Originally Posted by

**thom321**
Not sure if this will settle anything or add more fuel to the fire.

Since Monkey made it very easy to run multiple simulations, I decided to add some additional output variables and run batches of simulations to see if some obvious pattern would emerge.

I left the settings the way they were as far as edge, error etc. I adjusted the code to allow for running repeated simulations e.g. running 100 consecutive simulations where each simulation was e.g. 100 iterations of 1,000 plays. One “batch” as I refer to them is hence a simulation using x iterations of y number of plays.

I then calculated, for each batch, the average, median, max and min ending bank roll and also the % of time where the ending Kelly bankroll was larger than the ending Flat bankroll.

I ran this for

100 batches of 100 iterations times 1,000 plays

100 batches of 100 iterations times 10,000 plays

10 batches of 100 iterations times 100,000 plays

It was taking too much time for the 100,000 plays but when you see the output you will see that it doesn’t seem to matter. The results for each batch when running the simulations on 100,000 plays was very similar. This is either how the math works or it has something to do with the Excel random number generator not producing random enough numbers

.

The conclusion is that for simulations of 100 x 1,000 plays, Kelly produces a slightly higher average bankroll but only produces a higher average bankroll about 50% of the time. Kelly does generate a higher average max and a lower min.

On simulations of 100 x 10,000 plays, Kelly has a higher average ending bankroll but consistently has a lower median ending bankroll and has a lower ending bankroll that flat betting about 70% of the time.

In the 10 x 100,000 plays the average and median ending bankroll for Kelly is always lower than Flat and appears to generate a lower ending bankroll over 100,000 plays every time. Keep in mind this is using the default settings provided by Monkey as far as edge and error and could also be a function of some flaw in Excels random number generator. I don’t know enough about that or Kelly math to have a view.

I have included the worksheet that has the results from each simulation. Cell A1 has the settings that were used each time. Nothing changed between the different simulations other than the number of plays used.

If anyone cares, I can upload the adjusted workbook I used to generate these results.