Re: Effect of proportional betting on trip risk

From Stanford Wong's BJ21

Posted by DD' on 18 Mar 1998, 10:00 p.m., in response to Effect of proportional betting on trip risk, posted by Kim Lee on 18 Mar 1998, 3:56 p.m.

>A "Kelly" proportional bettor needs to carry a big >fraction of total bankroll to avoid short-term ruin on a >lengthy trip. Choosing bets in proportion to total >bankroll will reduce the probability of a trip ruin as >bets shrink with losses.

It is my personal opinion that resizing on a trip at all is a bad idea. So you go broke every once and a while. Those time when you don't bust out return more than adequate compensation for the times that you do.

The major disadvantage to the frequent resizing is that you severly lengthen the long run index. If one could resize optimally after every bet it would take exactly four tijmes as many hands for the expectation to overcome one standard deviation, or to achieve any confidence level of winning. The frequent resizer has a smaller probability of catastrophic loss, but a much greater chance of a net loss.

Those who wish to resize bets when a certain portion of the trip bank is lost should, if they want to do it optimally, should use a different risk formula altogether... the old double or bust formula. To be optimal, the fraction of your bank which you asign as your trip bank should be exactly proportional to your advantage over the casino in doubling your bank. If you play with a 20% risk of ruin vs doubling, then the odds are 80 to 20 in your favor. You have a 60% advantage and this is the fraction of your total bank that your trip bank should represent. If that seems to risky then you are not a Kelly player and should use a more tame utility. I now use 1/3 Kelly.