Let's say I have a biased coin that comes up heads 60% of the time. Using the Kelly criterion, I have an optimal bet of 20% of my balance on each coin flip. If I run a series of simulations, there are some where I end up with less money than I started and some where I go completely bust.
I control everything, including the probability, so how would I go about never ending up with less money than I started with?
I ran a series of simulations and noticed that early on, the ratio of heads to tails before flipping a head and before flipping a tail were different in a very structured way. I have attached this notebook which shows the distributions of H/T ratios before flipping a head is very different from flipping a tail.
Is there a way to use this information to avoid ending up with less than the initial balance?