Estimated Edge Error: A simulation of the Kelly conundrum

Originally Posted by SportsMushroom

yes, because you dont know what that figure really is


trying to calculate an incalculable number is something that boggles my mind

although I am sure that people that do use kelly believe that they are calculating their edge right, but I just dont see how that is possible

to calculate your edge accurately you need to know that

1. the odds setters price is not accurate
2. that you have the ability to calculate a more accurate price than the odds setter
3. that the odds setters have done such a horrible job that your edge is enough to cover the vig and produce a profit
4. to do all this I have to assume that the odds setter has incomplete information, and that you have more information than the odds setter
5. yeah right

Again, all of this is also true with flat betting.

For the third time the severity of run ups and drawdowns experienced as a result of variance are almost wholly dependant on the size of the bets made NOT the method used to arrive at that bet size.

The basis of making a bet utilising (fractional) Kelly is "I have an edge which I can quantify to within an acceptable margin of error". The basis of flat betting is "I believe I have an edge but I cannot quantify it". How can one of those "boggle your mind" and yet you find the other rational?

Monkey and Thom have provided a tool which gives some insight on the 'margin of error' issue, nothing more than that, it demonstrates to those of us that do use Kelly what we already believed.

Originally Posted by FourLengthsClear

The basis of making a bet utilising (fractional) Kelly is "I have an edge which I can quantify to within an acceptable margin of error". The basis of flat betting is "I believe I have an edge but I cannot quantify it". How can one of those "boggle your mind" and yet you find the other rational?

yes I cannot quantify my edge accurately, and that makes me a pragmatist


does believing you can quantify your edge make you right? no it does not, only when someone provides a method of accurately calculating edge I will choose kelly over flat betting, flat betting protects me from the downside of making a wrong calculation


anyhow I am not sure of this but didnt you state on this forum that you are an arbitrator? if so, how does an arbitrator advocate kelly? thats like a scientist advocating religion

Originally Posted by SportsMushroom

yes I cannot quantify my edge accurately, and that makes me a pragmatist

does believing you can quantify your edge make you right? no it does not, only when someone provides a method of accurately calculating edge I will choose kelly over flat betting

anyhow I am not sure of this but didnt you state on this forum that you are an arbitrator? if so, how does an arbitrator advocate kelly? thats like a scientist advocating religion

That is completely your choice but does not change the fact that what you said starting in post #2 was incorrect.

I have never been an arbitageur. I do engage in trading in addition to regular betting.

Originally Posted by FourLengthsClear

That is completely your choice but does not change the fact that what you said starting in post #2 was incorrect.

I have never been an arbitageur. I do engage in trading in addition to regular betting.

no it is correct, using subjective estimates in place of what should be a precise figure increases variance, its common sense, even the simulations the op run indicate that


but I will never convince you otherwise and neither will you convince me, so lets just leave it at the fact that we have differing opinions


let me just make a distinction here, when I say it increases variance I do not mean in the traditional sense of wins and losses, but rather, variance in the fluctuations of the bank roll

How can you be sure you have an edge yet be unable to quantify it?

Originally Posted by SportsMushroom

no it is correct, using subjective estimates in place of what should be a precise figure increases variance, its common sense, even the simulations the op run indicate that


but I will never convince you otherwise and neither will you convince me, so lets just leave it at the fact that we have differing opinions


let me just make a distinction here, when I say it increases variance I do not mean in the traditional sense of wins and losses, but rather, variance in the fluctuations of the bank roll

Just so I have your position straight, what you are saying is that a staking plan

a) Based on Kelly which results in an average wager size of 3% or BR

will produce significantly steeper run ups and drawdowns than staking plan

b) Based on a fixed wager size of 3% of BR.


Is that really what you are saying?

Originally Posted by FourLengthsClear

Just so I have your position straight, what you are saying is that a staking plan

a) Based on Kelly which results in an average wager size of 3% or BR

will produce significantly steeper run ups and drawdowns than staking plan

b) Based on a fixed wager size of 3% of BR.


Is that really what you are saying?

no, I am saying that using inaccurate calculations of edge will do that

you just said it yourself, kelly uses AVERAGE, AVERAGE , AVERAGE, which means that you could be betting max on losing streaks and minimum on winning streaks which will minimize wins and maximize loses. you could also miscalculate your edge and be betting max on games with a lower edge and low on games with a higher edge

in the end it should all even out, but that is not the point, my point is there is greater variance with kelly, and if you dont understand then its not my fault

Originally Posted by Kolotoure

How can you be sure you have an edge yet be unable to quantify it?

that is not exactly what I am saying

all I am saying is that varying betsize according to edge will increase variance because ultimately your calculations cannot not be accurate

if u run the sim for 20 minutes u might be surprised or maybe not...

people in here are supposed to be smart but I guess I was wrong, all I did was point out the obvious, but people choose to disregard it as non sense because it messes up their world view

I hate to go all wiki on you but I am too tired to search for a better source or run simulations of my own:

A natural assumption is that taking more risk increases the probability of both very good and very bad outcomes. One of the most important ideas in Kelly is that betting more than the Kelly amount decreases the probability of very good results, while still increasing the probability of very bad results. Since in reality we seldom know the precise probabilities and payoffs, and since overbetting is worse than underbetting, it makes sense to err on the side of caution and bet less than the Kelly amount.
Kelly assumes sequential bets that are independent (later work generalizes to bets that have sufficient independence). That may be a good model for some gambling games, but generally does not apply in investing and other forms of risk-taking.
The Kelly property appears "in the long run" (that is, it is an asymptotic property). To a person, it matters whether the property emerges over a small number or a large number of bets. It makes sense to consider not just the long run, but where losing a bet might leave one in the short and medium term as well. A related point is that Kelly assumes the only important thing is long-term wealth. Most people also care about the path to get there. Kelly betting leads to highly volatile short-term outcomes which many people find unpleasant, even if they believe they will do well in the end.




kelly is volatile fact, and for more than one reason, because of that it is more likely to go broke with kelly than flat betting


also in the long run, if the average wager for kelly and flat betting is the same then you will get equal results and with flat betting you dont get the increased variance (volatility)


in the begginning it was just friendly conversation, but it seems that some people have a problem with accepting different opinions, I guess the same people that are in players talk are in here as well

I cant believe that people in here pretend to be math wizes but cant understand the basic concept of variance in input = variance in results

sportsmushroom, wow dude...

i like money so i bet fractional kelly, variance is fine... not busto yet.

i don't see how any1 is giving u a hard time in here. i accept ur POV, that's all fine....

i get better results, maybe u don't.

Originally Posted by SportsMushroom

kelly is volatile fact, and for more than one reason, because of that it is more likely to go broke with kelly than flat betting


also in the long run, if the average wager for kelly and flat betting is the same then you will get equal results and with flat betting you dont get the increased variance (volatility)


in the begginning it was just friendly conversation, but it seems that some people have a problem with accepting different opinions, I guess the same people that are in players talk are in here as well

I cant believe that people in here pretend to be math wizes but cant understand the basic concept of variance in input = variance in results

I think you should try running the multiple iteration sim. I just ran a 1000 iteration sim 10 times with FULL Kelly versus 2% flat betting, 1000 plays, between -200 and +200, 0.5%-5% edge, and -1% to -5% error (meaning that I'm overbetting EVERY play) and Kelly outperformed flat betting every time. While that's just a small sample, surely you could track it yourself over a larger sample of runs and perhaps come to a different conclusion.

You might also want to try smaller fractions of Kelly as well.

If your goal is to minimize bankroll fluctuation, your bet size should be zero. If your goal is to maximize bankroll growth, well... some variant of Kelly.

Originally Posted by SportsMushroom

no, I am saying that using inaccurate calculations of edge will do that

a) you just said it yourself, kelly uses AVERAGE, AVERAGE , AVERAGE, which means that you could be betting max on losing streaks and minimum on winning streaks which will minimize wins and maximize loses. you could also miscalculate your edge and be betting max on games with a lower edge and low on games with a higher edge

in the end it should all even out, but that is not the point, b) my point is there is greater variance with kelly, and if you dont understand then its not my fault

a) I said no such thing.

b) You can repeat this another 50 times and it still will not be true. Volatility is a function of the amounts wagered and variance, that's all.

If I am offered +115 on 1000 coinflips, a scenario where edge is known, I am inevitably going to experience substantial volatility based on a full Kelly wager of 6.52%. I trust you would agree that this is still the optimal wager amount despite that prospect.

In terms of sportsbetting and the issue of miscalculation of edge there are two things.

i) I doubt you will find anyone here who applies full Kelly. A sensible Kelly multiplier that allows a margin of error to avoid overbetting is a must.

ii) The flat bettor is also prone to the same issue. Despite not having made an edge calculation he is still making a wager based on a perceived edge which correlates with a specific Kelly edge. You could argue that the flat bettor has a narrower range of potential error but that would be a tough case to make not least because of the issue highlighted by mathdotcom in post #11.