Quant Finance Challenge

I want to solve this problem and make a post out of it.

The puzzle:

A gambler has a 10% edge (60% win) and starts with $100 in a game of winning the amount risked or losing it. He uses the Kelly fraction to bet. What’s the probability (3% error) that in the course of playing 400 games the equity will drop to $10 (stopped out)?

BTW, for those who would like to simulate but are not familiar with the Kelly fraction, it is equal to K% = p-(1-p)/R, where p is the win probability and R is the payoff ratio. In this case, R =1, p = 0.6, and the Kelly fraction is 0.2, or 20% of equity risked at every step.

Michael Harris (Weekend puzzle)

This puzzle is inline with something I wanted to experiment. Which is about the advantage study on a similar problem. Like when people talk about Roger Federer 53% average point win made him the best.

Someone mentioned the following post the other day. Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin. I don’t think is a great paper, but it holds a study on the topic.