all strategies. It is easy to prove that is it +EV against some. But without the GTO solution we can't see how it will do against all strategies.

You can look at facts/history/examples and form an opinion, using logic and by thinking inductively. But a mathematical proof is much more than that.

So yes, it's not a stretch, but it's also not a proof.

We all have reasonable expectations of what the GTO solution will look like and what its win-rate will be against the various strategies.

But we don't know for sure it will be more than neutral EV against open-shoving, or other random types of play.

you do know that we can already calculate the GTO solution for calling open shoves HU, right?

i bet my money on gto beating every random strategy, unless there is a strategy which plays all relevant situations (gto is +ev against any other strategy, see my example) gto-like and magically only deviates in possibly non-existant spots where a non-gto strategy breaks even against gto. would not really be a random strategy though.

For continuity's sake, I wanted to follow up and say that I would tend to agree and even used this same example myself in the HULHE thread on beating the IGT machine.

I would probably bet the same way as you (that GTO is always more than neutral EV against non-GTO). I was just trying to make the point that we can't say anything more than: GTO is always at least neutral EV.

If open shoving is already solved (link which includes all the various stack sizes?), then I should just say "non-GTO" instead of open shoving.

NE for open-shoving/calling HU

so your random strategy better has this chart in case effective stacks get low..

That wasn't what I was trying to show. I was merely showing that a poker GTO strategy is +EV vs the set of all strategies, unlike the RPS GTO strategy.

Agreed. I realize that my first reply to you was wrong and that we can't know whether in poker a GTO strat is +EV vs every non-GTO strat.

But intuitively it seems extremely likely that it will be.

it very clear that majority of the individuals commenting in this posting have basically no knowledge what so ever of the manie theories associate with game theory. knowing that it is branch of mathematics with great deal of rigor behind it seem to be enough and provide comfort for most liberal application. 95% of this thread is balderdash 100%

There kinda needs to be a buyout. If someone is winning at 1BB/100, and it could easily be a lot more, that side wins $8MM in 200k hands of 2k/4k. I don't know how prepared to lose $8MM either of us is, but I'm pretty certain neither of us wants to risk $40MM+.

The nice thing about a buyout is that it allows us to escrow just the buyout amount and a bit more and whoever is losing can top up their escrow deposit as they lose or quit and forfeit the buyout.

On the same note, there needs to be a time limit. I don't know exactly how the interface for playing the bot will work, but let's say you get anywhere from 100 hands an hour to 400 hands an hour in. You're committing to somewhere between 500 and 2000 hours of play. With this much at stake, I can't just take you at your word that you'll make a good faith effort to put in up to 2000 hours of play at a reasonable pace until it's over.

edit for arithmetic fail