jason1990
01-15-2005, 12:52 PM
I have just finished an article which, among other things, discusses how close a player's empirical SD is to his true SD. It's long and full of lots of math. Here's an excerpt to give you an idea of what it's about:
"Methods for analyzing the mean are relatively simple and well-known (and will be reviewed in the next section). Methods for analyzing the standard deviation, however, are less well-known and will be our primary focus. There are at least two ways to view this article. On the one hand, it is an exposition on some of the more elementary methods of mathematical statistics. The use of poker as our driving example is simply a convenient tool to facilitate our demonstrations. A strong background in basic undergraduate probability is a prerequisite for understanding the material presented here.
On the other hand, this article is also a treatise on the specific methods and techniques needed to apply mathematical statistics to the data generated by an online poker player, particularly for the purpose of analyzing his standard deviation. To make an analogy with finance, the standard deviation represents the 'volatility' of the poker player's investment. An accurate analysis of volatility is essential to making wise financial decisions. In fact, the bankroll fluctuations of a poker player are quite analogous to those of a financial investor. The difference lies primarily in the fact that the rules of poker are more clear cut and the possible outcomes at each time step (i.e. after each hand) are more limited. This makes for simpler mathematical models and, as such, the topics in this article could serve as a good starting point for anyone interested in applying probability and statistics to finance."
As it stands, it is almost certainly not appropriate for the magazine, but I wanted to share it with everyone anyway. You can download it here:
http://webpages.charter.net/swanson.jason/stats_poker.pdf
"Methods for analyzing the mean are relatively simple and well-known (and will be reviewed in the next section). Methods for analyzing the standard deviation, however, are less well-known and will be our primary focus. There are at least two ways to view this article. On the one hand, it is an exposition on some of the more elementary methods of mathematical statistics. The use of poker as our driving example is simply a convenient tool to facilitate our demonstrations. A strong background in basic undergraduate probability is a prerequisite for understanding the material presented here.
On the other hand, this article is also a treatise on the specific methods and techniques needed to apply mathematical statistics to the data generated by an online poker player, particularly for the purpose of analyzing his standard deviation. To make an analogy with finance, the standard deviation represents the 'volatility' of the poker player's investment. An accurate analysis of volatility is essential to making wise financial decisions. In fact, the bankroll fluctuations of a poker player are quite analogous to those of a financial investor. The difference lies primarily in the fact that the rules of poker are more clear cut and the possible outcomes at each time step (i.e. after each hand) are more limited. This makes for simpler mathematical models and, as such, the topics in this article could serve as a good starting point for anyone interested in applying probability and statistics to finance."
As it stands, it is almost certainly not appropriate for the magazine, but I wanted to share it with everyone anyway. You can download it here:
http://webpages.charter.net/swanson.jason/stats_poker.pdf