I'm Mike Johanson, one of the authors on the recent "HULHE is solved" paper, and I wrote a fair chunk of the code for Cepheus.
kuzzooroo's link was the right one. At the link he gave (not reproduced here - new account, I have no reputation to post > 2 links), you can query any part of Cepheus' strategy, or play against it -- at least, you will be able to once the traffic lightens up, we've had to disable the play-Cepheus page for now. But the query service is running fine.
If you'd like to read the Science paper, you can find a link to it on my personal webpage. My earlier papers there will also give more detail on the algorithm it's based on, called CFR.
If you want the source code, that's available too - BSD license. link
As for other programs and groups, and the history of our effort... The University of Alberta's Computer Poker Research Group started in 1994, and we've had a considerable focus on heads-up limit hold'em since 2001. In 2003 we created the first decent game theoretic strategy for the game, called PsOpti (vlzvl mentioned Sparbot - it's the same strategy, renamed for Poker Academy). In 2007 and 2008, our program Polaris competed against human pros, narrowly losing in 2007 and narrowly winning in 2008, marking the first time that a computer has ever defeated human poker pros in a meaningful match. In 2011, we developed the first tractable algorithm for HULHE that lets us compute an optimal counter-strategy to defeat a given strategy, and measure how much that strategy loses for against the counter-strategy. That lets us measure how close to unbeatable play we are. Ever since, we've been driving closer and closer to perfect play (i.e., towards a worst-case loss of 0), and have been publishing our progress over the years in open, publicly accessible research papers.
In this paper, after 13 years of focus on HULHE from our first decent game theoretic strategy to this one, we're announcing that we have finally essentially solved the game. Cepheus is maximally beatable for under 0.000986 big blinds per game, or under 0.05 big bets / 100 if you prefer those units. It'd take more than 60 million hands of using the perfect counter-strategy to have 95% confidence of winning against Cepheus, which is why we say it's essentially solved: it'd take more than a human lifetime of play to statistically discern the difference between Cepheus and an exact optimal strategy. We go into much more detail on this in the paper.
So as far as Jim Beam's statement that we're claiming credit for something others have already done... I disagree. We've been in this space for 20 years, were the first to achieve the earlier big milestones in HULHE (first not-terrible strat, first program to beat humans, first measurement of worst-case loss), and have pushed the science by fully publishing our work at every step of the way. Essentially solving the game is the final step in a long line of research on this game.
Not much is known about PokerSnowie and the casino game - they don't release stats on how close to optimal they are, or any useful details of what algorithms they use or how their programs work. PokerSnowie claims to be close to equilibrium, but offer no proof at all, and from the discussions on 2+2 where they also claim to play optimal 6-player and no-limit, it's clear that they either don't know what "game theoretic optimal" play means, or they're exaggerating: no-limit is unfathomably larger than heads-up limit and it's nonsense to claim optimal play there, and an "optimal" strategy wouldn't have any theoretically useful properties in a 6-player game. Actually, in the 2+2 threads, they've admitted to this and removed most of the advertising from their webpage that mentions "optimal play", and have refocussed their marketing.
Cepheus is an essentially optimal strategy for heads-up limit hold'em, and it can play against either of them, or any human or other program, and be guaranteed to not lose. We're @PolarisPoker on twitter - we mostly use that for posting links to new papers that we publish.
