Kelly Criterion explained

[ico2525]

Nicky,

The assumption is that you have an edge to begin with. What edge do you have playing roulette (negative), so your bet is zero in that case.

No edge, no bet. Kelly is only applicable when you have a definite advantage.

Great video Justin! Thanks.

Here is one use for Kelly in the sports betting realm. Let's say you get hooked up (God forbid) with some big time handicapper like Jim Feist or one of his associates. Over the last 6 seasons, he has been correct 57% of the time when picking a team at -110. You could then figure out that your optimal bet is 3%. If he has only been right 52% of the time at -110, you get a negative K. In that case, you're going to lose in the long run.

[TLD]

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+%.

This is very consistent with the approach I use, though I don’t see it as deviating from a Kelly approach.

I generate my own numbers with my own handicapping, and I determine at what percentage I expect a game to fall on this number or that number. Simplistically, I could then shop for the best line, and use my numbers to estimate my chances of winning. (Example: My power ratings say a team X is superior to a team Y by a margin of Z. Historically, teams superior by a margin of Z in my system have defeated their opponents by 7 or more points 65% of the time. Therefore if I can bet X at -6.5, I have a 65% chance of winning.)

However, this fails to take into account the fact that the market, by making -6.5 available to me, is indicating strong disagreement with my prognostication. So in response, I feel I need to add a big dose of pessimism to my assessment. (I believe in my handicapping, but not to the point I assume I’m infallible and the market can be ignored.)

What I typically do is keep my (almost certainly unrealistically high) prima facie estimate of the likelihood of winning the bet where it is, but use a very, very small fractional Kelly.

But fundamentally I don’t see that as a deviation from Kelly, because it’s mathematically equivalent to substantially (appropriately) lowering my estimate of the likelihood of winning the bet, and then using full Kelly on that.

[donjuan]

Reno Cool,

I refuse to continue banging my head against the wall with you. Please do not respond until you have read and thoroughly understand these posts by Ganchrow:

http://forum.sbrforum.com/handicapper-think-tank/29009-expected-value-vs-expected-growth-kelly-criterion-part-i.html

http://forum.sbrforum.com/handicapper-think-tank/29841-maximizing-expected-growth-kelly-criterion-part-ii.html

[TLD]

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?

Nonsensical question.

Kelly is simply a mathematical formula where you plug in the odds, probability of winning, and bankroll size, and it spits out the bet size that will best serve the goal of long term bankroll growth.

As long as you don’t grasp that, you’re going to continue going around in circles, misinterpreting what people are saying, positing irrelevant or vague hypotheticals, etc.

As to which of your groups will fare better, if we’re talking about in terms of long term bankroll growth, the group that will do better is the one whose bet size matches what Kelly calls for given their odds, probability of winning, and bankroll size.

[The HG]

In defense of flat betting -

Flat betting would be justified if you had an overall edge, but didn't know your exact edge on any individual game. I know the smarties here will say that if you don't know your exact edge on individual games, then you can't know/can't have an edge overall, and that may be true.

I am just saying that in the hypothetical case where someone did have an overall edge, but didn't know the edge on any one particular game, flat betting would be justified.

Of course even in that case, the optimal flat bet amount would still be determined by the Kelly equation.

But that is the reason flat betting is so attractive to bettors who eyeball - they feel they have an edge on a sport overall, but don't feel as certain of their edges on the individual games.

[reno cool]

Its a fair question. just answer it.

give me the probability of group a having more $ at the end than group b.

If this isn't the heart of the question, or whats relevant then what is?

All you know is what "it spits out". Yeah I already know this.

[reno cool]

It seems to me that you like to hide behind pretty phrases but get offended if someone brings up real life scenarios. Do you actually gamble? Or just full of shit?

[TLD]

In defense of flat betting -

Flat betting would be justified if you had an overall edge, but didn't know your exact edge on any individual game. I know the smarties here will say that if you don't know your exact edge on individual games, then you can't know/can't have an edge overall, and that may be true.

I am just saying that in the hypothetical case where someone did have an overall edge, but didn't know the edge on any one particular game, flat betting would be justified.

Of course even in that case, the optimal flat bet amount would still be determined by the Kelly equation.

But that is the reason flat betting is so attractive to bettors who eyeball - they feel they have an edge on a sport overall, but don't feel as certain of their edges on the individual games.

I’d say your use of the adjective “exact” is inappropriate here. It doesn’t have to be exact; it just has to be better than any other way of implicitly or explicitly ascertaining the values relevant to Kelly.

Flat betting is the equivalent of implicitly assigning the same estimated edge to all your bets and then running Kelly on that.

Obviously that implied estimated edge won’t match your actual exact edge (barring an extraordinary coincidence).

So if imprecision is a fatal flaw for the non-flat bettor doing their best to estimate their edge, it is similarly a fatal flaw for the flat bettor.

But yes, I do agree that it’s possible for there to be a case where a flat bettor will do better than the person who is making poor estimates of his edge and varying his bets accordingly, precisely because it’s possible for the flat bettor’s flawed bet sizes to deviate less from Kelly than do those of the person miscalculating his edge.

Similarly, a person choosing bet sizes by picking numbers out of a hat might get lucky and come closer to betting what would be optimal under Kelly than either of these folks.

[donjuan]

Kelly is simply a mathematical formula where you plug in the odds, probability of winning, and bankroll size, and it spits out the bet size that will best serve the goal of long term bankroll growth.

As long as you don’t grasp that, you’re going to continue going around in circles, misinterpreting what people are saying, positing irrelevant or vague hypotheticals, etc.

Exactly. Although in his example one thing does need to be noted/questioned:

Are all of these people making different bets, the same bets or some of the same and some different? If they are all making different bets, then the group's effective bankroll size is $50,000, not $1000 and thus the group betting 20% of $1000 is betting more optimally with regards to bankroll growth than the group that is "betting Kelly".

[TLD]

Its a fair question. just answer it.

give me the probability of group a having more $ at the end than group b.

If this isn't the heart of the question, or whats relevant then what is?

All you know is what "it spits out". Yeah I already know this.

I’m not sure what odds your hypothetical groups are betting at. Nor do I know what it means for one to be betting 10% and one 20%, and yet for both to be adjusting their bet sizes according to what the Kelly formula calls for.

Once you determine the odds and the probability of winning the wagers for your hypothetical, you can then use the Kelly calculator provided on this site to determine the optimal wager.

If it is something other than 10% or 20%, and yet your groups insist on using 10% and 20%, and your question is which will do better, I don’t know the answer to that. Basically you’d be saying, if both groups deviate from Kelly, which of their strategies is the lesser of the evils?

I’m not sure what comparing two deviations from Kelly has to do with critiquing Kelly, but I’m sure Ganchrow or one of the math guys can run those numbers and help you with that question (once you specify the relevant values).

[Santo]

Flat betting would be justified if you had an overall edge, but didn't know your exact edge on any individual game. I know the smarties here will say that if you don't know your exact edge on individual games, then you can't know/can't have an edge overall, and that may be true.

Here is a hypothetical.

The sport is UK Horse Racing, and betting to lose rather than win, but I'm satisifed there is a substantial data set showing an approx 11% ROI.

I can't say with any certainty that any given selection has an 11% edge, just that the overall method has shown that return historically.

In some cases you're laying 1.4, in other cases 5s, so I suspect the edge is different in each case, and probably on some of the bets there is no edge -- I don't have the data that the bets are derived from - but breaking it down would reduce the sample size beyond a reasonable confidence level.

In this case, how do you determine your stakes?

[TLD]

It seems to me that you like to hide behind pretty phrases but get offended if someone brings up real life scenarios. Do you actually gamble? Or just full of shit?

It seems to me that when you don’t understand something, it impacts you emotionally to where you feel compelled to dismiss it as a bunch of big words or not relevant to the “real world” and to engage in ad hominem attacks.

If it pleases you, yes, I’m a non-gambler and full of shit. Neither of which has anything whatsoever to do with the pros and cons of Kelly. For that I suggest you focus not on the many flaws of my good self, but on better trying to understand the substance of what’s being discussed.

[TLD]

Here is a hypothetical.

The sport is UK Horse Racing, and betting to lose rather than win, but I'm satisifed there is a substantial data set showing an approx 11% ROI.

I can't say with any certainty that any given selection has an 11% edge, just that the overall method has shown that return historically.

In some cases you're laying 1.4, in other cases 5s, so I suspect the edge is different in each case, and probably on some of the bets there is no edge -- I don't have the data that the bets are derived from - but breaking it down would reduce the sample size beyond a reasonable confidence level.

In this case, how do you determine your stakes?

Santo, though the quotation in your post is labeled as "Originally Posted by TLD," that quote actually came from The HG, so I'll assume your question is directed to him.

Anyway, I'm sure he or many others here could better address your case than I could.

[Santo]

Yes sorry I got confused quoting from within a quote :P

Just an interesting example. In most cases I have access to the raw data, and bet kelly (well, a heavily diluted fractional version thereof), but sometimes you come across a method that looks reliable, but you can't quantify the individual edge, just the overall one.

[ico2525]

To estimate your percent win (P) based on your return on investment (ROI), you have to know how much you have bet total over your sample. You have to know how many games you've played and the bet odds of each game.

[Bullajami]

To estimate your percent win (P) based on your return on investment (ROI), you have to know how much you have bet total over your sample. You have to know how many games you've played and the bet odds of each game.

Great idea for another Ganchrow calculator.

[reno cool]

It seems to me that when you don’t understand something, it impacts you emotionally to where you feel compelled to dismiss it as a bunch of big words or not relevant to the “real world” and to engage in ad hominem attacks.

If it pleases you, yes, I’m a non-gambler and full of shit. Neither of which has anything whatsoever to do with the pros and cons of Kelly. For that I suggest you focus not on the many flaws of my good self, but on better trying to understand the substance of what’s being discussed.

the bets are even money----surely you can surmise this
one group is betting the Kelly #
group B is overbetting by 2x

these people are totally unrelated to one another, their bets are placed on different events.

According to what your implying as regards to kelly group 2 shouldn't make any money. ---of course this is false

Your the one trying to dismiss and belittle what I'm saying, where in fact my point is relevant. If you have any grasp of the concept your discussing (kelly) you should be able to answer my question head on.

Finally I question your experience because you seem to have a narrow scope and are quick to judge and dismiss anything that doesn't fit your limited paradigm.

[donjuan]

According to what your implying as regards to kelly group 2 shouldn't make any money. ---of course this is false

As usual, you have no concept of what the effective bankroll is. For Kelly purposes, the second group is not overbetting Kelly at all because their effective bankroll is 50 times what they think it is for the purpose of this exercise. Rather the first group is vastly underbetting with regards to Kelly.

[MrX]

--

[MrX]

--

[MrX]

According to what your implying as regards to kelly group 2 shouldn't make any money. ---of course this is false

It's not that the group does not expect to make money. Of course making a bunch of +EV bets means a positive expected return. The group, as a whole, has a positive expectation.

However, an average individual in this group does not expect to be up. Half of the group will be up and half down on average. When betting more than 2xKelly, more than half the group is expected to be down.

So, if I understand your question, both groups are expected to be up. Group A (Kelly) is expected, as a group, to be up less than group B(2xKelly). However, a randomly selected individual from group A is more likely to be up than a randomly selected individual from group B.

I think most people would rather be a member of group A.

[tomcowley]

You're not asking a relevant question. If somebody offers you +500 on a coinflip, and you have to bet the same percentage stake 5 times successively,is it better to bet the kelly stake (40%) of what you had, or to bet 80% of what you have? Let's start with 1000 roll.

If we take 32 people in each group

The 80% group will


0-5: 1 in 32, .32 BR
1-4: 5 in 32, 8 BR
2-3: 10 in 32, 200 BR
3-2: 10 in 32, 5000 BR
4-1: 5 in 32, 125000 BR
5-0: 1 in 32, 3125000 BR

for a total of 1.307m

The kelly group will:

0-5: 1 in 32, 77.76 BR
1-4: 5 in 32, 388.8 BR
2-3: 10 in 32, 1944 BR
3-2: 10 in 32, 9720 BR
4-1: 5 in 32, 48600 BR
5-0: 1 in 32, 243000 BR

For a total of 604.7k

Group 1 is richer as a whole. Group 1's median bankroll is much lower. That will happen for any variation where group 1 is betting kelly and group 2 is overbetting kelly. Any rational person would prefer being in group 2. Using EV as the final evaluation of a staking strategy is stupid for this reason.

Over the long term, anybody who bets 80% will need to hit 50% to break even (a loss means your bankroll is divided by 5 (1 - 0.8 = 0.2) and a win means your bankroll is multiplied by 5 (1 + .8*5 = 5). So half the people who bet double kelly will win, and the median is exactly breakeven.

Anybody who bets 40% only needs to hit 31.74% to break even- and the probability of that approaches 100% over the long haul. The median bankroll gets huge, since even hitting well below 50% (40%) will make you a strong winner.

[TLD]

one group is betting the Kelly #
group B is overbetting by 2x

Assuming nothing else in the hypothetical contradicts this, this little bit here is all one needs to know.

The answer to your question is that the first group has given themselves the best chance to grow their bankroll long term.

This is not, by the way, equivalent to saying that the people in Group 2 "shouldn't make any money." Not sure where you got that from.

Nor does it guarantee one group will do better than the other over any finite period. Proper bet sizing, like line shopping and numerous other factors, is something you do to give yourself the best shot at success, but there's no guarantee. I mean, some third group might take that same amount of money and spend the day gambling it all at the roulette tables on horribly –EV bets, and we certainly can’t say they “shouldn’t make any money.” They might even get lucky and outperform both of your first two groups.

But that doesn’t change the fact that if you’re in this to make money, Group 1 is the one you want to be in.



On Kelly in general, in order to understand the basic logic behind it, perhaps think of it this way:

Imagine a person with a net worth of, say, $100,000. Let's say he is able to identify various sports bets where he has a modest but significant edge, maybe something in the 55%-56% range for -110 plays. And you see he never bets more than 50 cents on any of them.

Well, maybe his betting serves some other purpose in his life--like just that he finds it enjoyable--but surely you can intuit without having to do a lot of fancy math that he is betting far, far too little if his goal is to make as much money as he can over the long term.

Now consider another fellow in the same circumstances, except he is betting $50,000 a pop. While it's certainly possible he'll have an incredible run of luck and turn his boldness into a vast fortune, I think you'd agree that intuitively he is betting very recklessly, and that he's giving himself very little chance for long term success, since even the most modest of losing streaks will wipe him out before he can ever get to the long run.

Clearly if one's goal is to make as much money as one can long term with this, there is some more prudent bet size they should be using. Something well above 50 cents, and well below $50,000. But how much precisely? Our gut by itself can't tell us that.

That's where mathematics comes in. Kelly is simply the mathematical formula that finds that golden mean for us. It's the fancy mathematical version of what your intuition already tells you, which is that someone underbetting when he has an edge is leaving money on the table, while someone overbetting when he has an edge is taking too great a risk that he'll destroy his bankroll before he can get to the "Promised Land" of the long term where those +EV odds enable us to live happily ever after.

[Stacocakes]

This thread was a good read
Lots of us, myself include, are always fighting the money management demons.
Congrats to those posters in here that can stick to a system like this and keep there emotions out of it. Its a priceless quality to have when in this industry

[reno cool]

I have to say the last few posts are much more worthwhile, especially tld.

If you remember, my original post was a reply to donjuan stating that you will lose if you overbet Kelly and not win as much as you can under betting.

Certainly in most cases I wouldn't advise betting 2x Kelly. My point is that there is nothing special about betting the exact Kelly #. And I don't appreciate successful bettors being told that they are doing something wrong if don't use Kelly.

My example shows that you will average more money betting more than K.
Off course this comes with a price. Betting 1xK you will make more than .25K.
But your risking loosing more often. -----its simply a trade off

As in Tomcowley example, if a person absolutely needed at least 100,000 then he should choose the more aggressive strategy.

Simply invoking Kelly is a poor substitute for determining proper bet sizes for specific individual scenarios that come up in gambling.

[donjuan]

If you remember, my original post was a reply to donjuan stating that you will lose if you overbet Kelly and not win as much as you can under betting.

You will.

My point is that there is nothing special about betting the exact Kelly #.

Yes there is. It's the bet size that maximizes your expected bankroll growth.

And I don't appreciate successful bettors being told that they are doing something wrong if don't use Kelly.

Good for you. Now if you are extremely risk-averse, of course you would want to bet fractional Kelly. However, understand that you will make far less money over the long haul.

My example shows that you will average more money betting more than K.

The Kelly criterion is for an individual bankroll. You are looking at a group of bankrolls that is effectively one giant bankroll 50 times the size of the bankroll you give for Kelly purposes. This doesn't really prove anything other than that you continue to ignore what a bankroll actually is with regards to Kelly.

As in Tomcowley example, if a person absolutely needed at least 100,000 then he should choose the more aggressive strategy.

Simply invoking Kelly is a poor substitute for determining proper bet sizes for specific individual scenarios that come up in gambling.

Does this situation come up frequently in your life? If it does, seek help.

[reno cool]

Donjuan pull your head out of your ass just once.

First there's 50 people like you. You can't combine the bankrolls.

Its a question of which group do you want to be a part of.
The one that will avg more money or the one that will have more people coming out ahead.

second.
Maybe nobody absolutely needs 100,000. But there are $amounts which are significant to bettors in various scenarios. A person might have too small a bankroll to make significant money using K. Its very reasonable for him to take a shot betting larger amounts. -----He is not a guaranteed loser.

[Bet Shooter]

Assuming nothing else in the hypothetical contradicts this, this little bit here is all one needs to know.

The answer to your question is that the first group has given themselves the best chance to grow their bankroll long term.

This is not, by the way, equivalent to saying that the people in Group 2 "shouldn't make any money." Not sure where you got that from.

Nor does it guarantee one group will do better than the other over any finite period. Proper bet sizing, like line shopping and numerous other factors, is something you do to give yourself the best shot at success, but there's no guarantee. I mean, some third group might take that same amount of money and spend the day gambling it all at the roulette tables on horribly –EV bets, and we certainly can’t say they “shouldn’t make any money.” They might even get lucky and outperform both of your first two groups.

But that doesn’t change the fact that if you’re in this to make money, Group 1 is the one you want to be in.



On Kelly in general, in order to understand the basic logic behind it, perhaps think of it this way:

Imagine a person with a net worth of, say, $100,000. Let's say he is able to identify various sports bets where he has a modest but significant edge, maybe something in the 55%-56% range for -110 plays. And you see he never bets more than 50 cents on any of them.

Well, maybe his betting serves some other purpose in his life--like just that he finds it enjoyable--but surely you can intuit without having to do a lot of fancy math that he is betting far, far too little if his goal is to make as much money as he can over the long term.

Now consider another fellow in the same circumstances, except he is betting $50,000 a pop. While it's certainly possible he'll have an incredible run of luck and turn his boldness into a vast fortune, I think you'd agree that intuitively he is betting very recklessly, and that he's giving himself very little chance for long term success, since even the most modest of losing streaks will wipe him out before he can ever get to the long run.

Clearly if one's goal is to make as much money as one can long term with this, there is some more prudent bet size they should be using. Something well above 50 cents, and well below $50,000. But how much precisely? Our gut by itself can't tell us that.

That's where mathematics comes in. Kelly is simply the mathematical formula that finds that golden mean for us. It's the fancy mathematical version of what your intuition already tells you, which is that someone underbetting when he has an edge is leaving money on the table, while someone overbetting when he has an edge is taking too great a risk that he'll destroy his bankroll before he can get to the "Promised Land" of the long term where those +EV odds enable us to live happily ever after.

I think this post should be moved into the FAQ thread in the Tank. This is an excellent way for the lay person to understand what everyone is talking about with Kelly. If someoen reads this FIRST and then takes it upon themselves to put the due diligence into learning Kelly, it will save the posters here a lot of time and energy posting for Noobs (like myself).

[coldhardfacts]

I have to say the last few posts are much more worthwhile, especially tld.

And I don't appreciate successful bettors being told that they are doing something wrong if don't use Kelly.



Simply invoking Kelly is a poor substitute for determining proper bet sizes for specific individual scenarios that come up in gambling.

Amen, brother. Amen.

[donjuan]

First there's 50 people like you. You can't combine the bankrolls.

You are effectively combining the bankrolls in your question. Rephrase the question or understand that this is what you are doing.

Its a question of which group do you want to be a part of.
The one that will avg more money or the one that will have more people coming out ahead.

Again, this is silly. If you made the 2nd group bet 100% of their bankroll on each bet, they'd have a higher expected value, but they'd all eventually go broke. If they all bet 99.9% of their bankroll, they would never go broke, but they would be expecting to diminish their bankroll every time they bet. And so on until you get down to the number that gives you zero expected growth. Why not bet the one that has the highest EG?

second.
Maybe nobody absolutely needs 100,000. But there are $amounts which are significant to bettors in various scenarios. A person might have too small a bankroll to make significant money using K. Its very reasonable for him to take a shot betting larger amounts. -----He is not a guaranteed loser.

If he can never gamble with any money outside of his current bankroll, then it's likely not very smart. If he can get money from outside sources in the future, you aren't sizing his bankroll correctly.

[TLD]

Simply invoking Kelly is a poor substitute for determining proper bet sizes for specific individual scenarios that come up in gambling.

This is an important point. But please understand, those who have tried to explain Kelly in this and other threads have not contradicted this point. In fact, many times Ganchrow and donjuan and others have explicitly pointed out that Kelly is not a system that tells you your ideal bet size no matter what; it’s a system that tells you what the ideal bet size would be for the purpose of maximizing long term bankroll growth.

So if one has different goals, then a different bet sizing approach will be appropriate. In an example like yours, where if you don’t win $100,000 right away there won’t be any long term in which to let those Kelly profits accumulate (maybe there’s a loan shark about to kill you if you don’t come up with the $100,000 by tomorrow for instance), then yes, something other than Kelly will likely give you your best shot.

There could of course be many other examples of gamblers who have goals other than maximizing their long term bankroll growth. There could be a person who enjoys gambling as long as the amounts are very small, but finds it highly stressful and unpleasant to bet more. If he puts some non-zero value on that enjoyment and avoidance of stress, he has reason not to bet above a certain amount, so it would make sense for him to deviate from full Kelly in those cases.

Or I might, say, have a big saucy blonde on my arm in a casino, and realize from my past knowledge of her that the one thing that will make me irresistible to her is if she sees me tossing around large bets at the roulette table without a care in the world. Well Kelly says—accurately—that my ideal size roulette bet for the purposes of maximizing bankroll growth is $0. But that doesn’t mean I should bet zero relative to my other goals, because if I bet zero, I ain’t getting any tonight.

Based on some of your posts, I think one thing you want to be careful of is sometimes the more mathematical or academic posters write in a precise or technical style. That is, if someone like Ganchrow tosses around fancy phrases like “maximizing expected bankroll growth” it probably has a very precise meaning. Too often I think you’re responding as if, to use the same example, “maximize expected bankroll growth” is just a vague term of praise no different from “do well,” or “be a successful gambler,” or “make a lot of money,” and so you object that, no, it’s merely one approach that can be a good and appropriate one, depending on the gambler’s preferences and situation. But once you understand that the Kelly proponents are not just using words in a casual way in an informal conversation, but are making technical points with specific precise definitions, you’ll see that criticism misses the mark.

Thanks also to Bet Shooter for his kind remarks. I know my limitations that I’m not a math guy like Ganchrow and some of our other most valuable posters, so I try to break things down for myself in layman’s terms and work out the logic or common sense behind the ideas, and sometimes I figure maybe other folks would benefit from that approach.

[coldhardfacts]

This is an important point. But please understand, those who have tried to explain Kelly in this and other threads have not contradicted this point. In fact, many times Ganchrow and donjuan and others have explicitly pointed out that Kelly is not a system that tells you your ideal bet size no matter what; it’s a system that tells you what the ideal bet size would be for the purpose of maximizing long term bankroll growth.

So if one has different goals, then a different bet sizing approach will be appropriate. In an example like yours, where if you don’t win $100,000 right away there won’t be any long term in which to let those Kelly profits accumulate (maybe there’s a loan shark about to kill you if you don’t come up with the $100,000 by tomorrow for instance), then yes, something other than Kelly will likely give you your best shot.

There could of course be many other examples of gamblers who have goals other than maximizing their long term bankroll growth. There could be a person who enjoys gambling as long as the amounts are very small, but finds it highly stressful and unpleasant to bet more. If he puts some non-zero value on that enjoyment and avoidance of stress, he has reason not to bet above a certain amount, so it would make sense for him to deviate from full Kelly in those cases.

Or I might, say, have a big saucy blonde on my arm in a casino, and realize from my past knowledge of her that the one thing that will make me irresistible to her is if she sees me tossing around large bets at the roulette table without a care in the world. Well Kelly says—accurately—that my ideal size roulette bet for the purposes of maximizing bankroll growth is $0. But that doesn’t mean I should bet zero relative to my other goals, because if I bet zero, I ain’t getting any tonight.

Based on some of your posts, I think one thing you want to be careful of is sometimes the more mathematical or academic posters write in a precise or technical style. That is, if someone like Ganchrow tosses around fancy phrases like “maximizing expected bankroll growth” it probably has a very precise meaning. Too often I think you’re responding as if, to use the same example, “maximize expected bankroll growth” is just a vague term of praise no different from “do well,” or “be a successful gambler,” or “make a lot of money,” and so you object that, no, it’s merely one approach that can be a good and appropriate one, depending on the gambler’s preferences and situation. But once you understand that the Kelly proponents are not just using words in a casual way in an informal conversation, but are making technical points with specific precise definitions, you’ll see that criticism misses the mark.

Thanks also to Bet Shooter for his kind remarks. I know my limitations that I’m not a math guy like Ganchrow and some of our other most valuable posters, so I try to break things down for myself in layman’s terms and work out the logic or common sense behind the ideas, and sometimes I figure maybe other folks would benefit from that approach.

IMO, achieving a "comfort level" is essential to successful gambling. If you're betting less than you are comfortable betting, then you are surely leaving money on the table. Plus, you will may have a tendency to get loose or sloppy. If you're betting above your comfort zone, then the resulting stress may impact your handicapping and, as you point out, your general quality of life.

Which is why I believe that the Kelly methodology isn't suited, and isn't optimal, for everyone. As I said earlier, I don't have a separate gambling bankroll. I know my financial situation and my gambling patterns well enough to know how much I can bet on each game to withstand the inevitable cold streaks without having to adjust my lifestyle or decrease my bet size. So when normalcy returns or I hit an exceptional hot streak, I'm betting enough to more than make up for the bad times.

[reno cool]

tld

I'm not in awe of phrases like "maximizing expected bankroll growth". I'm quite aware of what you're trying to get at when you as them. I'm simply pointing out the misleading implications of the statements being made. I think here the understanding of the concept "the long run" is poor.
I don't disagree that if you have an edge and bet the K# into an infinite # of trials you will make more than betting 2xK or flatbetting.---------but this is the same as saying "you will ultimately win doubling your bets after loses". You need to be aware of the relationship of these two things. Both are true, neither are highly relevant when deciding how to reach your particular goals.
I will propose that a much more relevant question on the topic is this:

What is the probability of your bankroll being within certain parameters after a given # of trials utilizing a particular bet sizing method?

Once you see these # you can decide if the method you intend on using is too risky or not aggressive enough. After that of course you need to view these numbers in light of your personal circumstances. And being aware of your emotions is O.K.---in fact its a good thing.

Seems to me someone like CHFacts has gone through this process whether mathematically or mostly intuitively. Kelly # on the other hand is a generic # for those who don't want to be bothered. There is nothing virtuous about it. If anything, using it is lazy and unimaginative.

[Dazzez]

I'm not in awe of phrases like "maximizing expected bankroll growth". I'm quite aware of what you're trying to get at when you as them.

Oh yeah?

Then define it.

[tomcowley]

I don't disagree that if you have an edge and bet the K# into an infinite # of trials you will make more than betting 2xK or flatbetting.---------but this is the same as saying "you will ultimately win doubling your bets after loses".
You need to be aware of the relationship of these two things. Both are true, neither are highly relevant when deciding how to reach your particular goals.

Actually, you go completely broke with nonzero probability doing the latter. You hit a log (base 2) BR/bet losing streak, and you're busto. If you flat bet (except for loss doubling) with any finite edge no matter how large, you go busto with probability approaching 100%.

I will propose that a much more relevant question on the topic is this:

What is the probability of your bankroll being within certain parameters after a given # of trials utilizing a particular bet sizing method?

I propose that I decide how much I like money. Having another 100k would be nice. Having another 500k would be nicer. Having another 2m would be nicer. Having another 4m would be nicer than having another 2m, obviously, but the difference wouldn't be twice as nice. Having 100k less would kind of suck. Having 200k less would suck more than twice as much as having 100k less. Having 500k less would really really suck. Having 1m less would be pretty close to an epic level of suck for me right now.

If I put numbers on those different levels of niceness and suckiness (call them the utility of having that amount of money), then I can decide- with every individual bet- how much to risk to maximize my expected utility. I don't need to analyze nebulous stuff like BR parameters, or to try to mentally take a weighted average of how the 2^n different outcomes can affect me (like anybody can do that)- Just from knowing how much I like money, I can figure out how much I should bet on any given edge.