Types of poker bot - The Optimal Bot

There are two distinctly different types of poker bot, the exploitive bot, and the optimal bot. These are very different ideas and require very different approaches.

Anyone who has played many poker tournaments will have heard of the Nash Equilibrium tables for poker. Nash Equilibrium is a game theory concept that says every game with 2 or more players has an optimal strategy, and no matter what someone else does, they will not be able to exploit that. This is the idea behind the optimal player, the optimal player is unexploitable, however, the flip side of this is that the optimal player does not exploit. "So that means it's possible to make an unbeatable poker bot" I hear you scream! Well, yes... in theory, and that's the important point here. Why do you think that the Nash tables have only been calculated for 2 player push / fold games? The amount of computing power and time required to calculate these strategies is huge, and with every bit of complexity you add, the required power increases exponentially. I doubt there is enough computing power in the universe to calculate these strategies for 3 player No-Limit, let alone anything beyond that.

The problem with No-Limit is that every different bet amount creates a different game state, so where as with Limit, you can fold, call or bet with No-Limit you can fold, call, or bet $1, or bet $2, or bet $1.33. If you've got $100 left if your stack, and the big blind is $1, that's 9,900 different possible game states created from different bet amounts. Now if every player at the table can create 10,000 possible different game states on every go, that's 1000000000000000000000000 possible game states with 6 players pre flop, and that's before we take into account every single possible combination of cards that can be dealt, future turns, and every possible combination of board cards. Abstractions can be used to simplify the game, but with every abstraction you're losing detail and are less likely to be able to find the true optimal solution. If short handed No-Limit hold'em is solved in my lifetime, I'll be very surprised.

The University of Alberta have been working on producing a world class poker bot for well over a decade now, and while their Heads-up limit bot is pretty damn good, and their Head up No-Limit bot isn't bad, anything beyond that is no where near being able to compete on the world stage yet.

So, optimal bots are a great theory, that's all they are, and when it comes to No-Limit Hold'em, that's all they'll ever be.