Kelly Criterion explained

[TLD]

The following is a true statement:

In sportsbetting, unlike certain games of dice and cards, you generally can only estimate your likelihood of winning an upcoming wager, not pinpoint it precisely.


The following is a false statement:

Unless you can precisely pinpoint your likelihood of winning an upcoming wager, you will better grow your bankroll by flat betting rather than by using Kelly.

[Dark Horse]

Kelly can produce astronomical bet sizes that are just not on the table for me. Playing around with the numbers and my own comfort level I came up with these personalized values. I would -conservatively- set 60% as the maximum attainable winning expectation for any system (even though that is not true), and bet 1/3 Kelly. That would mean that, at -105 odds, any betting system of 60% or higher would automatically result in a 6% bet size. If I never bet anything with a lower winning expectation than 54%, and always bet at -105 odds, that would give me seven bet sizes:

54% - 1.89%
55% - 2.58%
56% - 3.26%
57% - 3.94%
58% - 4.63%
59% - 5.31%
60% and above - 5.99%

The difference per percentage point is roughly 0.7% of bankroll:
6.0 - 5.3 - 4.6 - 3.9 - 3.2 - 2.5 - 1.8.

If my expectation was between 58% and 57%, I would take the lower of the two.

For comparison, for full Kelly a 54% winning expectation would produce a 5.68% (!) bet size (with -105 odds). That may work for some, but not for me.

======================= ===============

If my maximum bet size was not 6% but 5% of bankroll, then I would simply use 2.0 - 2.5 - 3.0 - 3.5 - 4.0 - 4.5 - and 5.0 % of bankroll for winning expectations 54% through 60+%.

[coldhardfacts]

Coldhard...

You look at 20 years of data, and determine that "X" will occur 6% of the time. You can bet the "No X" at -800. The market is very liquid - you are limited only by bankroll considerations. You will have this opportunity perhaps 30 times a year. How much do you risk?

This is not a hypothetical. This opportunity still exists. Other opportunities exist. One of my main roles in my group is risk management. If you don't have risk management problems on a weekly basis, you aren't looking hard enough for opportunities.

OK, I agree that if you have 20 years of data available to analyze, and you know which variables in your handicapping analysis are the most pivotal, then you can pretty closely approximate what your expected probability of winning is on any particular event, and you would adjust your risk accordingly. For most of us - at least most of us that are successful - sports handicapping is a lifetime learning experience wherein we continue to consider and weigh different factors in order to maximize our return. Because there are so many factors and variables in every sport (e.g., matchups, pointspreads, home vs road, etc. - and these are just the known variables), it is virtually impossible to maintain and process that much data over that long a period of time.

I'm not sure what you mean by "risk management problems". I have reached the point where I am comfortable that every bet I make provides adequate value, although I realize that there's always room for improvement. Why would I want to look for "problems"?

[Bullajami]

I thought the primary value of the video was in demonstrating that even if you have an edge it is possible to size your bets in such a way as to not be profitable in the long run. I suspect this is not as well known among members here as it should be.

[Art Vandeleigh]

Kelly can produce astronomical bet sizes that are just not on the table for me. Playing around with the numbers and my own comfort level I came up with these personalized values. I would -conservatively- set 60% as the maximum attainable winning expectation for any system (even though that is not true), and bet 1/3 Kelly. That would mean that, at -105 odds, any betting system of 60% or higher would automatically result in a 6% bet size. If I never bet anything with a lower winning expectation than 54%, and always bet at -105 odds, that would give me seven bet sizes:

54% - 1.89%
55% - 2.58%
56% - 3.26%
57% - 3.94%
58% - 4.63%
59% - 5.31%
60% and above - 5.99%

The difference per percentage point is roughly 0.7% of bankroll:
6.0 - 5.3 - 4.6 - 3.9 - 3.2 - 2.5 - 1.8.

If my expectation was between 58% and 57%, I would take the lower of the two.

For comparison, for full Kelly a 54% winning expectation would produce a 5.68% (!) bet size (with -105 odds). That may work for some, but not for me.

======================= ===============

If my maximum bet size was not 6% but 5% of bankroll, then I would simply use 2.0 - 2.5 - 3.0 - 3.5 - 4.0 - 4.5 - and 5.0 % of bankroll for winning expectations 54% through 60+%.

Good post, makes things reasonable, realistic, easy to use.

Only question is, how far off would one stray from Justin's optimal upward curving line, if this approach is used, i.e. what does one third Kelly really imply? Is it one third of the way between flat betting and optimal betting growth?

[Ganchrow]

Good post, makes things reasonable, realistic, easy to use.

Only question is, how far off would one stray from Justin's optimal upward curving line, if this approach is used, i.e. what does one third Kelly really imply? Is it one third of the way between flat betting and optimal betting growth?

If you modify the Kelly Multiplier value in the Kelly Calculator from the deafult value of 1 you can note the impact on expected growth and expected value. A Kelly Multiplier of 0.33333, btw, would yield stakes of roughly one-third of full Kelly.

[Art Vandeleigh]

OK. At 55% win probability, after 100 bets, expected bankroll is 176.9% for full Kelly (multiplier of 1), 121.0% for 1/3 Kelly (multiplier of .3333).

After 1000 bets, expected bankroll is 30004% for full Kelly, 675% for 1/3 Kelly.

For flat betting let's say I started with a bankroll of $10,000 and always bet 105 to win 100. After 100 bets at 55% win probabilty, I would expect a $775 profit, after 1000 bets of never adjusting my bet size, $7750 profit. So I guess 107.75% expected bankroll after 100 bets, 177.5% for 1000 bets.

EDIT: I noticed that in the post below this, coldhardfacts quoted my numbers when I incorrectly calculated using -110. I changed the numbers in this post to -105 after CHF's quote.

[coldhardfacts]

OK. At 55% win probability, after 100 bets, expected bankroll is 131.6% for full Kelly (multiplier of 1), 109.6% for 1/3 Kelly (multiplier of .3333).

After 1000 bets, expected bankroll is 1558% for full Kelly, 250% for 1/3 Kelly.

For flat betting let's say I started with a bankroll of $10,000 and always bet 105 to win 100. After 100 bets at 55% win probabilty, I would expect a $775 profit, after 1000 bets of never adjusting my bet size, $7750 profit. So I guess 107.75% expected bankroll after 100 bets, 177.5% for 1000 bets.

OK, now I'm beginning to get it. The problem is, I have a family to support, and it seems like in any short term there are unavoidably going to be sizable dips in your bankroll.

With flat betting, I am confident I'm going to get a good return on my investment, am able to avoid the dips, and don't have to worry about a separate gambling bankroll. I'm thus able to weather any losing streak without having to adjust my betting patterns - or my lifestyle, and am assured of a steady long-term source of income.

I guess, just like any form of investing, it depends on what your financial goals and needs are.

[donjuan]

OK, now I'm beginning to get it. The problem is, I have a family to support, and it seems like in any short term there are unavoidably going to be sizable dips in your bankroll.

With flat betting, I am confident I'm going to get a good return on my investment, am able to avoid the dips, and don't have to worry about a separate gambling bankroll. I'm thus able to weather any losing streak without having to adjust my betting patterns - or my lifestyle, and am assured of a steady long-term source of income.

I guess, just like any form of investing, it depends on what your financial goals and needs are.

It sounds like you should take a look at fractional Kelly.

[Nicky Santoro]

good vid, but kelly criterion, shmelly miterion, kamma kamma kamma kamma kamma camelion,, or whatever you want to call it..

bottom line is..

if you bet 1 million in volume and you have a 3% edge on the line on each game, you will end up with 30,000 in your pocket.. whether you like it or not.. doesn't matter how you bet them.. as long as you bet within your means. so whether you are using kelly criterion or karma chamelion, you will still end up with a 30,000 profit.

so anyone care to argue my point. you bet 1 million in action at 3% advantage on each bet.. you make 30,000 profit.. if you bet within your means.. if you bet using kelly at 3% advantage, you still make 30,000 profit..

anyone care to disagree?

which ever way you break it down, you will still make 30,000 profit.

[Art Vandeleigh]

kelly criterion, shmelly miterion, kamma kamma kamma kamma kamma camelion,, or whatever you want to call it..

bottom line is..

if you bet 1 million in volume and you have a 3% edge on the line on each game, you will end up with 30,000 in your pocket.. whether you like it or not.. doesn't matter how you bet them.. as long as you bet within your means. so whether you are using kelly criterion or karma chamelion, you will still end up with a 30,000 profit.

These guys aren't trying to sell you anything. They're only trying to help you make mo money, mo money, mo money (if you really do have an advantage).

[donjuan]

So what do you suggest doing instead of Kelly, given that you are attempting to grow a bankroll optimally?

[Nicky Santoro]

artie

all i know is that which ever way you slice it, betting 1 million in action on NY Giants getting 1.5 pts better on every game, you will end up with 30,000 profit, whether you play exactly 1k per game on every game, or use the Karma Kamelion system, you will still have 30,000 in your pocket at end of year..


anyone care to argue this one?

[donjuan]

all i know is that which ever way you slice it, betting 1 million in action on NY Giants getting 1.5 pts better on every game, you will end up with 30,000 profit, whether you play exactly 1k per game on every game, or use the Karma Kamelion system, you will still have 30,000 in your pocket at end of year..


anyone care to argue this one?

That's pretty much irrelevant. If you are betting too much on individual wagers with regards to your bankroll, you will lose money. If you are betting too little, it won't grow as fast as it could. If you choose to ignore this after reading Ganchrow's excellent posts on the subject, you shouldn't be complaining about losing like you were recently.

[Nicky Santoro]

That's pretty much irrelevant. If you are betting too much on individual wagers with regards to your bankroll, you will lose money. If you are betting too little, it won't grow as fast as it could. If you choose to ignore this after reading Ganchrow's excellent posts on the subject, you shouldn't be complaining about losing like you were recently.

i have been losing because i have been getting greedy, and i deserved it.. but i do get great lines, and i am confident it will start to turn for me. if i hadn't chased, i'd have been ok.. chasing is a sickness.. everyone does it, and so do you.. you have done it in the past on a certain mon night game, or any late game..

but my whole point is, if you never chase and always bet within your means and you have the control of always betting what you should be betting, never more or less.. you will end up with same profit if you bet karma kamelion, OR you just bet same on every game, (assuming you have the same edge)

the key is 2 things. get the best of every #, AND never bet above your head, and result will be the same as using karma kamelion..

[donjuan]

i have been losing because i have been getting greedy, and i deserved it.. but i do get great lines

Did you not get one of the key concepts Justin explained in the video? Basically you can get great lines all you want but if you overbet them in relation to your bankroll, you will diminish your bankroll.

if i hadn't chased, i'd have been ok.. chasing is a sickness.. everyone does it, and so do you.. you have done it in the past on a certain mon night game, or any late game..

I don't chase. I bet Kelly.

but my whole point is, if you never chase and always bet within your means and you have the control of always betting what you should be betting, never more or less.

Never betting more or less is silly. Your edge is not always the same. Would you bet the same amount if someone gave you +100 on a 52% chance as if that same person offered you +100 on an 80% chance?

you will end up with same profit if you bet karma kamelion, OR you just bet same on every game

No you won't. Run a Monte Carlo sim.

[LT Profits]

Nicky,

I noticed you listed Money Management at 4. Now, if you substitute Kelly Criterion for Money Management (i.e., USE Kelly as your MM) and use it after your first three steps, you are actually not that far off.

[Nicky Santoro]

donny, i say bullsht to what you are saying.. you are saying you NEVER chased or put more on one game in your gambling career?? if you say no, i am done with you. no one in the history of gambling has ever not bet 1 or more games above their heads.. also, of course you bet more on a game that has a bigger edge. i was just giving an example IF all games had the same edge, then you bet same on every game at 1k and your profit will be the same.. and if you bet 1k a game and you get a total that will close at 4 pts better, then you bet 1500 on that game, and if it is only 1.5 pts better, then you bet maybe 700 on that game to maximize your profits. IF i hadn't done this from day 1, i wouldn't be here posting today. i'd be broke.

[donjuan]

donny, i say bullsht to what you are saying.. you are saying you NEVER chased or put more on one game in your gambling career?? if you say no, i am done with you. no one in the history of gambling has ever not bet 1 or more games above their heads..

Plenty of people don't chase. These are people who are successful at gambling. It's not an emotional thing.

i was just giving an example IF all games had the same edge, then you bet same on every game at 1k and your profit will be the same.. and if you bet 1k a game and you get a total that will close at 4 pts better, then you bet 1500 on that game, and if it is only 1.5 pts better, then you bet maybe 700 on that game to maximize your profits. IF i hadn't done this from day 1, i wouldn't be here posting today. i'd be broke.

So if you are varying your bet sizes, why not find the amount that grows your bankroll at the fastest expected rate?

[LT Profits]

Yes, I chased in my younger years, but I learned my lesson amd those memories actually help keep me disciplined today.

[louisvillekid]

i liked the vid, it has helped me get a better grasp on the Kelly thing people always talk about, i have tried to read about it and it just boggles my brain, i'm still confused how people calculate they have a 60% or 57%, or whatever edge in a game. I just look at lines and look at previous results and factor in how team A is playing at the moment vs. team B , plus whether it is a big game or on national tv, or if there are key injuries, or suspensions, coaching change, inner turmoil in a team. I mean i just try to look at those kinds of things and decide if i like a game or not, now how i'm supposed to put all that together and calculate i have whatever % of an edge i'm clueless.

[Nicky Santoro]

i can't believe what i am hearing.. be careful donny, your nose is growing as we speak.. sure you dont chase, ever.. donny, you never went 1-13 on an NFL sunday at about 1k apiece, then realized your down 13,000 + going into the final game and then realized, wtf is 1k going to do me.. it will put me at -12k for the day OR -14k for the day. and i love this game the most.. so i will only put 1k on it, right? now that's funny..

you probably put 4k on it because wtf is 1k goin to do you. you are down so big, 1k wont help.. it's a mental thing donny.. all gamblers will up their bets on the fnal game. sure you've never chased donny.. sure sure sure.. you are teh only guy in the world who has never chased because you are a pro..

donny.. you might be able to fool jjgold or anyone of the 20 yr old kids at sbr, like aao or venditto, but you cant fool me.

[donjuan]

i can't believe what i am hearing.. be careful donny, your nose is growing as we speak.. sure you dont chase, ever.. donny, you never went 1-13 on an NFL sunday at about 1k apiece, then realized your down 13,000 + going into the final game and then realized, wtf is 1k going to do me.. it will put me at -12k for the day OR -14k for the day. and i love this game the most.. so i will only put 1k on it, right? now that's funny..

you probably put 4k on it because wtf is 1k goin to do you. you are down so big, 1k wont help.. it's a mental thing donny.. all gamblers will up their bets on the fnal game. sure you've never chased donny.. sure sure sure.. you are teh only guy in the world who has never chased because you are a pro..

donny.. you might be able to fool jjgold or anyone of the 20 yr old kids at sbr, like aao or venditto, but you cant fool me.

Again, I couldn't care less whether I'm down for some random period of time. It's all one big series of bets. If I'm down a sizeable portion of my bankroll on a weekend, I decrease my bets, not increase. You can call me a liar all you want, but you have to realize that you being unable control your emotions doesn't mean other people can't.

[pavyracer]

Kelly criterion is a good tool to have when betting football. It has made me ton of money through the years.

[Bread]

Justin,

You are brilliant and you intimidate me.

Love,

Bread.

[Justin7]

donny, i say bullsht to what you are saying.. you are saying you NEVER chased or put more on one game in your gambling career?? if you say no, i am done with you. no one in the history of gambling has ever not bet 1 or more games above their heads..

Chase? Huh?

These teams are just random number generators. There are no people, no coaches, no fans and no excitement. They are just random number distributions. If you get a handle on the distributions, you can optimize your withdrawals from sportsbooks. What does chasing have to do randomly distributed bell curves?

[durito]

I don't chase and I never have.

I rarely check scores during games and I almost never go to sleep at night having any idea how much money I made or lost during that day -- nor does it matter.

While I am always looking to learn more and refine my approach there is no emotion involved in it for me at all.

[Bread]

I don't chase and I never have.

I rarely check scores during games and I almost never go to sleep at night having any idea how much money I made or lost during that day -- nor does it matter.

While I am always looking to learn more and refine my approach there is no emotion involved in it for me at all.

Durito...good for you. I wish I could do the same.

When I sleep with open action, I dream about it. Every scenario. It's weird.

I end up waking up at 6am and going to check. Then I can go back to sleep happy or angry.

You possess a unique quality. You are a professional.

[Santo]

This thread is somewhat unique, it shows both why people win, and where the money they win comes from ;o)

[reno cool]

That's pretty much irrelevant. If you are betting too much on individual wagers with regards to your bankroll, you will lose money. If you are betting too little, it won't grow as fast as it could. If you choose to ignore this after reading Ganchrow's excellent posts on the subject, you shouldn't be complaining about losing like you were recently.

This all depends on how you run. If you overbet Kelly your simply giving yourself a smaller chance at a larger profit. I mean a bigger chance to bust but a bigger to chance to get to a given highpoint sooner.

[donjuan]

This all depends on how you run. If you overbet Kelly your simply giving yourself a smaller chance at a larger profit. I mean a bigger chance to bust but a bigger to chance to get to a given highpoint sooner.

We are talking about expected bankroll growth here, not how to reach arbitrary numbers as quickly as possible.

[reno cool]

bankroll growth=reaching arbitrary numbers as quick as possible

no?

[TLD]

This all depends on how you run. If you overbet Kelly your simply giving yourself a smaller chance at a larger profit. I mean a bigger chance to bust but a bigger to chance to get to a given highpoint sooner.

Correct, in the trivial sense that since Kelly determines the optimal bet for growing your bankroll, by definition overbetting or underbetting Kelly means your bet sizes are not optimal.

But if you are flat betting--or any other system you might prefer--and thereby making bets larger or smaller than what Kelly would call for, you are also making bets that are not of optimal size for growing your bankroll.

So yes, aiming for Kelly and missing is a problem. But you can't bypass that problem by putting on a blindfold and not aiming at all.

[reno cool]

optimal= meaningless words

If you have 100 people with $1000 bankrolls.

They have say a 10% edge.

half will bet 10% of bankroll for 500 games adjusting as in Kelly
half will bet 20% adjusting also

which group is likely to end up with more $ as a whole?

[durito]

<let's not do this again>