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Hi Brett. I have a question for you:
I assume you've recorded all your bets so far and know what your index number is, etc, having bet fully Kelly on them. These sample of bets are now a good testing ground. I'd like to know, and I am sure the results would interest yourself, how you would've gone if you were betting each of the following:
1. Full Kelly (as you have been)
2. 3/4 Kelly
3. 1/2 Kelly
4. 1/4 Kelly
If you've got records it'd obviously be a pretty simple matter in Excel to work those things out. You could graph them and have a look at the ups and downs based on that. Of course, the final index numbers (to this point) would be very interesting too.
I say it because although I personally focus on racing, I wouldn't bet more than 10% Kelly, and even that's pretty high, because there's absolutely no way that my price is accurate enough for that. I know when I've gone through periods of my own betting, if I'd bet Full Kelly it'd have been a disaster, whereas a 10% Kelly is a lot more smooth. To be honest, I usually bet around 7% Kelly, that's enough for me.
Obviously, racing and sports are very different and you can come up with a more accurate/reliable price on a sporting event, there's more chaos in a horse race. For starters, quarterbacks don't have Danny Nikolic pulling them up... So, 7% Kelly would be too weak on sports betting, but I'd be interested to know how those higher figures like 1/4, 1/2 look on your history this year.
Betting my picks at differing kelly fractions results in an exponential decrease in the amount lost, by 1/4 kelly, my BR index would be still at 86.
I really don't take stock in optimizing against one real betting run. This one real betting run is an iteration of a vast array of possibilities. It's unique in the way the bets came along (whether simultaneous or not), and sometimes I bet out of the 'kelly queue' when I want to lock in a line, which makes back fitting a betting strategy even more moot.
What's that program called? The Staking Machine? Where can you can back fit betting strategies? IMHO, a real betting run should only be used as a guide to set the parameters for rigorous simulation. There's no point in finding out some BS betting strategy like Fibbonacci does best over the sample, as it takes advantage of the peculiarities/nuances of that particular betting run.
I simulated by a distribution of my expected win % 1000 times X 1000 bets per run. I plotted the end state bankrolls for each run to see the distribution. I plotted it at different Kelly fractions. I even did level staking.
Whatever betting strategy you choose, it needs to be simulated in order for you to plot the distribution of possibilities.
Then you need to go with what your comfortable with, what maximizes your expected utility/contentment. With ATS betting, I'm not content with anything that does not maximize BR end state growth. The volatility is great, but relative to money line betting (which you do as a horse player), ATS betting at full kelly would be FAR from as volatile as money line betting at full kelly.
Yeah, I'd definitively adopt a Kelly fractional for horse racing. Maybe not as low as yours though.