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DEBUNKING THE KELLY CRITERION Here's how to compare betting systems /// I apologize
up front, but this article isn’t for everyone. It’s aimed specifically at
sports bettors who are using  or that are planning to use  the socalled
"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 halfhour 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 viceversa. 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
50orso 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 5060orso observations with the
reshuffled deck, it’s time to compare your results using the Kelly criterion
against socalled ‘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
suchandsuch percentage they risk $120, or $130, or whatever, and if their
expectation is even higher than suchandsuch 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 5842. I hate to burst their balloon, but when
you go 5842, 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. Thatway, you’re risking the
same total amount against the same overall wonlost 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 Kellypromoters choose to
ignore. They want so very hard to believe their fantasy they won't be made to
face facts, no matter what. Comparing flat betting against a "1star,
2star, 3star" system, for example, and going 5842, if all your flat
bets are only as big as your "1star" 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 doubledeck of cards. Time to
check the profits from flat betting against the record of the Kelly
criterion, and tadaa! 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 "1star, 2star,
3star" system. You don’t have to flip the cards again; instead, you can
use the same wonlost progression you got while testing the Kelly criterion.
Set your own parameters concerning when to use a "1star" bet, a
"2star" bet or a "3star" bet. Perhaps between 55 and 58
percent you could use a "1star" 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. 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 redouble and keep redoubling
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 lose 12 bets in a row you’d have to
risk $409,600 to win $100, but how often is that going to happen? As it turns out, plenty. Modifications of the Martingale can make it 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 all progressive
betting schemes the ratio of risk rises or falls in direct proportion to the
ratio of "guaranteed" profit. This fact includes 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 shortterm profit is not so absolute, so
the potential for shortterm disaster is not so absolute. Nevertheless, you
can be sure the potential for disaster is increased dramatically. Over a
relatively short period of time you will invariably go broke due to the
vagaries of binomial distribution concerning your winners and losers. (See
our article, "Binomial Distribution and You.") NOTE: According to expert researcher Dr. Nigel E.
Turner, Ph.D., Scientist, Centre for Addiction and Mental Health (
ntsci@hotmail.com ), incremental betting is one of the telltale signs of
someone with a gambling problem. The Kelly criterion is sometimes touted as the best strategy against
casino 21, but during my years as a card counter I finally learned otherwise.
Against casino blackjack you will be urged by a lot of "experts" to
use graduated bet sizes, depending on whether your expectation of winning the
next hand is 51 percent or 53 percent or 55 percent. Frankly, I think that’s
a lot of hooey, and I’ve played an awful lot of blackjack. My strategy
finally evolved into trying to risk my maximum bet  my "real" bet
 whenever the deck was in my favor and whenever I felt no heat from the
floor people, and trying to risk as little as possible or nothing at all when
the deck was negative. Any other bet size, including whatever size bet made
after the dealer shuffles, is nothing but camouflage in order to hide from
the pit boss. The key phrase, of course, is "maximum bet size."
Supporters of the Kelly criterion are apparently espousing that when you have
a 55% winning expectation you’re supposed to use a bet so large that it would
bankrupt you if you had only a 52% winning expectation. I can pretty much
guarantee that if your bets are big enough to break you with a 52% winning
expectation, they will sooner or later break you with a 55% winning
expectation. Blackjack players using the Kelly system are simply kidding
themselves. If they could go back and average all their Kelly bets and simply
bet that average amount every time the deck was in their favor they would end
up with a lot more profit and a lot less risk. At least, good card counters can know relatively
clearly what the expectation of winning might be. The numbers on the cards
speak for themselves. Against sports, however, you can never know that. There
are countless variables involved in deciding which team is going to win a
football, basketball, baseball or hockey game. These subjective and abstract
factors are not so precisely calculable. In other words, you can never know
what your winning expectation might be against a sports event. The best you
can hope for is to believe you have at least a 55%60% chance of winning. It
is futile to try to handicap your own handicapping. In our books and articles and in
Professional Gambler Newsletter I repeatedly warn bettors that the size of
their bets cannot be used as a prybar to win more than they deserve. If
you’ll do the exercise above, you will prove it for yourself. …But y’know what? I don’t expect a big upsurge in my
mail due to Thank You notes. Hardly any believer in progressive betting
systems will actually do the test. People want very hard to believe what they
wish to be true, and they simply choose to disbelieve what they wish to be
untrue. Once people denied the earth was not the center of the universe, or
denied it was round. Users of progressive betting schemes want very much to
believe they can earn more than they deserve. They refuse to be confused with
facts. facts. Related articles: 
