Let there be two bots.

Bot #1 is called Sammy Solver

Sammy has the most complete poker game tree in the world, and each hand Sammy plays adds to his solution, but is otherwise forgotten.

Bot #2 is called Marty Memorizer

Marty remembers every hand of poker he plays, and does not posses any solved game tree other than the hands he has played, and the identity of the opponent. All hands Marty plays are remembered forever.

Both bots are sophisticated, such that they can play hands of poker which are new, and make correlated decisions about similar situations, such that neither bot is easily exploited (they are not breakable by crafty human degens).

Now, a poker website has purchased these bots exclusively and advertises a leaderboard challenge to “beat the bots” and humans are invited to play 6-max no limit Hold’em with both bots, such that there are 4 humans and 2 bots. The humans have avatars and are individually identifiable.



Question: Will Marty ever win more money from humans than Sammy? If so, why?

The question as far as I can tell is whether a perfect GTO bot will be as good as the most exploitative possible bot at beating humans at poker... I think there's really no match. An exploitative bot *could* be much much better than a GTO bot. It would be even better if it could sit as an actual robot at a live poker table with the humans and make reads on various gestures, eye movements, and what not... I don't think the technology required for this type of AI is really all that far away.

Well, sorta. Lots of info is left out about the Marty bot and the skill of the humans.

It is not a given that Marty will eventually outplay the humans at all. I admit that it is implied that Martybot will do so, but implied should not be assumed. All that is guaranteed is that Marty is not exploited by tricks such as minraises and check-minraises etc.

For instance, the humans are also learning from Sammybot. Martybot will have to be quite a creation to learn poker, without any game tree, faster than the humans. If the only poker Marty learns is from humans, he may possibly not ever learn it faster than humans.

Will Martybot eventually learn GTO from Sammybot? Or will Martybot always be one step behind Sammy, and one step ahead of the humans?

What if the humans are so good at mimicking GTO that Marty can not distinguish their play from Sammy, other than by avatar?

The info left out about Marty Memorizer is also the “why” part of the question. The ways in which an ideal exploit bot would be programmed are quite ambiguous. I suspect that attempts at exploit bots were routinely crushed by top pros in the years before Libratus.

To answer we really need to theorize about the way Marty is programmed.

Well the thing here is that humans are currently much much better than any AI at inductive learning. For example, I could show you a single instance of a character written in a language you don’t know, and you would easily be able to recognize that same character written by other people/fonts/etc. Computers on the other hand would (generally) need thousands of examples.

Same thing with poker. You can very quickly determine various aspects of someone else’s styles by a relatively few hands; or you can pick up on the way people are adjusting to you, or predict the way people have adjusted to you when similar situations have happened in the past. And generally you can do all of this without a ton of data.

While humans are *currently* better than AI at this kind of stuff, there is no reason to believe it will always remain that way. So basically my belief is that someday a software program (perhaps matched with hardware sensors like cameras to recognize live tells) will be by far the strongest poker player (and live poker player), and it *will* exploit weaknesses better than any human can.

So basically what happens is Marty loses a bit to Sammy at first, and then less and less. It will continue to try to exploit Sammy, and will continue to lose because of that, but the losses will eventually become negligible - especially compared to the money Marty is able to scoop off the humans, which will greatly exceed what Sammy does.

Well there are basicaly 6 unknown players, we do not know whether any of the bots is better than human players. We do not know how good are human players/bots.
We do not know how fast any of them improves.

Looks like there is no good answer, maybe it is a task What is better, solving game by a decision tree or by a brutal force? Chess bots showed force is good, even though the chess game is not solved the programs are very strong with ability to improve beyond human possibility.

Hmm. We do know that Sammy > Marty since Sammy starts out with more game tree and adds whatever Marty experiences to that info. It is safe to assume Marty will always lose to Sammy, in the long run, as will the humans.

So, at the start of the process, we have:

Sammy Solver Bot> Humans > Marty Memorizer Bot

The humans are caught in the middle. Marty is remembering and reacting to the actual actions of the humans (positive theory) and Sammy is holding firm on GTO (normative theory).