# Simulation of the growth of a poker player's bankroll

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I need some help with some statistics stuff. Right now I need it to understand one particular discussion in a poker forum, but I also think that this is a good opportunity for me to learn these things better. That's why I'm posting my questions here instead of in the poker forum.

Someone claimed that http://pokerfilz.50megs.com/variancedemo.xls does a reasonably accurate simulation of the growth of a poker player's bankroll, given that we know the player's win rate in ptbb per 100 hands ("ptbb/100") and the standard deviation per 100 hands ("sd/100"). A "ptbb" is 2 times the size of the big blind.

One person who replied said that the Excel document is fine, but some of the assumptions that it's based on are not. His main objection seems to be that the simulation is messed up because the profit per hand is not normally distributed.

I would like to understand these things and maybe do a better simulation myself.

The first step is to try to understand the simulation. You're supposed to use a program called Poker Tracker to find out your win rate and standard deviation, and input them into the document. The simulation is built around the following formula:

=SQRT(-2*LN(RAND()))*SIN(2*PI()*RAND())

The function rand() returns a random number between 0 and 1. Then the following expression is used:

= B40*$D$4+$D$3

That's the result of the previous calculation times the sd/100 plus the ptbb/100. These two calculations are repeated many times (one time for each point on the x axis). The profit so far is calculated from these results and plotted against the number of hands played. Each point on the x axis is 100 hands. Each point on the y axis is one buy-in, i.e. 50 ptbb or 100 big blinds.

Now, the first thing I need help with is the "random" formula above. I'm hoping that someone can explain it to me. I don't even know what the log and sin functions are doing there.

This is a link to the thread in the poker forum, if anyone's interested.

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