How to compare the value of betting systems
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I apologize up front, but this article isn’t for everyone. It’s aimed specifically at sports bettors that are using – or that are planning to use - the so-called Kelly criterion to size their bets.
The Kelly criterion is essentially a progressive betting system wherein the higher your probability of winning, the more you’re supposed to risk; the less your probability of winning, the less you’re supposed to risk. (Sounds reasonable, all right.) We won’t describe the Kelly system in detail here because it’s boring and it takes too long. Those of you who are using it already know how it works. Besides, by now there are so many variations that the one you might be using could be a lot different from any particular one we might describe.
I’ll cut right to the chase. None of the variations work; - at least, not against sports betting. I’m going to explain to you right here, right now, once and for all why the Kelly criterion as applied to sports betting would be better called the Kamikaze criterion. You can prove it for yourself, and here’s how:
Here’s what you’ll need, along with at least a half-hour of time:
1. A hand calculator
2. Two decks of ordinary playing cards
3. Lined paper
4. Pen or pencil
5. A ‘Thank You’ note to send me after you complete this exercise and realize how much money I've saved you.....
Pick any size fantasy bankroll to use as your total bankroll. Why not $10,000? Thoroughly shuffle the 2 decks of playing cards together and place them face down in front of you. We’re going to turn one card at a time and count it as a win, loss, or tie. Everything 7 through King will be a ‘winner,’ everything 2 through 6 will be a ‘loser,’ the Aces will be ties. With those rules, the double deck contains 56 ‘winners,’ 40 ‘losers,’ and 8 ‘ties.’ That makes an overall winning expectation of 58.3 percent, but that expectation will vary widely – just as it does in sports betting - as you turn the cards and the deck turns ‘positive’ and ‘negative.’
Figure the sizes of your Kelly bets accordingly. If the first card is a ‘loser,’ there are only 39 losers left in the deck, but still 56 winners. Your winning expectation for the second draw (’bet’) increases to 56 out of 95, or 58.9 percent. If the first card is a ‘winner,’ your winning expectation for the second draw drops to 55 of 95 or 57.9 percent. This, of course, is where the hand calculator comes in.
Be sure to record whether you won or lost the first bet, and how much you won or lost. Go ahead and do this 50-or-so more times before reshuffling the deck and starting over. (Don’t do it more than 50 or 60 times without reshuffling. Always reshuffle when you've been through about half the double deck.) Remember, according to the Kelly criterion if the deck goes ‘negative’ and you do not have a positive expectation don’t bet anything. Just flip the next card and the next until you do have a positive expectation.
To make the exercise more realistic, as when actually betting against sports, flip several cards at once. After all, NFL, NBA, MLB and NHL games often go off several at a time and cannot be bet sequentially. You have to lay several bets at once. Try flipping 3 or 4 or more cards at once, - maybe even a dozen or so.
After doing another 50-60-or-so observations with the reshuffled deck, it’s time to compare your results using the Kelly criterion against so-called ‘flat’ bets.
Here's where the Kelly promoters always screw up. If they cite a sample of, say, 1,000 bets wherein they win, say, 580 and lose 420, (a win percentage of 58%), they don't stop to think that the total amount risked by using the Kelly criterion over the 1,000 bets is a whol-l-l-le lot higher than the total amount risked by using a simple flat bet.
Consider that fact for a moment.....Hell, if you win 580 of 1,000 bets, the more you risk on the 1,000 bets, the bigger your profit.
That's no surprise, is it? The way to fairly compare the Kelly system (or the so-called "star" system or any other progressive betting scheme) to flat betting is to use a flat bet the same size as the average size of all your Kelly bets. That way, you’re risking the same total amount against the same overall won-lost results. No fair risking more money overall with one system than the other. That obviously skewers the results. Or, another way to fairly compare betting systems is to keep track of the winnings as a percent of the total amount risked. If Betting System A wins 8 percent of all monies risked while Betting System B wins 10 percent of all monies risked, Betting System B is obviously better than Betting System A.
This is precisely what Kelly-promoters choose to ignore. It is critical to your results that the total amount risked be taken into account. Comparing flat betting against a "one-star, two-star, three-star" system, for example, if all your flat bets are only as big as your "one-star" bets, you are not using a fair comparison.
All right, time to check the profits from flat betting against the record of the Kelly criterion, and ta-daa! There’s your proof. The Kelly loses, and it loses every time. In fact, using most forms of the Kelly criterion, I would be surprised if after 70 or 80 ‘bets’ you are not - for all intents and purposes – broke.
You can use the same results to compare the old "one-star, two-star, three-star" system. You don’t have to flip the cards again, you can use the same won-lost progression you got while testing the Kelly criterion. Set your own parameters concerning when to use a "one-star" bet, a "two-star" bet or a "three-star" bet. Perhaps between 55 and 58 percent you could use a "one-star" bet, etc. (Of course, when your winning expectation is less than 53 or 54 percent, there is no reason to bet at all.)
The cold hard fact is that all progressive betting systems are nothing more than modified versions of the Martingale system.
In the Martingale, you risk one unit, and if you win you keep risking one unit. If you lose, you double your bet, and if you lose again you re-double and keep re-doubling until you finally do win. Then you go back to risking one unit. As any fool can plainly see, the Martingale can’t miss, so long as you win one more bet before you die you’re going to be a winner.
Well, yeah, if you lose10 bets in a row you’d have to risk $102,400 to win $100, but how often is that gonna happen?
As it turns out, plenty.
Modifications of the Martingale have been devised to be more "forgiving." One of the ways to soften the Martingale is to double your bet after two losses instead of after every loss. Or how about increasing the bet by only 50% instead of doubling?
You see, with progressive betting schemes the ratio of risk rises or falls in direct proportion to the ratio of "guaranteed" profit. This is true of all progressive betting systems, including the Kelly criterion. With the Martingale, the promise of profit is essentially absolute, so the potential for disaster is also essentially absolute. With the Kelly criterion the promise of short-term profit is not so absolute, so the potential for short-term disaster is not so absolute. Nevertheless, you can be sure the potential for disaster is increased, and increased dramatically. Over a relativle short period of time you will invariably go broke due to the vagaries of binomial distribution of your winners and losers. (See our article, "Binomial Distribution and You.")
