This is according to Bill Chen and Jerrod Ankenman, authors of "The Mathematics of Poker". The unexploitable strategy for a heads-up, capped, limit holdem game is just barely within the limits of what can be reasonably calculated with computers, from a computational complexity perspective. The reason this is possible is that heads up limit holdem has been theoretically 'solved'. The Bellagio game got a lot of attention at the TwoPlusTwo forums some time ago. I'm surprised there is not more buzz about it. The dealer position alternates, starting with the machine. As I recall, it was a $2/$4 structured game. The game is near the poker room and uses dollars as the denomination. I played it for about ten minutes and came out well ahead, but I'm sure that was mostly luck. As far as I could tell there was no rake or rules favoring the machine. On this topic, I saw a game at the Bellagio that specifically was playing against a bot. I'd be okay with using a bot online as long as it wasn't specifically forbidden. However, I think the best human players are much better than the best bots. My opinion is that good bots can beat low-limit games online. For a bot, such an option is much more often favorable, because it's inherently weaker at complex tactics, but very strong at playing by the book - check the outs, subtract false outs, play the implied odds - even good players can't do it as well as a computer. The issue is the cost of mistakes being pretty high, so it's sometimes better to ignore mixed signals and just level down to ABC strategy, even for a human player. And then, it's difficult to combine the first cue with further cues, I just can't think of a way to algorithmize that, while recalling when I played just like that myself and comparing it is pretty easy. It's just that sometimes a human will not have that hand, either because he isn't considering position, or sends the signal intentionally.
Why could I not teach the bot the same logic? If the bot ever got to see the cards in this situation it could validate (or discredit) its own assumption about that particular player. The human brain uses logic, so can the bot, so what does the human have that the bot cannot replicate to pin someone on a hand?įor example, a raise under the gun usually signals huge strength, so a human might put the player on a big pocket pair, or at least ace-king, or a stone cold bluff.
Ok, its pretty obvious you know what your talking about, but if a human can pin someone on hand, why not a bot? After-all the bot is going to know the players history flawlessly, where as the human would need to remember everything. At least some poker bot makers eventually went down in complexity, because increasing alterations in basic play resulted in a decreased effectiveness. That is not in question the hard part is not playing at level 6, but getting better results from that than from playing at level 1. One can implement algorithms that can be considered level 3, 4, 5, and why not even 6.
Of course, you have to take some level 2 considerations into account, such as increasing fold bias against tight players, but the spectrum of factors required for fully moving to that level is not well algorithmized. You are limited to either using predefined classifications or a weighted coefficient adjustment, while a player can often actually pin another on a hand. But never near as well as a medium-skilled player.
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