I was playing around in Excel the other day, simulating possible equity curve/P&L paths for a simple game I designed. The game is really trying to find an optimal risk managment strategy.
I start of with an initial Capital: 100. In each time increment you have the opportunity to risk a % of your capital on a coin flip, at each time period, you can either gain/lose the amount you bet on each flip. E.g. in the initial flip, if you gambled 25% of your capital, you can gain 25 or lose 25. The possibility of winning on each coin flip is 50% and the possibility of losing is 50%.
I simulated over 4000 possible P/L paths over 10 coin flips and I kept coming out with a win ratio less than 50. The more I increased the amount invested on each flip, the more I lost. The more coin flips I played the more my win% dropped. (Note, my definition of a win ratio is by the end of the 10th toss, how many of the simulations ended with a final capital greater than my initial capital of 100)
So I decided later to alter the % I invest on each coin flip based based on whether I won/lost the prior coin flip. In other words, if the last coin flip was win, the % amount I invest would be $x$ and if I lost the prior coin flip the % amount I invest would be $y%$. I came out with pretty startling results. I found that if I lost the prior flip, I should increase the amount I invest on the next flip. For the 4000 simulations among 10 flips, I came out with a 53% win ratio for % amount invested $x=3$ and $y=16$, ie, your increasing your bet size as you lose more. Is there any justification for this? Has anyone come to a similar conclusion from a similar simulation. Would love to post the excel spread sheet if anyone would like to take a look it.