Quote:
Originally Posted by mythrilfox
samooth, you're missing the point. obviously there's value in computing exploitability and sam never said otherwise. the question is what value is there in computing exploitability using an abstraction. if we're exploitable for 5 bb/100 using an abstracted tree, what does that translate to in terms of exploitability using the full game tree? i'm guessing from sam's comments that meaningful translation of this sort is nontrivial if not impossible.
punter never really addressed this and instead asked what's the value in creating a strategy without being able to assess how far from equilibrium it is, which imo is a silly question. of course there's value. if, for instance, your algorithm generates successive strategies such that strategy n beats all strategies 1 to n-1, then you're still getting closer to equilibrium with each successive iteration without ever knowing how far you are from it, and inevitably you will eventually arrive at equilibrium with enough iterations.
this relies on testing the value of the strategies empirically (i.e. by actually playing bajillions of hands), so as you got far enough along and started generating successive strategies that were extremely close to equilibrium, the edges would be so small that you would never be able to peg down precisely where equilibrium was. that doesn't mean there still isn't immense value in getting close to equilibrium, or at the very least demonstrably improving. it would be like saying we can't measure how far we are from a complete understanding of the laws of physics, so what value is there in even trying to understand them in the first place? literally all of science is measuring how a method/model compares to our current understanding & how well it performs empirically, not some sort of ground-up value assessment which would require complete omniscience of everything in the universe. generally speaking we only have the luxury of ground-up assessment in small and controlled systems that we humans created.
I definitely think that computing exploitability is important. Many of my papers use exploitability calculations whenever applicable/feasible, e.g.,
http://www.cs.cmu.edu/~sganzfri/Translation_IJCAI13.pdf,
http://www.cs.cmu.edu/~sganzfri/Puri...on_AAMAS12.pdf.
The first approach for computing exploitability in LHE was just developed a few years ago, and involved sophisticated techniques to be feasible,
http://webdocs.cs.ualberta.ca/~bowli...ijcai-rgbr.pdf. There are no known approaches for doing this in NL. I suppose the techniques from that paper could be applied for computing exploitability in NL if restricted to one betting size everywhere. Researchers from University of Alberta presented preliminary results of doing this at the AAAI Computer Poker and Imperfect Information Workshop back in 2012 or 2013 on their prior year's NL competition strategies. The exploitability that was reported was extremely high. They did not end up publishing this result, and when I followed up they were still looking into verifying the results to ensure correctness.
It seems like this approach would be totally infeasible for computing exploitability with more than one bet size.
Some posters have talked about computing estimates of exploitability, e.g., fixing preflop strategies and computing "postflop exploitability," computing exploitability within some abstraction, etc. I'm just not sure what the merit of such a value would be. If I say "I computed approximate exploitability using abstraction A and assumptions X, Y, and Z and it was 27.2 BB/100," there are probably two people in the world who would care.
Like I mentioned, I'm also not really sure how feasible these computations would be for strategies based on imperfect-recall abstractions.
It's possible that there is something interesting here, but I just haven't had much time to look into this problem very carefully, and as described above my instinct is that it would not be very valuable scientifically at this point (and would possibly require a lot of time and effort).
What I do think would be valuable would be an efficient general algorithm for computing best responses in games with imperfect recall, which would not be poker specific and could theoretically have broader applications. If I'm able to come up with an algorithm for that, then I would be interested in applying it to NLHE.
Last edited by Sam Ganzfried; 05-09-2015 at 07:01 PM.