Thoroughbred Handicapping Tools


"Learning, earning and loving the track."


NetCapper Store
New Stuff

The Grandstand
Capper Demo
Spot Play Demo
New Features
Track Tracts
TTs Archive
Contact Info
More Books
Capper Email























Track Tracts

Full Kelly/Fractional Bankroll
by Gordon Pine

It�s commonly agreed among money management experts that wagering a percentage of your bankroll based on the Kelly Criterion is the optimum way to bet. The Kelly Criterion recommends a bet size based on your edge over the game divided by your odds. For instance, if you have demonstrated a long-term profit of 15% of the amount you�ve wagered, at average odds of 3/1, then your optimum size bet would be 15% divided by 3, or 5% of your bankroll. It has been mathematically proven that using the Kelly bet size would leave you with a larger bankroll than any other method over a very large series of bets, given a random set of wagers. (Now, as I've stated in previous articles, I have a problem with the description of any series of horse racing bets as random, but let�s set that aside for now.)

Some money management experts have built on this, and espoused what they call a "fractional Kelly" bet amount. Instead of betting the constant Kelly percentage of bankroll, they advocate taking some fraction of that percentage and using that as the bet amount instead. For instance, say your records indicate a Kelly percentage of 4% -- your "half-Kelly" bet size would then be half of that, or 2% reasoning is, even with the Kelly percentage, you risk tapping out your bankroll. Because you�re betting smaller amounts, the fractional Kelly method offers increased safety from losing your capital.

But is this really a good idea? What�s the cost of a fractional Kelly strategy? It can be very substantial. That�s why I came up with the notion of "mini-bankrolls." Mini-bankrolls are based on the idea that rather than betting a fractional Kelly with your full bankroll, you�re better off betting a full Kelly with a fraction of your bankroll.

Before, if I had a Kelly percentage of 4%, I would bet around 2% of my entire bankroll each time, utilizing the half-Kelly method. Nowadays, say I�m trying out a new handicapping method that my research suggests dictates a full Kelly percentage of 5% or more. I will take a separate $40 mini-bankroll and bet the full 5% each time. The initial size of the bankroll is tiny, so the worst-case scenario of tapping out is unimportant. But the power of this method is in the substantiality of the full Kelly bet size. If your method stinks, you�re out 40 bucks. If it works, your bankroll increases exponentially. The mini-bankroll strategy combines a great upside with a trivial worst-case scenario. It�s the best of both worlds. If you do tap out, you can then reassess your handicapping method and try again with a new mini-bankroll.

Here�s an example: you have a 16% edge and you make 5% bets with a $40 mini-bankroll. After 500 bets, you should have something like $2149. Compare that to the same 16% edge, using fractional Kelly 2% bets with a starting bankroll of $400 (10 times as big). After 500 bets, you should have something like $1976.

Another example: say you took two $500 bankrolls. You have a 20% edge and a full Kelly bet size of 5%. With one of these bankrolls, you bet 5%. With the other you bet a fractional Kelly 2%. On average, after 500 bets, you have $71,743 with the full Kelly as opposed to $3671 with the fractional Kelly.

"If you want low risk, why not bet zero percentage? Then your risk will be zero. The goal should be to bet the optimum amount, where the risk/reward ratio is the best it can be."

Yeah, your risk is less when you bet less than the Kelly percentage. Reducing your risk is nice, but is it $68,072 nice? If you want low risk, why not bet zero percentage? Then your risk will be zero. The goal should be to bet the optimum amount, where the risk/reward ratio is the best it can be. If you have an edge over this game, you should take advantage of it, but do it with the track�s money by using a small initial bankroll.

The one drawback of full Kelly wagering is that it can have a higher level of risk than some other betting methods. Mini-bankrolls remove that one negative because you�re starting with a trivial bankroll. Full Kelly wagering provides such a dramatic advantage over fractional Kelly wagering that it surmounts the obstacle of a small starting bankroll and still triumphs handily, given enough distance of ground to do its magic. And the longer you give it, the better it gets.

To recap in practical terms: I suggest you keep records and know the edge and average odds of your handicapping method. Assuming you�re making a flat-bet profit, from that you can calculate your full Kelly percentage. Unless you�re already betting with the track�s money and are still using the same method that you used to win it, start with a mini-bankroll. (The sheepishness that you might feel betting small amounts should not be long-lasting if your method is good. Your bet size will increase soon enough.) Finally, I think the full Kelly percentage should be modified up and down within a certain range using Samovitz-type variable percentage wagering as you proceed with your betting. But that�s a subject for another article. NC

Copyright �2001 NetCapper Inc. All rights reserved.

Back to Top