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I'm sure there's a mathematical justification behind the authors' claims. I assume the computer just goes down the branches of the decision tree until every possibility is enumerated, and then works backwards to find an unexploitable strategy. The fixed bet sizing of limit poker severely limits the size of the decision tree, and given the power of computers nowadays, it seems very plausible that a computer could be programmed to play limit holdem close to perfectly.
If you knew you were up against A-5o, then you would call with [A-5o+, 2-2+] and that's what the computer would EXPECT you to do for that hand. If you knew you were up against the upper end of the range, 9-9, you would call with [9-9 to A-A], a much tighter range but the range the program would expect you to call with. The median range you should call with might be denoted as Rmedian. A good player would be able to calculate Rmedian. That good player would then tighten his or her range in this situation, so that instead of always using Rmedian, s/he would be calling with a tighter range of Rtighter-than-median.
The result of THAT would be +EV for the human, I believe. If not, I'd have to see some math to prove it. The reason I think it would be is that the human would lose more 1BB by folding more often, but would win more 20BB by winning more of the calls at the higher end of the program's range. The 20-to-1 ratio decides it over many thousands of hands in favor of the human, if the range was tightened optimally. However, in Limit that ratio might be much smaller, so the tightening adjustment has to be less to compensate.
…
Probably going to be my last post, but hopefully this makes sense:
The whole point of an unexploitable range is that even if you know exactly what "Rmedian" is, you can't create a calling range that is profitable. That unexploitable range exists, Nash says it exists, it's not THAT hard to prove (again, the internet is a great resource here), it's just a matter of finding it. Any good player tries to find these ranges against random opponents (the best players come pretty close), until they've gained more information and can adjust their play to take advantage of their opponents' tendencies. These authors claim that they've created a computer that finds these unexploitable ranges (or something very close to it). That claim is not unreasonable for limit poker, especially considering there is already software that can find that range in extremely simple NL scenarios (again, short-stacked, short-handed).
In your example, the computer's unexploitable range is chosen so that your range Rtighter-than-median is still not profitable… sure, with your range you're +EV in pots where you actually call, but you're losing enough in the pots that you don't that it doesn't matter. The best you can do is find a game theory optimal calling range and break even, but you can't profit.
Last edited by Tyler Longo; Saturday, 10th January, 2015, 01:21 AM.
Reason: clarity/spelling
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