Issues with Kelly -diverted-

donjuan · 07-10-08, 01:52 PM

I've yet to see what makes Kelly inherently superior to any other betting scheme.

It maximizes expected growth, which is basically the most important thing in gambling if you like money.

Sure, you want to make a sensible bet in accordance with what you're trying to accomplish.

Making money. Kelly does this best.

But is raising your bets proportionally after every bet the best way to go?

Betting in proportion to the size of your bankroll is absolutely correct and logical.

First off, when do you truly know your edge in handicapping.

You have a pretty good idea if you have a decent model.

Secondly and more importantly, its impossible to predict what you're "edge" will be at the end of a finite # of trials, like a season of baseball say 500.

Your edge doesn't change based on the results. If you are talking about ROI, that's irrelevant.

Lets say your expected edge is 5%. But after a season you ran at a flat betting return of 1%. Using Kelly you'd probably be a loser. So if you wanted to take a shot and had a mediocre year that would be o.k. But if you had a huge bankroll, and would have made a significant amount with that 1% then Kelly is not good for you. And by the way this is very common. Now what If you ran at 10%?

You would be a winner betting Kelly.

The problem is expectancy can be a long long way from actuality.

So?

If there is something inherently special about Kelly, I'm missing it.

It maximizes expected growth. There is nothing special about Kelly if you hate money. If you like money, it's awesome.

It also seems that streaks have an effect which I'm not clear on.

What do you mean by an effect? Obviously losing 10 bets in a row is not good under any "system", but your bankroll should be the same after 20 bets with the same edge at +100 if you win 11 and lose 9, no matter whether you lose the first 9 and win the next 11 or whether you win the first 11 and lose the next 9.

reno cool · 07-10-08, 03:41 PM

I do believe there is a significant difference in when you win or lose for kelly. And that is what I mean by streaks. You can go 320-280 and have a vastly different final bankroll.
Your ROI is whats important. Kelly only works optimum when your actual result is close to your predicted result. If this was always true then martingale would be a world beater.
Certainly in a very long session of a million decisions youd be almost certain to be within a percent of your expectancy. And Kelly would be optimum if you didn't run into bet minimums early.
But in handicapping, where your edge is dwarfed by variance in a given season, other betting schemes are often better.

RickySteve · 07-10-08, 07:39 PM

Originally posted by reno cool

I do believe there is a significant difference in when you win or lose for kelly. And that is what I mean by streaks. You can go 320-280 and have a vastly different final bankroll.
Your ROI is whats important. Kelly only works optimum when your actual result is close to your predicted result. If this was always true then martingale would be a world beater.
Certainly in a very long session of a million decisions youd be almost certain to be within a percent of your expectancy. And Kelly would be optimum if you didn't run into bet minimums early.
But in handicapping, where your edge is dwarfed by variance in a given season, other betting schemes are often better.

You have it figured out. Best of luck to you and be sure to use the links at the top of the page.

donjuan · 07-10-08, 08:11 PM

I do believe there is a significant difference in when you win or lose for kelly. And that is what I mean by streaks. You can go 320-280 and have a vastly different final bankroll.

Well you are simply wrong. It's quite easy to put it in an excel spreadsheet and see what happens. Try any combination you like for 10 bets with a 5% edge at +100 with a starting bankroll of $5000 where you win 6 and lose 4. Your answer should come out to $5457.58 every time.

Your ROI is whats important.

Personally I care more about my bankroll growing than an almost meaningless "stat".

Your ROI is whats important. Kelly only works optimum when your actual result is close to your predicted result. If this was always true then martingale would be a world beater.

Results oriented thinking does not belong in the Handicapper Think Tank.

Certainly in a very long session of a million decisions youd be almost certain to be within a percent of your expectancy. And Kelly would be optimum if you didn't run into bet minimums early.

WTF?

But in handicapping, where your edge is dwarfed by variance in a given season, other betting schemes are often better.

Since I could use a good laugh, feel free to name one.

reno cool · 07-11-08, 05:51 PM

Flat betting is an obvious method that has some merit. I do believe that a discussion of betting schemes is worthwhile. Depending on the bankroll you have, what your trying to accomplish, how long are you willing to stick with your methodology all play a part. Most good handicappers are always looking to improve. A long but typical losing streak using Kelly can decimate a large bankroll. In a case of a large bankroll that incorporates most of a persons money Kelly would suggest bets that are too high. Kelly could turn a modestly successful year flat betting into a loser.
In a case of someone taking a shot with a small bankroll, a more aggressive system than Kelly might be warranted.
Its good to come up with an ideal betting system for what your trying to do. This isn't easy and some discussion on various scenarios would be helpful. Assuming Kelly is always the way to go seems wrong.

As I said earlier, Handicapping is fluid, nobody has to stick with a certain system forever. If I go on a particularly bad streak I might be tempted to quit, reevaluate what I'm doing and so forth.
Lets say that going through half of a given bankroll using Kelly is enough to make me quit or take a break or whatever. In this case I can base my bets on twice my bankroll size to start. If things go bad I'll be ready to quit at the same time I go bust, and I'd be giving myself a chance for a bigger score.
In gambling these things matter. And of course your actual results matter which is your roi.

rcn848 · 07-11-08, 05:53 PM

Originally posted by reno cool

Flat betting is an obvious method that has some merit. I do believe that a discussion of betting schemes is worthwhile. Depending on the bankroll you have, what your trying to accomplish, how long are you willing to stick with your methodology all play a part. Most good handicappers are always looking to improve. A long but typical losing streak using Kelly can decimate a large bankroll. In a case of a large bankroll that incorporates most of a persons money Kelly would suggest bets that are too high. Kelly could turn a modestly successful year flat betting into a loser.
In a case of someone taking a shot with a small bankroll, a more aggressive system than Kelly might be warranted.
Its good to come up with an ideal betting system for what your trying to do. This isn't easy and some discussion on various scenarios would be helpful. Assuming Kelly is always the way to go seems wrong.

As I said earlier, Handicapping is fluid, nobody has to stick with a certain system forever. If I go on a particularly bad streak I might be tempted to quit, reevaluate what I'm doing and so forth.
Lets say that going through half of a given bankroll using Kelly is enough to make me quit or take a break or whatever. In this case I can base my bets on twice my bankroll size to start. If things go bad I'll be ready to quit at the same time I go bust, and I'd be giving myself a chance for a bigger score.
In gambling these things matter. And of course your actual results matter which is your roi.

take rickysteve's advice

Data · 07-11-08, 11:14 PM

I think that making sarcastic remarks and talking down to the posters who are looking for the answers and getting educated in the process is not in the spirit of the Think Tank forum.

Data · 07-11-08, 11:17 PM

reno cool, it seems that using fractional Kelly instead of full Kelly addresses your concerns

Thremp · 07-17-08, 11:42 AM

Originally posted by Data

reno cool, it seems that using fractional Kelly instead of full Kelly addresses your concerns

I don't think he's gotten past the part where the timing of wins and losses don't matter.

He seems to thinks 2 losers followed by two winners is better than the opposite.

dwaechte · 07-17-08, 12:32 PM

Originally posted by Data

I think that making sarcastic remarks and talking down to the posters who are looking for the answers and getting educated in the process is not in the spirit of the Think Tank forum.

Donjuan doesn't believe in social skills.

LT Profits · 07-17-08, 01:33 PM

I think Data meant Ricky.

reno cool · 07-17-08, 02:41 PM

I'm not talking about two wins or losses, I'm talking about a session of hundreds of trials. Streaks and chopiness has an effect.

reno cool · 07-17-08, 02:44 PM

betting Kelly of course you will be a loser going 2-2. Which is a good point in and of itself.

Ganchrow · 07-17-08, 02:56 PM

Originally posted by reno cool

I'm not talking about two wins or losses, I'm talking about a session of hundreds of trials. Streaks and chopiness has an effect.

When it comes to betting unconstrained Kelly you're simply mistaken -- the precise timing of wins and losses does not impact returns at all. Whether you win your first 500 bets and lose your next 500, or lose your first 500 and win your next 500, or alternate wins and losses over 1,000 bets, in each case your results would be identical (assuming all bets are at the same odds and edge and you're not constrained my minimum or maximum bet sizes). This is true with with any staking strategy that that determines bet sizes based on bankroll percentages.

This isn't a matter of opinion but rather one of clear mathematical fact.

If you don't believe it you're welcome to attempt to provide an example to the contrary.

durito · 07-17-08, 03:03 PM

Originally posted by reno cool

I'm not talking about two wins or losses, I'm talking about a session of hundreds of trials. Streaks and chopiness has an effect.

As thremp pointed out, you need to realize that that ordering of wins and loses does not matter under kelly.

Kelly maximizes your expected growth of your bankroll. If that is not your goal in betting then perhaps it's not for you. If you don't have logarithmic utility perhaps not as well. But, please get your facts straight.

While a flat betting staking strategy may be more likely to show a profit over a season, it does not maximize long term bankroll growth. See http://www.amazon.com/Fixed-Odds-Spo...6324929&sr=8-1

In this case I can base my bets on twice my bankroll size to start.

Or you can bet half kelly.

Originally posted by reno cool

betting Kelly of course you will be a loser going 2-2. Which is a good point in and of itself.

what

reno cool · 07-17-08, 03:15 PM

Like I said, I'm not clear on the effect of streaks. It seems that when I ran some simulations before I had some results that were out of line. There were some sessions that were very close in wins and losses that had very different results.
Now my simulations had some limits based on actual size of bets that were available.

Since your all so sure I will deffer to you on this. However, this is a minor issue in what I'm trying to address.

durito · 07-17-08, 03:18 PM

What would your preferred money management strategy be and why?

reno cool · 07-17-08, 03:42 PM

I'm not saying I have one, for all cases. But examples of attempts of different strategies would help people come up with ideas for their particular case. To always preach Kelly is a mistake.
The example given at the start of the original thread is a good one. The man thought he made a good play by fading someone a large bet relative to his bankroll on craps. Sure in his case he might not have been aware of what he was doing, but I'll point out how in certain situation his action had some merit.
Taking a bet for his entire bankroll as a slight favorite and winning, might have launched this guys career. Does he have the balls to do it? If he shows to be afraid to take action he is hurting himself as well.
Sure he had to drink Milwakkees Best for a year. But with a little luck he could have been a high roller. Is it worth it? Thats a matter of personal goals.
The guy probably didn't understand clearly his options and consequences, and he had to make a quick decision.

Thremp · 07-17-08, 05:06 PM

Kelly isn't for everyone. But it is for everyone who knows their edge fairly well and wants to make as much money as possible as quickly as possible.

Note: I'm trying a less scornful approach. Feedback is welcome.

reno cool · 07-18-08, 05:38 PM

If Kelly has worked well for you all then great. I'd like to know if you all had been using it and for what kind of betting.
A couple of points on Thorp, he was brought up earlier. He took a game that was being beaten by countless pros. He "perfected it",publicized it and effectively ruined it for a number of people who were making a living at it. And for that he deserves a kick in the ass.
But certainly his work on Black Jack in and of itself is worthy. Here are a few reasons why I believe a Kelly type approach makes more sense in his case.
1. He had a bankroll of undetermined value to him. (Certainly he wasn't paying his bills with it.)
2. He was playing a game where you can have thousands of decisions played out in a short amount of time.
3. His edge was around 1% so he never made huge bets relative to his bankroll.
Regarding the last point. I don't know if betting 1% with a 1% edge is safer than betting 5% with a 5% edge. I think I would feel safer betting 1% of my bankroll with a 50.5% chance of winning than betting 10% with a 55% chance.

reno cool · 07-18-08, 06:15 PM

Instead of making generic remarks why don't you guys give me an example of session of realistic size where kelly beats flatbetting and tell me why this kind of session would be more common.
Since betting method doesn't change expected value it seems to be a trade off of one thing or another. I recently looked at a session of about 150 2team parlays that ran at an edge of 25%. Betting 10% of bankroll as in Kelly (its not exact kelly but sure its close enough) it turned $500 bankroll into $4000. Flat betting turned it into 4500. Flat betting was nice and steady relatively speaking. Kelly style was stuck halfway, got up to 20,000 3quarters of the way, and ended up at 4000.
Of course at some point you would like to raise your bets, if your bankroll is small. Maybe a gradual, tiered approach is good.
Trying to keep the influence of luck and wild swings down if you have a healthy edge is the basis of good betting system.

Ganchrow · 07-18-08, 08:19 PM

The proper way to approach advantage betting is not by picking out a particular betting session, noting the results, and then declaring one betting scheme "superior" simply because it happened to produce higher returns over that single realization of event outcomes.

Rather, one should first clearly articulate one's goals (which as you correctly point out are necessarily a function of one's personal preferences) and then select the staking strategy which serves to best meet those goals.

For example, were your goal to maximize expected value of your wagering then your optimal strategy would be to wager as much as possible on the highest edge bet available (up to the smaller of the wagering limit across all books offering the or the player's total bankroll), and then as much as possible after that on the 2^nd highest edge bet possible, and so on down the line.

On the other hand, were you goal to maximize the expected growth of your bankroll over time, then Kelly would represent your optimal strategy.

I'm going to disagree with donjuan's earlier response and state that absolutely nothing makes Kelly inherently superior to most other staking strategies. In economic theory rational decision making is based around the notion of individual preferences. For example, I might prefer vanilla ice cream to chocolate, while you might be indifferent between the two. Neither set of preferences is inherently superior to the other in any other normative sense they're just ... different.

Now what would be decidedly irrational would be to choose a betting strategy that failed to optimally further one's goals. For example, were one's goal to maximize expected bankroll growth over time then (all else being equal) flat betting could certainly be considered irrational.

The problem here is that you've yet to clearly articulate any coherent set of preferences, instead using nebulous terms such as "luck", "wild swings", "choppiness", and "have the balls to bet it". Clearly articulating your preferences needs to come first -- only then can you select an optimal strategy that best fits those preferences.

I'd suggest picking up a copy of Joseph Buchdahl's Fixed Odds Sports Betting (the smae book previously noted by durito), which provides an excellent introductory discussion and analysis of the pros and cons of various staking strategies including both Kelly and flat betting.

Dark Horse · 07-18-08, 09:20 PM

It is probably safe to say that for the vast majority of gamblers Kelly is not only just a theory, but should remain that.

Kelly requires that you have a very precise number for your edge in each bet. That may work fantastic in theory, but in reality you're going to have a large sample size for each system you use, as well as a scientifically correct way of measurement while establishing the system; otherwise you're just estimating your edge. Kelly would expose the error in that estimation exponentially. Proponents of Kelly, quite typically, spend little time on this absolute requirement, in a rush to move swiftly to the majestic beauty and simplicity of the system.

It is not good enough for Kelly to use one's overall winning percentage. Because that's an average. It has to be a precise edge for each wager, based on pure and reliable numbers. How many bettors do you know with a database worthy of Kelly?

(It may be different with Poisson calculations for props, because that's strictly math, and does, to the best of my understanding, not include the intangibles found in typical betting systems. - Poisson means Fish, by the way. You can't kill anybody with it.)

reno cool · 07-19-08, 12:28 AM

I think Dark Horse addresses what I've been talking about. Handicappers who use Kelly would have one hell of a wild ride. For professional gamblers who stake their livelihood this is what we try to avoid. I also appreciate that he agrees with one of my original points that truly knowing your edge is a big problem. In blackjack it is not. But in racing or sportsbetting it is.
The rest of you seem to ignore my original points and attack a straw man. I'm sure reading the suggested book is good advice and I appreciate it. As for your other points:
1. You understand that the betting session sample I gave is just that. I'm not basing a system on it. I'm showing you a situation where I figured Kelly to do well and it was out performed. So your statement on that is neither here nor there.
Everybody should be interested in actual results of actual sessions. Some are more common than others and we need to beware of things that might happen to our bankrolls.
2. One should clearly articulate ones goals. This is true, not always easy. My goal maybe making sure I have winning season with a smaller chance at big wins. I imagine the need for this is common.
3. Regarding my nebulous terms I think they were appropriate when used. Maximizing expected bankroll growth seems a nebulous term.
And come on, can you agree with me that your friends craps bet could have had some merit? I mean someone aware of bankroll requirements could have faded that bet in same situation.

donjuan · 07-19-08, 05:03 AM

I think Dark Horse addresses what I've been talking about. Handicappers who use Kelly would have one hell of a wild ride.

There are ups and downs, yes. It is maximally aggressive.

For professional gamblers who stake their livelihood this is what we try to avoid.

Then go fractional Kelly as someone suggested earlier in the thread.

I also appreciate that he agrees with one of my original points that truly knowing your edge is a big problem.

This has been stated many times in the past but if you can't reasonably quantify your edge, what makes you think you actually have an edge in the first place?

In blackjack it is not. But in racing or sportsbetting it is.

He's wrong about blackjack. If your edge is 1% counting cards, that does not mean you bet the same % of your bankroll on each hand that a 1% edge would suggest. Rather you will be betting much more when the count is high (note: calculating Kelly for BJ is more complicated than sports because part of your edge comes from doubling down, splitting and blackjacks so you can't just bet the % of your bankroll Kelly suggest for an x% edge at +100).

Everybody should be interested in actual results of actual sessions.

This is vague and strange. What is a session and why does it matter? This sounds like you are practicing what is known in the poker community as results-oriented thinking.

Some are more common than others and we need to beware of things that might happen to our bankrolls.

Again, vague. Explain further.

Regarding my nebulous terms I think they were appropriate when used. Maximizing expected bankroll growth seems a nebulous term.

If maximizing expected bankroll growth seems nebulous to you, then you should definitely re-read Ganchrow's 2 part series on expected growth until you understand it.

And come on, can you agree with me that your friends craps bet could have had some merit?

In very rare circumstances, yes.

reno cool · 07-19-08, 06:07 AM

the edge in given scenario in blackjack can be mathematically calculated on any given hand and its rarely over 1%. not so in handicapping. (i'm not saying its easy but it can be done)

Its a lot easier to know that you're a winning player than to know your exact edge on any given bet.

a session can be a year, and it matters because you need to live for a year.

I don't know what results oriented thinking is but it sounds like a good thing

Aren't we interested in the likelihood of certain scenarios happening to our bankroll over a given time frame?

donjuan · 07-19-08, 01:29 PM

the edge in given scenario in blackjack can be mathematically calculated on any given hand and its rarely over 1%. not so in handicapping. (i'm not saying its easy but it can be done)

If your edge is 1%, and you are playing hands where the count is ever 0 or negative, there have to be plenty of times your edge is over 1% to counteract this.

Its a lot easier to know that you're a winning player than to know your exact edge on any given bet.

So you have no idea of the edge on a bet you are making but you are sure you're a winning player?

a session can be a year,

How many bets are you making in a year?

and it matters because you need to live for a year.

Again, you probably aren't defining your bankroll correctly if this is one of your issues. Basically, you should have some money set aside to live off of during a downswing if this is a major concern for you.

I don't know what results oriented thinking is but it sounds like a good thing

It's a really bad thing. In poker, the equivalent would be cold calling an all in preflop with 98s for 50 big blinds and beating AA, and then going on to say that 98s was a good play because it won. You can't go back and look at a limited sample size and say that you should have used a different betting system simply because it would have made more money, at least not if you want to make as much money as possible in the future. To carry that way of thinking out to its logical conclusion, you should have bet your entire bankroll on every game that won and not bet at all on every game that lost. This way of thinking is counter-productive and accomplishes nothing positive.

Aren't we interested in the likelihood of certain scenarios happening to our bankroll over a given time frame?

Yes. Use Excel.

Thremp · 07-20-08, 12:46 PM

Ganch,

I'm going to nit you a bit and qualify your comment on preferences. I'd say most people don't even know what is the best choice for them and make irrational decisions complicating the issue further.

reno cool · 07-21-08, 02:59 PM

Originally posted by Thremp

Ganch,

I'm going to nit you a bit and qualify your comment on preferences. I'd say most people don't even know what is the best choice for them and make irrational decisions complicating the issue further.

this is why I say discussion of various scenarios would be beneficial to many

reno cool · 07-21-08, 04:27 PM

regarding blackjack during Thorps time overall edge may have been more than 1%. Now a days your unlikely to find such a game.
Also remember that since your betting a lot more when you have a higher edge your overall payback is skewed towards the high figure.
My point simply was that a common bet for Thorp would have been no more than 1%.

2. The difference between knowing your winning player and knowing your edge even within 1% is huge. I may think I have a 5% edge based on a huge database, analysis whatever you like. Whats more certain? That my edge is at least 1% or at least 4%.
3. lets say I will usually make about 500 bets, now what is a bankroll is a good question. All the $ I have in the world. All the money I intend to possibly risk gambling. Or all the money I intend to risk on a particular play--- say a year of sports. Hopefully if I'm doing o.k. all three are different.
4. I'm not concerned with gamblers who don't need to make money in a realistic time frame. Maybe a lot of you are in that position. Most serious gamblers who are dependent on money made from it would like
a. Once they find an edge, make sure they can realize it as close as possible.
b. Make a consistent profit of a meaningful amount.
I will later describe a system that I currently feel is better than Kelly for that, and explain why it is better in more common cases. But you can see where its going.
5. regarding the card example. Of course this is not what I'm doing.

Dark Horse · 07-21-08, 05:09 PM

Originally posted by donjuan

So you have no idea of the edge on a bet you are making but you are sure you're a winning player?

You make it sound like the two - knowing your winning percentage and knowing your precise edge per bet - are even remotely in the same class.

Knowing your winning percentage requires no more than keeping a record of all your bets.

Knowing your edge per individual wager is a far more complex question. For instance, fluctuations for a winning system, from one season to the next, can be quite spectacular. Let's say a system hits 64% one season, and 56% the next season. Or a system that has gone 57% over seven seasons suddenly produces a 42% season. How would you know in advance?

Dazzez · 07-21-08, 05:13 PM

Originally posted by reno cool

this is why I say discussion of various scenarios would be beneficial to many

You do realize Thremp was talking about you, don't you?

reno cool · 07-21-08, 05:24 PM

Originally posted by Dazzez

You do realize Thremp was talking about you, don't you?

Maybe I would be more offended by your little statements if you actually had something worthwhile to say

Thremp · 07-21-08, 07:08 PM

Originally posted by Dazzez

You do realize Thremp was talking about you, don't you?

I'm not sure what either of your think I'm talking about. I was referring to most people's problem of overweighting the swings in their happiness. Most people return to a median level of happiness pretty quickly from most problems. Losing your BR and getting a job is not something that should really dissuade one from betting a kelly fraction.