Scientists "solve" Heads-up Limit Hold’em

[Isgrimnur]

Business Week

A breakthrough in artificial intelligence has mastered the simplest two-person version of the poker game, working through every possible variation of play to make the perfect move every time. When performed without mistakes, just like the childhood game tic-tac-toe, there’s no way to lose. In this case the player is Cepheus, a computer algorithm designed by Canadian researchers.
...
You don’t have to take their word, though, their work is published today in the journal Science. The researchers are calling for poker players to test the program for Limit Texas Hold’em by challenging Cepheus online. The results may cause gamblers to rethink some common moves, Bowling said in a telephone interview.
...
The results apply only to the most basic form of the game, known as Heads-up Limit Hold’em, where there are two players and bets and raises are limited. Even with those restrictions, there are more than 10,000 billion decision points in the game.
...
Solving the game required even deeper control than when the computer-program Chinook took the world championship title in checkers against humans in the 1990s or when International Business Machines Corp.’s Deep Blue beat Garry Kasparov in chess in 1997. While a computer program may one day beat the world’s best players of No-Limit Texas Hold’em, the most popular form of the game, it’s unlikely anyone will ever solve it by identifying the perfect way to play because there are so many more decision points and possible moves, Bowling said.

[coopasonic]

Even with those restrictions, there are more than 10,000 billion decision points in the game.

That's the best way they could come up with to express that number? Ten thousand billion sounds like something my five year old would say.

[BooTx]

A BILLION KAJILLION

[The Meal]

This seemed inevitable. When it comes to N > 2 participants, however, everything changes. (My understanding of Game Theory is rudimentary, but my research showed that heads-up games are nearly infinitely easier to solve.)

The switch from Limit to No Limit is not a terrific jump. The switch from 2 players to 3 is outrageous.

Science

[paulbaxter]

It isn't at all clear to me what this "solving" consisted of. It sounds like it's some sort of optimal strategy for 2-player limit HE. I'm just trying to think through how you would know it was optimal. I guess you could simulate an opponent for 10k hands each with a variety of opponent strategies and make sure you at least broke even against all of them. But, as The Meal said, that doesn't seem to get you very far in larger table sizes.

I suppose it would be nice to know all the criteria they found so I could use them when I got to heads up situations.

(May check that issue at my school library)

[coopasonic]

It isn't at all clear to me what this "solving" consisted of. It sounds like it's some sort of optimal strategy for 2-player limit HE. I'm just trying to think through how you would know it was optimal. I guess you could simulate an opponent for 10k hands each with a variety of opponent strategies and make sure you at least broke even against all of them. But, as The Meal said, that doesn't seem to get you very far in larger table sizes.

I suppose it would be nice to know all the criteria they found so I could use them when I got to heads up situations.

(May check that issue at my school library)

Dig here:
http://poker-blog.srv.ualberta.ca/

[paulbaxter]

It isn't at all clear to me what this "solving" consisted of. It sounds like it's some sort of optimal strategy for 2-player limit HE. I'm just trying to think through how you would know it was optimal. I guess you could simulate an opponent for 10k hands each with a variety of opponent strategies and make sure you at least broke even against all of them. But, as The Meal said, that doesn't seem to get you very far in larger table sizes.

I suppose it would be nice to know all the criteria they found so I could use them when I got to heads up situations.

(May check that issue at my school library)

Dig here:
http://poker-blog.srv.ualberta.ca/

Thanks. I was thinking about it more in the shower after I posted and I got to that thought about trying to learn opponents bluffing tendencies, but I'm quite willing to believe that that sort of analysis is mostly irrelevant, as your link suggests.

edit: I love this bit "Poker players, being rational people, did the only sane thing they could do, which was decline to play anyone who appeared to be of even remotely similar skill"

By far the best poker advice I've ever seen has been "play against people who are much worse than you." Can't be overstated.

[Jeff V]

By far the best poker advice I've ever seen has been "play against people who are much worse than you." Can't be overstated.

Corollary -- don't drink as much as the rest of the table. When I used to play a lot, I'd often have a late rally after everyone else gets stupid-drunk.

[Pyperkub]

I've always been better @ heads-up than a full table of hold-em. I think it's because I play (too?) aggressively. I like the action, so I gravitate more towards Craps and Blackjack table games when I'm in Vegas.