The post below is correct, of course - I was writing in the context of the original topic of reducing the chance of going broke, but of course Kelly works at both ends of the bankroll – minimizing / controlling losses, and optimization of growth. That particular sentence was in contrast to some more arbitrary way of determining a stop point no matter how one was sizing one’s bets – but the point is also well-taken that you can further minimize the chance of getting to the stop point, however it is determined, by minimizing one’s bets as well.
In fact, when I played blackjack, the latter was exactly how I played, to some extent. I could have played at a higher minimum / unit bet, and according to Kelly, I should have – but I chose to bet at a somewhat lower level – because continuing to play at
that level without losing a lot was more important to me than bankroll growth. Also, even though my total bankroll would have supported a higher level of play, my trip bankroll (what I brought with me, beyond which I wouldn’t play anymore) might not have, and I didn’t like the idea of potentially having to stop playing on a given trip because I ran out of trip money, even though the total bankroll would have supported higher-level play according to Kelly.
Again, I didn’t fully understand the math involved, but I had read articles telling me what percentage of my total bankroll should be my unit bet based on Kelly, and I chose to play at a lower level. I knew that I was trading off greater (and less than optimal) bankroll growth in exchange for less chance of losing everything on a given trip. I suppose I could have traveled with more money or established a line of credit, but with just 3-5 trips a year (this
was before universal casino presence), and therefore limited opportunities to play, this was how I chose to play.
–BG
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Barry,
You make a number of excellent points, but you wrote “All Kelly does is minimize the chance of getting to the stop point.” This is incorrect. Kelly maximizes bankroll growth which is a trade off between risk and reward. You can play at the smallest stakes possible with a large bankroll and have almost zero chance of hitting the stop point, but also very little bankroll growth.
Chris