Simulation of the growth of a poker player's bankroll

[Fredrik]

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.

http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=8457727&page=0&fpart=all&vc=1 is a link to the thread in the poker forum, if anyone's interested.

 

[Evalesco]

Hi there! It sounds like you are trying to understand the simulation mentioned in the poker forum. The formula you mentioned is a randomly generated number based on the ln (natural logarithm) and sin (sine) functions. The ln function returns the natural logarithm of a number, while the sin function returns the sine of an angle. The random number generated by this formula is then multiplied by your standard deviation per 100 hands and added to your win rate per 100 hands to simulate the growth of a poker player's bankroll.

If you are looking for more information, I recommend checking out some online resources like Khan Academy or Coursera which offer tutorials and courses on statistics. I also suggest searching for some specific questions related to this topic on StackOverflow, as it is a great resource for programming and mathematical questions. Good luck!

 

[tacman]

The formula being used in the simulation is known as the Box-Muller transform, which is a way to generate random numbers from a normal distribution. The first part of the formula, SQRT(-2*LN(RAND())), generates a random number with a mean of 0 and a standard deviation of 1. This is then multiplied by the standard deviation inputted in the Excel document (sd/100) and added to the mean inputted (ptbb/100). This gives a random number with a mean of ptbb/100 and a standard deviation of sd/100, which is what is needed for the simulation.

The log and sin functions are used to convert the random number generated into a normal distribution. The log function helps to spread out the values, while the sin function helps to make them more evenly distributed. This is important because in poker, the profit per hand is not normally distributed, but the simulation needs it to be in order to accurately represent the growth of a player's bankroll.

As for the objection about the profit per hand not being normally distributed, it is true that in poker, there are many factors that can affect a player's profit per hand, such as skill level, luck, and table dynamics. However, the simulation is still a useful tool for understanding the general growth of a player's bankroll, as it takes into account the player's win rate and standard deviation, which are the most important factors in determining long-term success.

If you want to do a better simulation yourself, you can try using different distributions or even adding in other variables such as skill level or luck. However, the current simulation is a good starting point for understanding the basics of bankroll growth in poker.