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Yes, as indicated by my earlier post, I agree that Kelly is not appropriate for all gamblers in all situations. It is appropriate for those of us who seek to maximize long term bankroll growth. For those with different goals, it makes sense for them to seek out other approaches.Originally Posted by reno cool
No problem.
Just to make sure I understand your post, do you agree that always betting the amount called for by Kelly will maximize long term bankroll growth? I know you are making other points, and some or all of them might well be correct, by I just want to make sure you don’t believe said points to contradict this basic claim about Kelly.
If:
1) You have a set, defined bankroll;
2) that bankroll is everything you are willing to risk - no more, no less; and
3) you are very confident that in the long term you are going to show a profit;
then, yes, I from what I understand of Kelly it will enable you to maximize your ROI.
When people (rarely) ask me, I usually recommend fractional kelly. Simply because it covers you if you're slightly off with your edge. Slightly over-estimating your edge will kill you full kelly.
Thanks coldhardfacts.
What about without those qualifications? Would the Kelly wager amount be the amount that maximizes long term bankroll growth?
TLD is easily in my Top 5 posters on SBR
When does the game-picking dart board come in??
As nice guys as they might be in real life (in other words it's nothing personal), I find it rather amusing that the two posters who clearly know the least about Kelly (coldhardfacts and reno cool) are also the also one arguing so vehemently against it.
reno cool unable to to define expected bankroll growth ... coldhardfacts claiming that Kelly maximizes ROI .... I really think this thread belongs in the Player's Talk section .... at EOG.
CHF and reno cool need to to actually read what people are writing and realize thet as smart as the tow of them may be they aren't arguing rocket science. They're arguing against very established facts of fincial economics.
I suggest the two read http://www.sportsbookreview.com/forum/handicappe...on-part-i.html and http://www.sportsbookreview.com/forum/handicappe...n-part-ii.html be specfic about what parts they don't understand or agree with.
Great video Justin thank you for the breakdown!!!
Dazzez
Address my points directly. I know that you like being a smartass. Who are you trying to impress?
The problem is that for the most part your points are belligerently vapid, antagonistically inconsistent, laughably irrelevant, and completely ignore the established mathematical theory being presented over and over by your clear intellectual superiors ("intellectual superiors" in this one particular field of study, I'm not generalizing about you here, for all I know you could be a brilliant doctor or lawyer or anything else).
You wrote:So go ahead, I'll ask it of you again, can you define "maximizing expected bankroll growth"?
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%.
Please elaborate on how this works, especially the last sentence.
I don't think your criticism has any bases. Show me where I'm wrong.
My only interest is to see why people here insist on promoting a particular money management system. I'd be happy to acknowledge its virtue if something worthwhile was presented to me. Instead I'm presented with narrow minded responses. I believe people here have a poor understanding of the implications of the system they are so fond of. ---Particularly they are mislead by the term "long term", and are quick to mislead others.
This goes right into the term "expected bankroll growth".
As the number of trials increases results tend to get closer to our expected edge. Now it seems that ultimately we'd like a system that would do best when this result is achieved. ---this is primarily the allure.
If I'm wrong please enlighten me.
For the most part the problem is the effects of variance. In a realistic # of trials however nothing is expected, there are only probabilities of various outcomes. And gamblers should decide for themselves what kind of risk is suitable for them.
flat betting is the only way to consistently win long term. kelly criterion is crap
Well that settles that. I guess we can close the thread now.
sounds good to me pal. I like the video but theres no way to determine the exact edge of a game. And bad beats happen. If a play have a decent ammount of edge for one side you should be betting it. Just because you have a win probability of 85% on a game does not mean you should risk 85% of your roll thats how u lose long term.
What a great mix of analysis, intellectual debate and complete buffoonery all in one place.
This thread delivers!
I don't know. But unless you're more comfortable using it than any other wagering discipline, I would pretty confidently say "NO".
Let's say you start with 127000, and you have a base bet of $1000 on a 10000:1 payout that's 50% to win. That's a pretty good edge, and you're massively underbetting it, but... Right off the bat, you have a 1 is 64 chance of going busto by martingaling out losing 7 in a row. It doesn't matter how you plan to adjust bet sizes, you have some chance of going broke instantly by martingaling.
If your plan is to keep betting $1000 (doubling if you lose), you'll eventually bust. The proof I came up with is kind of esoteric, and ganchrow probably has a better one. Once your BR gets large compared to the bet size (I'm giving you this for free, so I'm actually calculating a lower bound.. as well as "letting" you get paid off as if you truly bet double when you're all in for less than that on your last bet, also another reason this is a lower bound), you'll be at a point where it takes N consecutive losses to bust you, and you need to win K martingale bets to double up- your actual odds don't matter at all, they just set a relationship between N, K, and BR.
The odds of winning the martingale are 1 - 1/2^N, and you need to win K of them, so the odds of doubling up are (1 - 1/2^N)^K. Assuming you do, the odds of doubling up again uses the same formula, except N is replaced by N+1 (since you can fade one more loss now that you've doubled up), and K is replaced by 2K since it takes twice as many wins to double up your BR since it's twice as big now. So the probability of going on forever is the product of getting each doubleup without busting, which is
product (i= 0 -> infinity) (1 - 1/2^(N+i))^(K*2^i)
That product is zero (ratio test consecutive terms), so you have no chance of permanent success.
Actually, it is easier. Given a bet's payout odds and win%, there's some optimal percentage of BR to bet to maximize the chance of martingaling to a doubleup, but it obviously still has a nonzero - and constant - chance of failure each time you try to double up. So the odds of one doubleup success are (1 - failure%). So the odds of N doubleups are (1-failure%)^N, which obviously goes to 0. That's an upper bound of success rate- wagering any different amount will simply increase your odds of busting before N doubleups.
How does one's being comfortable or not comfortable using Kelly affect whether the Kelly wager amount is the amount that would maximize expected bankroll growth?
What I mean is, I don't want to worry about changing the size of my bet relative to my bankroll. I don't have a gambling "bankroll".
As I understood ArtVandaleigh's explanation in a previous post, the main benefit of Kelly to someone like me, who has no basis for assigning different winning probabilities to different wagers, is that it would enable me to bet the optimal percentage of my (non-existent) bankroll at any one time so that in the long run, if I hit the percentage of winners I expect to hit (also imprecise, btw) I would achieve the maximum return on my investment - i.e., my "bankroll".
Did I misunderstand?
Everyone has a bankroll.
Could you afford to lose $10 in the next year? How about $1000? $1,000,000, $10,000,000... somewhere in there is your bankroll.
I don't think of it in those terms. I am confident that I am going to win longterm. I also know that I am going to hit some very cold streaks and some very hot streaks. Although I don't know when these are going to happen, of course, or when they're going to end. I bet enough so that I can earn a decent income, but am still able to weather the cold streaks without having to decrease my bet size (which would no doubt reduce my earnings when things reversed) or adjust my lifestyle.
I believe from your posts you (and some of the other Kelly critics) are alleging that it is difficult and/or inadvisable for certain gamblers in certain situations to implement a betting system based on the Kelly formula.
However, many folks seem to assume, falsely, that this constitutes a criticism of the Kelly formula itself.
I’m confident you’re doing the first, and I believe if you stopped and thought about it, you’d see that provides no warrant for doing the second.
Once you understand this distinction, I think you’ll see that the answer to my question (Will always betting the amount called for by Kelly maximize expected bankroll growth?) that best represents your position is “Yes, but.…” rather than “No, because….”
tomcowley.
I think I misunderstood what you were referring to.
I thought you were talking about the probability of busting flatbetting.
None the less when betting into infinity a lot of strange things will happen. Eventually you will lose enough trials in a row to bust a Martingale.
Eventually you will win a bet and get your money back.
My point was referring to one Martingale. The reason you can't depend on a Martingale is because you're expectancy often will not be realized soon enough or close enough to avoid giant bets.(I'm talking about the expectancy of winning at least one in 7 even money bets, for example) ------this works similarly in Kelly.
tld,
Nobody's debating whether the Kelly formula is properly calculated. When you're asking the above question your begging the question.
The issue here is whats the best way for gamblers to stack their bets? Is following Kelly best? And my view is there is no reason to believe this. Kelly is not the safest method, nor is it the one yielding the highest possible "average return". ---as per the Tomcowley example.
Furthermore there are many other problems looking at gambling through the Kelly paradigm. Why don't we ask how much of his winnings does CHfacts use to live on? And what does that do for his expected bankroll growth? The problems with estimating ones edge in handicapping is a whole other issue. What I'm saying is we need a better paradigm.
Infinity discussions are meaningless, and only one of these statements is relevant. It's not the second one.
The two have absolutely nothing to do with each other. For one, when you're betting kelly, and you lose one bet, your next bet will be SMALLER, not bigger. Are you channeling JR Miller's crapsite here or something?My point was referring to one Martingale. The reason you can't depend on a Martingale is because you're expectancy often will not be realized soon enough or close enough to avoid giant bets.(I'm talking about the expectancy of winning at least one in 7 even money bets, for example) ------this works similarly in Kelly.
Kelly, at its simplest, is a formula to size ONE BET at ONE TIME for optimal expected BR growth after ONE BET (yes, it can be extended to contemporaneous bets, parlays, etc, of course). It doesn't matter one bit if I'm going to get 1 bet, 100 successive bets, or 10000 successive bets. I'm going to bet the same amount on the first bet. As it happens (shockingly), given successive bets, making the optimal expected growth bet for each bet will give you the optimal expected growth for that series of bets.
Average return is a completely useless statistic. Nobody would bet everything they can beg, borrow, and steal to bet +10001 on a +10000 shot, which is what improving average return would suggest that you do.
Somebody with a BR drain is going to be more risk-averse (since getting low is worse that it would be if you had no expenses). Your BR isn't as big as it nominally appears, so you'd bet less. Somebody with other income > expenses is going to be less risk-averse (for the same reason, reversed) and is going to bet more. That's been covered in plenty of depth around here.Furthermore there are many other problems looking at gambling through the Kelly paradigm. Why don't we ask how much of his winnings does CHfacts use to live on? And what does that do for his expected bankroll growth? The problems with estimating ones edge in handicapping is a whole other issue. What I'm saying is we need a better paradigm.
So by “the Kelly formula is properly calculated,” you mean it does what it purports to do, namely translates bankroll/likelihood of winning/odds into optimal bet size for the purpose of maximizing expected bankroll growth?
Or are you (still) disputing that?
Let me try it this way:
I think what you and the critics are saying, or should be saying (I just wish you’d be clearer) is something like this:
We do not dispute that the Kelly formula does exactly what its proponents claim, which is to take the odds, likelihood of winning, and bankroll size for a given wager, and calculate the ideal bet size for the purpose of maximizing expected bankroll growth.
However, we contend that the use of Kelly ought not be advised for all gamblers in all situations for at least two reasons:
1. It is possible for a person to attempt to ascertain the correct Kelly bet amount and fail, because he does not know what his bankroll is, and/or because he does not know his likelihood of winning a given wager. The formula will certainly reveal the optimal bet size for the odds, likelihood of winning, and bankroll size he happens to enter into it, however, if one or more of the three figures he enters is significantly inaccurate, then on the principle of “garbage in/garbage out,” the resulting bet size will not be optimal.
For example, his likelihood of winning might be 53%, and the correct Kelly wager based on that be $20. However, because he falsely believes his likelihood of winning is 65%, and he plugs this into the Kelly formula, he comes to the false conclusion that he should bet $500. Thus he is betting 25 times his optimal Kelly bet and doesn’t know it.
2. Not all gamblers in all situations are seeking to maximize expected bankroll growth. Sometimes they have other goals in addition to or instead of that one. Kelly is specifically designed to maximize expected bankroll growth, and there’s no reason to assume it will also be ideal for serving all of the myriad of other possible goals, or combinations of goals, that gamblers might have.
Let me hasten to add, I’m not trying to put words in your mouth. I genuinely think something like this is what you’re trying to say.
So let me ask you two questions:
1. Is this a fair representation of your position?
2. Do you believe that those who in this and other threads have taken what might loosely be called a “pro-Kelly” stance—such as Ganchrow, donjuan, Santo, myself, etc.—disagree with this position?
tld--- I appreciate your efforts in trying to make the points of contention clearer.
The issue in contention is the significance of Kelly to actual gamblers. Should they use it?
I don't disagree with the idea that Kelly maximizes "expected" bankroll growth. Rather that looking at gambling through the eyes of "expected bankroll growth" is problematic.
The points you bring up in 1.and 2. are designed to show why Kelly is ill-equipped for dealing with actual circumstances. So your interpretation of my position is close. I don't feel its inappropriate for a few fringe cases, but rather in the majority of cases, especially when it comes to handicapping. As I've stated elsewhere, its less problematic for a game like Blackjack.
I do feel that some people on here make misrepresentations of what betting systems do to your bankroll. It feels that they are repeating someone else's words and refusing to look at the bigger picture.
Great post Facts. If this doesn't illustrate Kelly's lack of utility, nothing will.
This is an important point. Your ether ignoring it on purpose or you don't understand it. But I'd like to know your view on this once I feel were both talking about the same thing. So humor me.
Many famous money management systems are based on the idea that as long as you run close to your expectancy, you will win. Martingale is the simplest one. They are ultimately ineffective because in any session of reasonable size there is a possibility of running much worse than your expectancy.
The idea of "expected growth" is based on the same principal. The closer you are to your expectancy the better off that particular %size bet would have served you. So if you overbet Kelly 2x+ you will loose when you run at you're expectancy. But those times when you do run at 2x you will make so much more, that you will make up for the other losses. You're earlier breakdown example illustrated this well.----Hence it becomes a matter of personal preference.
This makes perfect sense to me. Am I missing something?
Instead of spending so much time writing here, why don't you take an hour or so and conduct a straightforward, super simple simulation.
Give yourself a mythical bankroll of $10,000.
Take a coin.
Call heads or tails.
Flip coin. Bet 1% of your original bankroll, i.e. $100.
If you call it correctly, add $110 to your bankroll.
If you are incorrect, subtract $100.
Do this 100 times. See what your bankroll is after 100 flips
Now do it again. This time, before each flip, use the Kelly calculator to calculate what your optimal bet size is (actually since advantage is the same on each flip you just need to multiply this Kelly percentage times your bankroll size before each flip).
Do this, meticulously, for 100 flips (subtract what you bet if you lose, add 1.1 times your bet if you win).
See what you get at the end of this trial.
Repeat this trial 5 times.
Then come back here and report your findings.
Last edited by Art Vandeleigh; 08-09-08 at 07:46 AM.
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