Texas Hold-Em -- An Evolutionary Approach Part 6

© 2006 Richard P. Ten Dyke

I played about 70 million games of Poker last night. And about 70 million the night before. You would think I would be exhausted by now. Of course, you know the secret: the computer played the games. The Poker simulations are now running as planned. Seventy million games reduces to about 500,000 tournaments and takes about six hours of computer time to complete.

I also bought a book about playing Poker on line. It =s about time, wouldn =t you say?

To refresh your memory, we start simulated tournaments with a pool of 32 players who play seven-player games with players drawn at random from the total pool of players. After each tournament, poor players in the pool are replaced with semi-clones of the better players. Over a period of a few thousand tournaments, only better players remain in the pool. This is an implementation of Darwinian evolution. Better players are those who win the most money in a tournament. Each player plays a Astrategy @ that takes into account the quality of the hand, the amount of money he/she has, the strength of the strongest and the weakest player in the game, the number of players remaining in the game after some of them have folded, and the position at the table related to the first bettor, and an occasional bluff.

One of the limits to the simulations was computing power, since it takes lots of it to evaluate a hand. We solved this problem by dividing the process of play into two pieces: hand evaluation and betting strategy. Hand evaluation is based on the probability that a particular set of player cards, combined with the community cards, will win against a random opponent. After the hand evaluation part is complete, the simulated player is only interested in the probabilities, so it becomes a game of probabilities not a game of specific hands or card combinations. Since this is the case, we can separate the simulations into these two distinct components, and run them individually. The betting strategy part then runs with the hand evaluation probabilities predetermined. This cuts the run time of a simulation by over 90 percent and permits more computer time for the evolution process.

After reading the book on Poker, I learned that I had made a mistake in the design of the game, which I have now corrected. In the game as played, there are two blind bets, a small blind made by the first player following the dealer, and a big blind by the next player at the table. The simulation now uses that procedure.

So what have been the results? Some are good and some disappointing. The good is that the games are played in a manner that is consistent with general good sense. Factors which the book says are important really are. One of these is where you sit at the table relative to the dealer. Being the last better (the dealer) has an advantage. (Betting starts with the first player following the dealer, you recall.) There is no dealer in internet Poker, so there is a Avirtual @ dealer position that rotates around the table at each game.

A second obvious result is that it is better to have more money than less. A winning player will take into account the amount of money he has, and be more aggressive with more money and more conservative with less. Makes sense.

The more compelling result is that the conservative player (almost) always wins the tournament. That is to say, the players who survive play conservatively. They fold early and often. The time for that decision is the betting after the flop. Before that and after, you can be a little more loose. Also, as a strategy, bluffing is overrated.

It was disappointing that overly aggressive players could not survive in the long run. An aggressive player will win a tournament rarely, and in the long run, all were eliminated, and new ones did not emerge. This is disappointing not from understanding the results, but disappointing in the sense that we were hoping for a possible bifurcation of species, but it did not occur.

This may make sense. After all, Poker is a simple game. Once you reduce it to a game of probabilities it almost isn =t Poker anymore. Now, if you are an experienced player sitting across the table from an adversary, and you are looking for changes in facial expression or other clues, you might make more of a game out of it. You train yourself to be a lie detector. Maybe. Maybe you think you can do it. Maybe you are the one who is fooled by the fact that you succeed from time to time due to mere randomness. Perhaps. Watching Poker on television, one gets the impression that this is a key part of the game. Personally, I doubt it. And there is little to observe when playing on the internet.

One of the differences between the simulation and a real game is probably the fact that in our simulations all players eventually play similar strategies. As a result, most simulated games are over quickly and the pots are small since most of the players fold. Observing real games with several players, this seems not to be the case. One interpretation of this is that real games have more poor players in them than the simulations. Another may be that real players have more complex strategies, and that the simulations are unrealistic. Time will tell. Both theories may be true and false at the same time.

In games of chance, such as Roulette and Black Jack, a player plays against the house, and the house wins in the long run. In Poker one plays against other players, and when there are weak players in the game you can help them to give you their money. This makes Poker different from Roulette and Black Jack. In a sense, a good player in the Poker game almost becomes a partner of the house. And there are lots of weak players.

To try out a theory, I ran a simulation in which a small percentage of the players consistently played more aggressively, that is to say, more recklessly, than the evolving players. The results were clear and statistically significant. The games lengthened with more betting and with the size of the pots increased.

Now, I must confess that I actually bought not one but three books. One entitled AInternet Poker for Dummies @ is a thin book which I found at the cash register of a local grocery store. It is a perfect example of a book with an appropriate title. Mostly, it tells you how easy it is to sign up for on‑line Poker and the best ways to send them money. Oh, yes, I think it did mention getting some money back as well. I found the other two books at Borders, which has a whole section devoted to gambling. I picked a couple at random. They are interesting in the sense that they spent a great deal of space on how to evaluate a hand and a competitive situation. They also say that it is a good idea to play a conservative game, for which I give them credit. They also advise you not to play too many games at once (on- line, that is) because you might become confused and fold when you should raise. Go-o-o-d advice!

I do not claim that the simulations accurately represent the way an individual should play the game, but I do think that they teach something useful about what to look for and how to go about it. We will continue the simulations to look at other factors, such as the number of players at the table, to determine how this affects a betting strategy. We will also start to explore some situation‑ specific strategies. For example, suppose you are the small blind bettor, and after the big blind, every player checks or folds. Would it be appropriate at that time to bluff with a raise? We will try it and see.

In the next installment, we will finish up this series with a summary of what we have learned.