It’s probably useful to understand the difference between, say, a biased coin (a discrete calculation) and a stock price (a continuous situation). A stock price is an independent variable, with variance. A coin which is biased to return heads 53% of the time, requires only p-q=f*.

It’s interesting, though, that options are more similar to biased coins -in that the delta is a useful approximation of the likelihood that an option expires essentially worthless. Note though that the Black-Scholes calculation of delta allows us to skip several statistical steps-so all we need to do is assess the option chain information. For example, an option showing a delta of .47 suggests a ‘biased coin’ of p=.53. The basic allocation of our wealth is 6%.

I think a major psychological impediment is to extrapolate based on the ‘law of small numbers.’ If you study Thorp, Ziemba and numerous academic articles, the simulations are in the thousands. There is a similarity with the simulations, in that ‘full Kelly’ results are extremely volatile.

In looking at a simulation, we see the final outcome. The results seem ‘obvious’. However, the vast majority of people, unable to visualize the final outcome, will likely throw in the towel after a couple of severe downturns.