There have been a number of arguments over the merits of the Kelly Criterion in sports betting in the Think Tank. However, there was this post in one of Ganch's threads that had always intrigued me...
So what I decided to do was write a simulation to prove/disprove this theory. I have attached an Excel spreadsheet which enables you to do this exact thing, comparing flat betting to the Kelly Criterion. Let me know how many times through the deck (cycles) it takes you to go broke using the Kelly Criterion as the author asserts...
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.
The only way to fairly compare the Kelly 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 the 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 12 percent of all the monies risked, Betting System B is obviously better than Betting System A.
This is precisely what Kelly-promoters choose to ignore. Comparing flat betting against a "1-star, 2-star, 3-star" system, for example, and going 58-42, if all your flat bets are only as big as your "1-star" bets, of course you will win more with the star system. You're risking more and you're winning 58% of your bets.
All right, back to our double-deck of cards. Time to check the profits from flat betting against the record of the Kelly criterion, and ta-daa! There’s your proof. Using the average size of your Kelly bets as your flat bet, 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 "1-star, 2-star, 3-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 "1-star" bet, a "2-star" bet or a "3-star" bet. Perhaps between 55 and 58 percent you could use a "1-star" bet, etc. Of course, when your winning expectation is less than 53 or 54 percent, there is no reason to bet at all. Bet any system - including flat betting - only when you have an acceptable winning expectation
----------J.R.Miller "Debunking the Kelly System"
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.
The only way to fairly compare the Kelly 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 the 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 12 percent of all the monies risked, Betting System B is obviously better than Betting System A.
This is precisely what Kelly-promoters choose to ignore. Comparing flat betting against a "1-star, 2-star, 3-star" system, for example, and going 58-42, if all your flat bets are only as big as your "1-star" bets, of course you will win more with the star system. You're risking more and you're winning 58% of your bets.
All right, back to our double-deck of cards. Time to check the profits from flat betting against the record of the Kelly criterion, and ta-daa! There’s your proof. Using the average size of your Kelly bets as your flat bet, 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 "1-star, 2-star, 3-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 "1-star" bet, a "2-star" bet or a "3-star" bet. Perhaps between 55 and 58 percent you could use a "1-star" bet, etc. Of course, when your winning expectation is less than 53 or 54 percent, there is no reason to bet at all. Bet any system - including flat betting - only when you have an acceptable winning expectation
----------J.R.Miller "Debunking the Kelly System"
So what I decided to do was write a simulation to prove/disprove this theory. I have attached an Excel spreadsheet which enables you to do this exact thing, comparing flat betting to the Kelly Criterion. Let me know how many times through the deck (cycles) it takes you to go broke using the Kelly Criterion as the author asserts...
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