Quote:
Originally Posted by roasthawg
Great, thanks for the link! So let me get this right...at 63% winning percentage you can expect to roughly triple your roll after 100 bets at 1/4 kelly, almost 10x it at 1/2 kelly, and multiply your roll 80 times over at full kelly?!? If that is the case then my conservative betting is costing me A TON of money indeed.
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And at double Kelly your expected bankroll would be almost 3,700 times higher, while at decuple-Kelly (10x Kelly) your expected bankroll would be over 69
thousand times higher.
The problem is that you're looking at this in very much the wrong way. There are two major problems with your analysis:
- The entire point of Kelly is that it defines one's utility function differently from the simple risk-neutral (i.e., "linear") function that would inspire a bettor to maximize expected utility. As such, it's unfair to compare fractional-Kelly strategies on the basis of expectation alone. The value of an expected bankroll needs to be tempered by the inherent riskiness of that expectation. The higher the Kelly fraction the necessarily higher the expected bankroll, but also the more risky the outcome distribution.
- Your 63% figure is an ex post figure (a Latin phrase loosely translated as "after the fact"). Bet sizing decisions, however, need to be made ex ante ("before the fact", the opposite of ex post). A 50% bettor who somehow magically knew ex ante over which stretches of 10 games he was going to win 60% or more (a feat that would occur roughly 37.7% of all discrete 10 game stretches) could make lots of money even while picking at only 50% over the long term. The problem with this, of course, is that such information is only available to nonprescient bettors ex post, and so can't be used directly in bet sizing decisions. Now that isn't to say that frequent out-of-sample stretches of 63% success rates shouldn't influence one's estimates of long-term success, but such evidence (like all additional evidence, whether tending to refute or confirm), should be carefully considered from the standpoint of Bayesian Inference and taken in light of one's prior hypotheses.
In general, for straightforward models, one's expected win percentage should be estimated from careful study and in-sample refinement of one's hypothesis, further refined by realized out-of-sample performance.
One's Kelly multiplier, on the other hand, should, for a given model, be taken as a measure of the inherent level of relative risk aversion at play when trading that model.
If people are interested I'll try to throw together an Excel spreadsheet that attempts to back out a Kelly multiplier in response to a users' answers to several questions.
Yet another Kelly question
Linear Mode
