with a 57.5 % winning expectation......

on each of your next 21 bets, you can expect a result of:

article:

Even if you have a long term advantage against pointspreads and over-under lines, you will go broke with the use of faulty money management. For our purposes here, we'll say you have a 57.5% winning expectation on each and every bet. (Of course, the actual winning expectation is rarely the same on any two bets, - but our record shows we average between 55%-58% over the very long term.)

...So, how many winners can you expect in the next, say, 21 bets? Well, 57.5% of 21 is 12.075, so the answer figures to be 12, producing a win-loss record of 12-9.

Trouble is, a record of 12-9 is not the only thing that can happen. There are several other results that are also very likely, and some of these other results are not good. The graph below shows the binomial distribution of all the possible outcomes.

With a 57.5% winning expectation on each of our next 21 bets, we can expect a result of...
...3-18 or worse 0.01% of the time

...4-17 or worse 0.04% of the time

...5-16 or worse 0.18% of the time

...6-15 or worse 0.71% of the time

...7-14 or worse 2.22% of the time

...8-13 or worse 5.81% of the time

...9-12 or worse 12.82% of the time

...10-11 or worse 24.21% of the time

...11-10 or worse 39.61% of the time

...12-9 or worse 56.98% of the time

...13-8 or worse 73.25% of the time

...14-7 or worse 85.83% of the time

...15-6 or worse 93.77% of the time

...16-5 or worse 97.80% of the time

...17-4 or worse 99.40% of the time

...18-3 or worse 99.88% of the time

...19-2 or worse 99.99% of the time





Notice that although a result of 12-9 is the most likely of all outcomes, a result of precisely 12-9 will occur only slightly more than 17% of the time. That's only about one time in six. In real life, you can figure on a record of something other than 12-9 about 5 out of 6 times.

With a 57.5% expectation-per-bet, you can plan on making any profit at all only about 60% of the time over your next 21 bets. In 4 out of 10 cases, you can expect to win less than twelve out of 21 bets. Even with a 57.5% winning expectation on every bet, you must be aware that it is just as easy to go 7-14 (or worse!) as it is to go 17-4 or better. Once in about 8 times you can expect to lose 13 or more of your next 21 bets. By understanding the consequences of the probabilities involved, you can avoid the disastrous results of using such nonsensical money management traps as the so-called 'Kelly criterion' or the suicidal 'one-star, two-star, three-star' nonsense, or other progressive betting schemes.

In our book, How Professional Gamblers Beat The Pro Football Pointspread, we explain why most people go broke betting on sports because they don't understand the ramifications of the probabilities; - not because they can't call winners. They are victims of the fallacy that progressive betting schemes can produce more profit than they deserve.

Over the course of an entire NFL season we figure to have upwards of 210 opinions against pointspreads and totals, - but that does not mean we can view those 210 opinions as though they were ten individual 'blocks' of 21 bets. The 210 opinions can be regarded as a continum of bets from 1 through 210, or a continum of 21-block units from 21 through 210. Bets 1 through 21 comprise the first such block, bets 2 through 22 comprise the second block, bets 3 through 23 comprise the third block, etc...Within 210 consecutive bets there are 189 blocks of 21 consecutive bets.

Since there are 189 'blocks' of 21 consecutive bets in a series of 210 bets, it's virtually a sure thing that we will have more than one block wherein our record will be WORSE than 8-13, and it's also pretty much guaranteed that we will have more than one 'block' wherein our record is better than 16-5. Neither of these results means we are 'hot' or 'cold,' or that we are performing better or worse than our normal level of handicapping. Such results are caused by wholly normal and natural fluctuations from the mathematical expectation - binomial distribution.




The trick is to be ready for the ups and downs that are bound to occur simply due to the mathematics of the situation. With upwards of 210 opinions against NFL lines, we do expect an overall win rate in the area of 57.5%, but we also fully expect a very bumpy ride along the way. Against the NFL, to insure that you'll still be alive in January, we highly recommend a bet size of no more than 2% of your bankroll. Guarantees come with toasters, not football bets. How many bets we might win over the next ten or twenty tries, however, is hardly more than a guess. Scale your bet sizes so you'll be alive in January. Refrain from 'jiggling' the size of your bets; keep all bets the same size.

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.

Did you get that last paragraph? If you absolutely cannot resist betting more on some plays than others, if you cannot resist increasing your bet size to either catch up or to press a winning streak, you may have a gambling problem.

Sports betting on a professional level must be approached as an investment, not a bonanza. Understanding that fact may be the biggest difference between successful bettors and chronic losers. Sports betting is not a means to get rich overnight. Think "stock market," NOT "lottery." Think "investment," NOT "Brink's truck explosion."

What a trainwreck of misinformation this article is.

First the author "expects" to hit around 57.5%, but says he cannot distinguish between his 54% type plays and his "60%" type plays. Then he bashes Kelly, the optimal method for sharp players to maximize earnings.

Sounds likes the "old school" drivel of JR Miller, the most overrated handicapper on the planet.

Fezzik.This is a Miller article.

Disagree with you on the Kelly Criterion. Do the math. It doesn't pan out. My 14 year old showed me. Optimal method for sharp players??

Only thing sharp about Kelly is the pointed dunce cap that the losers wear.

Show me your math, Falco.

Remember one thing: resize your bet after each wager.

I'd love you to show me how a Kelly bettor loses. To make it easier, assume a 57% hit rate, risking 10% on each play. 100 plays, again to make it easy. The Kelly bettor will destroy the flat bettor.

Daringly, from JR millers site. Changed the name to you. Keep an open mind and become enlightened


I apologize up front, but this article isn’t for everyone. It’s aimed specifically at Daringly who is using – or that is planning to use - the so-called Kelly criterion to size his 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 Daringly, 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’ or ‘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 per bet, 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 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 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 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 whenever the deck was in my favor and whenever I felt no heat from the floor people, and trying to risk nothing at all when the deck was negative (and I could get away with passing the hand). 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 abstractual 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 my books and articles and in Professional Gambler Newsletter I repeatedly warn bettors that the size of their bets cannot be used as a pry-bar to win more than they deserve. If you’ll do the exercise above you will prove it for yourself. (This means you Daringly)

…But y’know what? I don’t expect a big upsurge in my mail due to Thank You notes. Hardly anyone will do the test. People tend to believe what they wish to be true, and to disbelieve what they wish to be untrue. (That's how the human race got saddled with religion.) Using a flat bet is the most boring of all betting "systems" because it does not offer more profits than you deserve. Nevertheless, it is the most effective over the long haul largely because it is certainly the safest. We recommend using an absolute maximum of 2 percent of your working capital for individual bets, and not changing your bet size until your bankroll has increased or decreased by about 50 percent. Many non-professionals think 2 percent is too conservative, but most professional bettors use much less than 2 percent. The consensus among pros I’ve known is about 1 percent.

-- J. R. Miller

Your welcome Daringly

Daringly, Miller talked about different varients of Kelly. Here is my simple understanding of Kelly. Lets say that you have a win percentage of 60% that means that you lose 40% of the time. 60%-40%= 20% Kelly says that you have an advantage of 20% over the game and that is what your bet size should be. Now start off with a 10,000 fantasy bankroll. and on paper bet 100 times at that 20% of bankroll. Don't forget juice. WWWLWWWLLL. WWWWWWLLLL. WLWLWLWLWW. LLLLWWWWWW. WWLLWWLLWW ETC ETC. The previous 5 sequences represent 60% winning percentage. 6 wins 4 losses do another 95 and compare them to 100 flat bets don't forget the juice and and resize the bets keeping them constant to your 20% advantage. Surprise

Falco -

The "2-decks of cards" example has a massive error in it. The example you cited does NOT use Kelly criterion, because it misanalyzes simultaneous bets.

Pretend I'm placing 4 simultaneous bets. Analyze all the win/loss permutations with various bet sizes. You'll quickly see that when you make multiple large bets (40% of your bank at once is roughly the critical point), you must lower your average wager due to variance, since your return on that SERIES OF SIMULTANEOUS BETS is less than the sum of individual advantages. We held a contest for a solution to THIS EXACT type of problem on SSB last fall.

If you attempt to Kelly bet, and overestimate your edge, you will lose. The example above (which I admit I didn't go through because of the obvious error) overestimates the player's edge, since it doesn't adjust for multiple bets.

I kid you not. I have been using precise Kelly betting since day one, any the results have been amazing. But if you don't understand what exactly you are doing (such as JR Miller), you won't succeed. Fully half of my team's efforts go not to picking which teams we like, but assessing our exact advantage on various plays.

Another fallacy in JR Miller's the argument... The most important thing to an investor is the net return, not the return on risk, if maximizing your ROR means minimizing your actual gain.

Assume you have a bank of $10k. Through a promotion, you can make a 60% play, but only for $100 "juice free" and more at -110. How much do you bet? Miller would bet $100, since the ROR is higher. A kelly bettor will slightly lower his ROR by betting more at full juice, to increase his net return.

Falco, your second example doesn't make any sense. If I'm winning 6/10 wages, my bankroll grows 12.7% each 10 wagers. If I'm laying -110, my advantage drops, but I'm still making a mint (as long as I recognize the reduced advantage, and bet-size appropriately).

You know, your second advantage is even better for showing why intelligent Kelly blows away flat-betting.

100 wagers... My bankroll is now 1.127^10 as large, or roughly 3.3 times as large as it began.

Now, you are flat-betting. Pick any amount - say 5% of your bankroll? Pick a different amount if you like. 100 bets, you'll make 20 units, and double your money. Unless through some terrible fluke, you start off badly and "wipe-out". At 60% win rate with 5% units, it's not likely, but it is finite. While Kelly's theoretical ROR is 0%, you'll quit betting at a certain point... But even then, Kelly's ROR is much lower than flat-betting.

And... in a "short run" of 100 games, who's better off? Go to 1000 games, who's better off? After 1000 games, Joe Flat-bettor has now multiplied his bankroll 10-fold. Joe Kelly? Roughly 150,000-fold.

Proper execution of Kelly analysis means your money grows exponentially (as in your example) instead of linearly, at least until you want to bet more than anyone will take (which happens surprisingly fast).

Daringly

daringly, i too at first bought into this nonsense about flat betting and it was partly because of jr miller which who by the way can't pick his ass with both hands. but i saw the light mainly from fezzik who gives the vary good example in football of a play that has value at +3 obviously has to have increased value at +3-. it has to over the long run so why would you not play more at 3- than you would at 3. ps i have seen you posts here and at some of the other forums and greatly appreciate them.

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by daringly:
Falco -

The "2-decks of cards" example has a massive error in it. The example you cited does NOT use Kelly criterion, because it misanalyzes simultaneous bets.
<HR></BLOCKQUOTE>

Sorry, but this "massive error" you are talking about isnt there. Miller dos'nt say how you should figure your kelly stakes, he says just take any kelly system you like, it dos'nt matter.
Falco just gave one example of kelly staking.
So we basicly allready agreed that this particular system dosnt work.
Now please make the card test with your particular system.

Roger_H (newbie?):

Do you know the exact way to determine a Kelly-scale bet with multiple bets? There is EXACTLY one way to determine your risk using Kelly. "Kelly" proportional betting maximizes the expected logarithm of your bankroll.

I assure you, if I am making 4 simultaneous wagers, each of which has a 15% advantage, you do NOT risk 60% of your bankroll at once. I'll wager you 10 dimes I can prove it. JR Miller's example makes a similar mistake.

My expectation is that if you play the 2-deck example, flip one card at a time, and bet-size properly (which means reducing your advantage is laying -110), you'll do very well. Would you care to offer that game to me for real money?

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>Originally posted by daringly:
Roger_H (newbie?):

Do you know the exact way to determine a Kelly-scale bet with multiple bets? There is EXACTLY one way to determine your risk using Kelly.
<HR></BLOCKQUOTE>
No I dont know.

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>
"Kelly" proportional betting maximizes the expected logarithm of your bankroll.
<HR></BLOCKQUOTE>
Prove it.

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>
I assure you, if I am making 4 simultaneous wagers, each of which has a 15% advantage, you do NOT risk 60% of your bankroll at once. I'll wager you 10 dimes I can prove it.
<HR></BLOCKQUOTE>
I dont really get what you want to tell us with that last sentence. I could also wager 10 dimes if I had them.

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>
JR Miller's example makes a similar mistake.
<HR></BLOCKQUOTE>
Where is the mistake?

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>
My expectation is that if you play the 2-deck example, flip one card at a time, and bet-size properly (which means reducing your advantage is laying -110), you'll do very well.
<HR></BLOCKQUOTE>
Your expectation is not relevant .

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>
Would you care to offer that game to me for real money?<HR></BLOCKQUOTE>
What game? Why should I offer you anything? I dont get what you mean.

If you would explain to me the exact method you do your kelly stakes I would be willing to do this card-test. I'm really intrestet what the outcome is.

Roger_H,

I can show you to the water, but I cannot make you drink. It amazes me that you argue so vehemently about Kelly, when you don't even know what the definition of Kelly betting is.

Do a google search for "kelly betting defition". By definition, you select a risk amount which maximizes the ln of your bank's EV. If you can solve differential equations, you can determine the proper amount to risk in any situation, IF AND ONLY IF you know the odds of winning each contest, as well as the payout odds. (note that there are simpler ways to solve these than differential equations, especially for only 1 bet).

Try the card trick yourself. Use 1 deck to make it simple. 28 winners, 20 losers, 4 ties (this is similar to the Miller game). Make it simple, call it a 58% hit rate. Since you are not paying juice and getting 1:1 odds, your advantage is (58/1 - 42/1) or 16%.

Simplify it further. Don't adjust your advantage for cards leaving the deck (this will make the experiment much faster and lower your profit slightly, but this example can still prove the validity of Kelly, if you don't "pull a Miller").

Method #1: Start with 10k. Wager EXACTLY 16% on each card. If you win the first wager, your bank is multiplied by 1.16. If you lose, it is multiplied by 0.84.

Method #2: Same. Instead of doing book-keeping after each draw, just tally your wins and losses. With communicative property of multiplication, the order of wins/losses doesn't matter.
Your new bankroll = 1.14 ^ (wins) * 0.86 ^ (losses).

Try his experiment, share the results.

daringly, i understand what you are saying but many beginners and those unfamiliar with kelly will not that is why i used the basic example of bet sizing to take advantage of value. of course percent of bankroll has to be taken into consideration but sometimes if you use a very basic example of how something can be useful others will see some light and research on their own further

why systems like the kelly progressive/aggressive system is less than optimal for the majority of bettors: you cannot predict what your future win rate will be.

62% one year, 53% the next, 9 out of 10 kellys will see this, especially if you bet all sports.

I dont see how hitting 57% over 1 million bets somehow correlates to hitting 57% over the next 100. One thing that is overlooked IMO, is that no one facilitates a constant 57% all the time. We all have cloudy days.

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>
Method #1: Start with 10k. Wager EXACTLY 16% on each card. If you win the first wager, your bank is multiplied by 1.16. If you lose, it is multiplied by 0.84.<HR></BLOCKQUOTE>

I did this test, thou I think this isnt really kelly staking.

number of bets: 100
winners: 51
losers : 41
ties : 8

kelly
-----
starting bankroll : 10'000
end bankroll : 15'233.80
total amount staked: 202'881.54

flat staking
------------
stake=2'028.82
starting bankroll : 10'000
end bankroll : 30'288.20
total amount staked: 202'882.00

flat betting wins, atleast in this example.

nicely weighted.

Problem #1: You only hit 55% winners, instead of your long term expectation of 58%. If you try it for 1000, things will change.

Problem #2: You selected over 20% of your bankroll as your "standard" unit. That's not realistic. But even using a 20% standard wager, Kelly will eventually lap the flat bettor. Try again, with just say... 300 picks.

atx-when bet sizing your plays in real life you shouldn't have the same probablity on all your plays. you are exactly right no one hits at a constant 57%, 60% or what ever win rate you are using. thus the edge of kelly, you weight more heavily plays where you have a bigger advantage. this is why as daringly says kelly will out perform flat betting hands down. when you flat bet you are not taking full opportunity of advantages that arise and in other cases you will be overbetting your edge.