+1. And a sorta lousy one. Limit holdem hasn't been solved by checkers experts? ::shrug:: When all you have is a hammer, everything looks like a nail.

To again quote Al Gore on Futurama:

In deciding what to tell it to do you are basing that on reasonable ranges of opponent. And deciding whether or not to bet a flush draw on the turn or check it on an ace high board is pretty trivial. A more difficult program would be deciding whether to have the program call flop, turn and river bets with ,K, Q, J high on a dry board. If the GTO is based on how experts generally play which is to open 90% of buttons and c bet always I'm sure the correct play would be inputted to call, fold, raise on occasion but against someone opening 30% of buttons you aren't losing enough in pf folds to account for the bot calling you down and raising with sh** every hand playing against you like you are one of the experts that helped create the bot.

From the example that pointer gives and how he describes it, the GTO is based on playing against another player that utilizes the same strategy. And he seems to think that there is this solution out there in never never land. He also believes, as he states that once this strategy is developed that you will be able to tell your opponent what you are doing and he will not be able to do any better than break even. And will lose if he varies from the GTO. O.K.

What you describe only partially addresses the issue of creating a GTO but is a good starting point.

Not going to bother finding the post but I think pokervintage tried to pull me up for the spelling of 'realise' or something. Wow. Do we need to educate you about the existence of countries outside of the United States as well now?

Now for the last time (naively hoping): solving most poker games is likely impossible with today's technology. We may need quantum computers to do it (but those may not be far away). But what we can do is prove that such a solution exists. It's. Really. That. Simple.

My first post in this thread was done to discuss this machine at Bellagio's. I was diverted by GTO interjections by supposedly in the know game theorists. I've heard about and discussed these GTO solution claims for almost 15 years. I found them interesting because although I am not a mathematician I believe that without a solid grasp of at the minimum calculating certain elements of poker one will not be able to win. I am interested in winning and winning only. If someone could actually develop a HU holdem GTO I probably wouldn't play it anymore. Although, I was hoping to actually put this GTO to rest because at first I thought that someone here might actually know what they were talking about given all the work that has been done in GT. But that was not the case. I don't believe a GTO will ever be developed and do not accept that it can be done because someone here says that it can be done. So, I apologize for hijacking this post. But it was in pursuit of a good cause, in my mind, winning. For those of you interested in winning poker here are a few facts. I played Stud poker in Atlantic City, New Jersey and Foxwoods, CT from 1993 to 2000. Retired from my job in 2000 at age xx and moved to Las Vegas. I met David Sklansky and Mason Malmuth and with their help and the help of their books I learned Holdem poker. I played Holdem mid limit, granted mostly only 15-30, poker at Bellagio through 2009 when I got tired of playing and moved to be around my Son's family, especially my grandson. From the time I first studied 7 Card Stud in 1993 for advanced players until the the time I left Las Vegas in 2009 I never had a losing month playing poker. So from an old timer that still plays well enough to win consistently online (mostly small buy-in pass, the time tournaments now, including a lot of HU NL, if anyone is interested in whether I'm lying about being a winner I'll post my umimpressive but positive stats), here is something to think about. If you want to be a winner at limit holdem read everything Sklansky and Malmuth write about it and learn from them. They still know more about the game than anyone. Well, present company excluded of course. And don't waste your time looking for a GTO unless GT is your thing.

Oh, I do not apologize to Twoplustwo. They got a lot of hits from my arguments. I do not apologize to the big mouth non-add anything dopes that called for my banning or started with the name calling. Again, I do apologize to the rest of you for hijacking your thread.

ah, sweet. apology accepted. catch you later.

this thread reminds me of the AQ/JJ one for some reason (but with added trolling).

I call BS on this one. There's no UTG in heads up!

And this again. Can we put a FAQ or something ?
GTO strategy doesn't care how opponent play. In fact you could not only publish it but tell opponent what you are going to do with every possible hand in given spot once it's happening. For example:
We play raise-call preflop, the board comes Qs7h3c
A player using GTO strategy could say : 'now i am going to bet 90%/check 10% with AA, bet 95%/check 5% with KK etc. etc.' for every possible hand. He could ever say things like 'with 7s2s i am going to check call and then on the turn if it comes Kd I am going to bet 60% and check 40% etc.' again for every hand and every turn card.
This is constant and always the same on given board. You could play in w/e way you please against it and you would still either lose or break even.

>>implying that anyone can beat the current limit HU bots...

I just dropped $200 playing the $0.50-$1.00 I got owned. Somewhere in the middle of a cold deck, I flopped top set and got max bet by what I hoped was a set over set situation. Robot called my turn bet and raised the river and won when robot's gutter ball made his straight. What the hell was that!?! I think that tilted me. What program tells the robot to do that? I don't think I'm terribad....a winning low limit player...fml. Never going to play this again.

the gto would be more reasonably understood and truly unbeatable if everyone played x % of hands pf ... All post flop gto has to be based on "typical" or "average" or "expected" ranges. If for some reason everyone played precisely 75% of hands it would be theoretically possible to solve the game . But since they don't I believe that the conditions do not and cannot exist for the game to be solved using gto theory. I'm not a mathematician so if I'm wrong than show me how. I'm just a guy that has played millions of hands and knows that he would kill a bot knowing that he's playing a bot programmed to play against a 90% open raiser.

try playing against that poker academy bot imo (the limit one), there's a 6 hour trail version.
I feel like I'm beating it slightly, and results say so too (well results say I'm beating it big), but I don't have a huge samplesize. But I'd definitely say it's going to beat a lot of decent players. (I'm playing up to 10/20 LHE online, not a lot of HU though)

Anyway, what I'm asking myself. If HU LHE is "solved", it is so called 'weakly solved', and thus can only be solved if perfect play is in order from start up. But if you play against a human opponent, he's not going to play perfect. So the human is losing value preflop and on the flop for example, but therefore can exploit the bot on later streets. Is this correct or am I overlooking something?
Although my limited samplesize with the poker academy bot I do feel like that's where you can have an edge. By really playing random cards, and making a lot of pure bluffs.

Jesus dude how long were u there for?
Did you have like random passers by stopping and saying "I think you've had enough sir"

Maybe that's part of its M.O. It makes plays to put you on major tilt (something you can't do to it), and it wipes you out after that.

forgive my candid mind, but why no one have considered the possibility that the machine knows your hole cards, and even if it is supposed to reward the player sometimes, it is programmed to win x% of the time (x being greater than y% of the time the human player wins) ?

Read the thread. It has been mentioned then pointed out that his would not be allowed by the Nevada Gaming Commission.

Thanks Eponymous

i just had a quick look at their site :

And IGT is bringing live table game interaction to the video poker machine in a big way with the Texas Hold 'Em Heads Up theme, in which players have the opportunity to match wits against sophisticated neural net technology.

again forgive my ignorance, but isn't "neural net" a kind of learning AI ? (as opposed to what have been discussed and mentionned here in this thread about this particular machine)

I'm going to try one final time to clear up some misconceptions going on (not so much for pokervintage who seems completely uninterested in learning anything and is probably just trolling, but for other people who seem to have similar misconceptions.)

1) There absolutely is an equilibrium for every poker game, including NL games where you can bet arbitrary fractions of cents. The proof is almost 60 years old and is due to John Nash (and Kakutani on who's theorem Nash piggybacked.) The equilibrium strategy will not lose to any other strategy or manner of play in expected value, as long as the button is determined randomly (and in a rake free environment-if there is rake, it is still unbeatable, just that possibly both players lose to the rake.)

2) It absolutely does not depend on what anyone else is doing in the game. It does not assume the other player plays the same strategy. Indeed, it doesn't depend at all on what other strategy anyone else is playing. This is why you could publish your strategy or announce it before each action and it would not have any impact on the ability of people to beat you (keep in mind strategy specifies what you would do with any hand in any situation, not for example what you will do on the river with the hand you actually have.)

3) No one currently has found the equilibrium for any poker game. For games like 9 person NLHE, the equilibrium will probably not be known for hundreds if not thousands of years. It is just way too complicated of a game for even very fast computers to solve quickly. For games like HU LHE, it will probably be known in the next 10 years or at least within our lifetimes, although we won't know for sure how long it will take until someone finds it.

4) The impact on live poker of it being discovered is unclear. The strategy is certainly too complicated for even people with exceptional memory to memorize, but it could easily be programmed into a cell phone or computer. Likely result is that such devices are banned from live HU play. People could try to memorize a simplified version of such a strategy, which may or may not be exploitable by a good player. In online play, it probably results in the complete breakdown of HU matches once it is discovered (although since there is rake, the equilibrium strategy may not do well enough to cover the losses from rake and so might not be worth using there either.)

5) Whether or not a strategy is "best" depends on what criteria you are using to determine "best". The equilibrium strategy never loses (in expectation), but will not exploit weaknesses in the opponent's strategy. Therefore, against a population of players who are not playing optimally (like actual poker players) you might (indeed probably will) make more money with a non-equilibrium strategy. However, you would be open to being exploited by some other strategy. That is why you probably want to program a bot to play the equilibrium strategy or something as close to it as you can get-because if you don't some smart person figures out how to exploit your strategy and then proceeds to do so changing the population of players into one your strategy loses to instead of beats. The equilibrium strategy never has this problem.

6) None of this tells us anything about what strategy this particular machine is playing, except that it isn't the equilibrium because that hasn't been discovered yet (unless the developers of this machine discovered it and did not announce is publicly, which is unlikely.) My guess is that the strategy it is using is designed to be close to the equilibrium strategy and that to the extent that it is exploitable the low stakes will prevent people from actually doing so. However, this is a purely empirical question and the outcome remains to be seen.

EDIT: Parts of number 1 are (probably) wrong for non-HU games. If you played the 9 player NLHE Nash equilibrium against non-equilibrium players it is possible that you actually lose money. You could think of this as analogous to the reason the FTOP is wrong for non-HU situations. However, everything I said is correct for HU games which are the only ones for which equilibrium is likely to be known anytime soon.

Everyone should read this!

lol at this. as long as it pays out what is required by law, they dont give a **** what the computer knows.

because most of the people who post here believe software programmed by people is always going to be legit.

Isn´t this untrue for more than 2 players?!

Yes, see the edit at the bottom of my post. (To be clear, the equilibrium existence part is still true, just the part about not losing regardless of what anyone else does becomes false.)

Yes, but many/most neural nets learn during training only. Once they are released, as in this machine apparently, they neither learn anything new, nor modify their play based on their opponent's tendencies.

Very good post overall, but I don't think this is correct. shortstacked/CAP HU NLHE games have been solved as far as I know (at the very least games in which players are less than ~1.5bb deep, BB: all in w/ every hand, SB:all in w/ every hand)