well it's possible we never compute the strategy. but it's being knowable isn't in question really. we have algorithms to find it, just not the computing power. the point is it makes perfectly good sense to talk about GTO solutions, and approximations to them.

Even in regard to a machine that is going about it another way?

sure. the machine came up with some strategy, by whatever method you like. it is still perfectly reasonable to talk about how close that strategy is to GTO, even if the method used has no concept of what GTO is.

Doug, just as an example Sonia was not developed as a GTO bot, but as an exploitive one. Yet she was able to beat Polaris, and so it makes it sense to say that Sonia is capable of converging to an approximate GTO strategy when her opponent is also GTO-approximate.

I get what you're saying, and I'm enjoying the derail of David's thread.
Doesn't it make it harder to analyze the strategy when even the people who wrote the code may not know what the machine is doing? Our only view into the machine behavior is through looking over the shoulder at people plugging tokens in the machine. If you want to start analyzing it, how would you go about it? You could feed truth serum to the programmer and ask him what it was up it in a given situation. His answer may well be, "I have no idea".

He may have some idea, but maybe he didn't tell David or David didn't tell us. If I'm sitting in front of it, I can't generalize its play like a could a person. Obviously, "folds the river w/o the mortal nuts" is exploitable. Since it is not a sucker, any thoughts on how to go after it?

from a practical pov, as a consumer of the machine, if you will, i have no advice, but my guess is that it can't beaten for a lot.

my guess is that they would have tested the code against bots like polaris and sonia before putting it in the casino, and that it did just fine. even if they did not do this, i am pretty sure they would have calculated a theoretical best response to the machine's strategy (i'm not 100% sure but i believe this is computationally possible) and that they know the limit of what it can be beat for. the practical limit is obviously much lower.

NVG version took an interesting turn.

I think I have enough to go to gaming with as well. I'm going to figure out how to do that and post my results.

anyone lost a lot of money to this thing?

Not cool, he just took away my personal ATM. My win rate is over 6BB/100 with a reasonably large sample size of over 6,000 hands to know that I can beat this game for sure, I have come to understand it's core weaknesses, its a really tough game to beat but if you study hard it can be crushed. I am not at all phased by the oddities shown in the NVG thread, these situations are so rare that I toss it up to poor programing and/or a statistical oddity.

Glad to hear you're crushing the thing. It is nice when the good guys win. I hope you're smiling when you say the above. As a live player, 6000 hands seems like a ton. A lot of online guys see your sample as a good 2-3 days.

I'm no expert at this, but I believe that to do a one sided CI for "do I win" you go something like this.
n=100*(z*wr/sd)^2

If we take you 6BB/100 and guess your SD is 28 playing HU against a LAG, you'd need 8700 hands to be 95% confident you win at all. I think the 3 sigma number is closer to 20K hands. If we use 22-23 as your SD, you're around 95% confidence to win, right now.

Also, from our point of view, you're self selecting in the winners group. We've seen about 6-10 people report playing the machine. One of them should have run better than the rest. As an observer on the side, I'm forced to wonder about reporting bias. However, I don't have a cohort of "people who rock just as much as TT does" to average that out.

Again, no insult to you. You've got a pretty good chance to be beating the machine since one of you played it, and one of you made adjustments and are currently beating the thing up. Even with the equivalent of 200 hours of live table play, you're nowhere near having enough "hands to know that I can beat this game for sure". Maybe someone actually math-skilled can verify that I ran the numbers right. I started from here. Maybe you should send the machine a picture of you rubbing your winnings on yourself; it is traditional.

I'm no neophyte Doug, I know that the sample is ridiculously small vs a standard sample of players, and still really really really small vs any one heads up limit opponent online. But the mathematics can be thrown out the window in this situation because we are playing against a machine that has exploitable weaknesses - its just something you got to trust me on, take a leap of faith with me since as you pointed out I am not the only one reporting back with positive results. I agree that my real win rate is probably not 6BB, I have no clue what it may be - and in fact it may be lower (perhaps even higher - unlikely but possible) . Regardless, I would be shocked to discover I am not winning at a fairly solid regular rate after a 100,000 hand sample. This is something I could not state with any confidence vs a human opponent, but it is something I am willing to go out on a limb against when we are discussing this specific bot.

PS: you really need to come out here and play the machine sometime soon!

Somebody just sent a tweet that the machines at Cosmo were moved to the area by the craps tables, they have not been removed after all - whew, thats a relief! I haven't confirmed yet though, hope its true.

I think your chances of your real WR being 12BB/100 are just as good as your chances of it being zero. Not really my specialty, so don't bet anyone on that. The exploitable machine thing is good. The variance is all about the cards and the amount of luck in HU LHE. The math doesn't care about you or your opponent, as long as both remain relatively constant throughout the sample. It is entirely possible that the machine has holes that can be exploited.

I'll be out in July for the meetup. I'm more that happy to take a course in Crush LHE HU Machine 101. I'm more than a little curious to see the thing.

You could be winning, but I would definitely not trust your feeling that you just know you are winning because you've found things you take to be weaknesses. Very good players said the same thing about Sonia and Polaris, and were wrong. GTO play can be really deceptive. Just saying....

Of course, the other explanation is that you are simply right.