I did go a bit further towards alief by putting into my toy MC study, with the simple coin-toss game in your link, a bettor who puts in 50% of his bankroll every time—way, way beyond the Kelly fraction, and then having a think about how he managed to lose all his money. (Not literally, but enough that the remaining bankroll was 0 to my printout accuracy.)In ten thousand iterations my longest win and loss streaks are both of ten games. A loss streak of ten games will reduce this bettor’s bankroll by a factor of 1024. But ten winning games will only increase it by about a factor 80. On the other hand, with the Kelly fraction of 4.5%, ten losses reduce your bankroll by about 40%, while ten wins increase it by 62%. The asymmetry in these specific examples is somehow more convincing than the final numbers from the toy MC run.
I did go a bit further towards alief by putting into my toy MC study, with the simple coin-toss game in your link, a bettor who puts in 50% of his bankroll every time—way, way beyond the Kelly fraction, and then having a think about how he managed to lose all his money. (Not literally, but enough that the remaining bankroll was 0 to my printout accuracy.)In ten thousand iterations my longest win and loss streaks are both of ten games. A loss streak of ten games will reduce this bettor’s bankroll by a factor of 1024. But ten winning games will only increase it by about a factor 80. On the other hand, with the Kelly fraction of 4.5%, ten losses reduce your bankroll by about 40%, while ten wins increase it by 62%. The asymmetry in these specific examples is somehow more convincing than the final numbers from the toy MC run.