Current Approaches:
In two-player poker games, the most successful approach to date is based on game theory. A Nash equilibrium is a set of strategies, one for each player, where no player can increase the amount they win by changing to a different strategy. In two-player zero-sum games, such as two-player poker games, one player using a Nash equilibrium strategy is guaranteed to not lose against any adversary, even a worst-case adversary that knows what the strategy is. If the adversary makes mistakes, then a Nash equilibrium strategy can win. If a Nash equilibrium strategy is computed before the game is played, it can be used against any adversary without needing to know anything about their strategy. This is a nice property in poker, because it means that we can use it to at worst tie the game, while learning what mistakes the opponent is making so that we can change our strategy in response. The Annual Computer Poker Competition has driven significant effort towards approximating Nash equilibrium strategies in very large games, and the best programs in two-player limit Texas hold'em are now very close to a Nash equilibrium strategy. This approach was used in the 2007 and 2008 Man-vs-Machine Poker Championships, and is also used by most of the top competitors in the Annual Computer Poker Competition.
The other popular approach in the Computer Poker Competition involves observing strong players, such as good humans or good computer programs, and learning a strategy that mimics their behavior. Recently, this has involved case-based reasoning, in which a program's current decision is compared to a set of examples stored in memory. The most similar examples are used to choose a response.