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How to test the Kelly Criterion

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, and that would be a great long term winning percentage against sports betting.

But that expectation will vary widely as you remove cards from the deck. As you turn the cards and remove them from the remaining deck the deck will turn ‘positive’ or ‘negative'; – that is, if you remove more ‘losers’ (2’s through 6’s) from the deck than ‘winners’ (7’s through K’s), the remaining deck will offer a higher expectation of ‘winning’ on the next draw, and vice-versa.

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. As a Kelly bettor, of course, your bet sizes will vary up and down as your winning expectation goes up and down. Go ahead and do this 50-or-so 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. Don’t go through the entire 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. Size your Kelly bets exactly as you do against sports, and 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 – just like when you’re betting on sports.

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.

Right here is precisely where Kelly promoters always screw up. Let’s say they have 100 actual bets wherein they win, say, 58 and lose 42. That’s a great winning percentage of 58%, of course. Now, they’ll explain that their basic bet is, say, $100, but if their expectation is higher than such-and-such percentage they risk $120, or $130, or whatever, and if their expectation is even higher than such-and-such they might risk $200 or more.

Then they compare what they won by using the Kelly system to what they would have won had they been risking only $100 on each of the 100 bets.

…..Duhhh!…..They risked more money with the Kelly system and they made more money after going 58-42. I hate to burst their balloon, but when you go 58-42, the more money you risk the more money you figure to make. Sorry, boys, but that is not news.

To be continued…