Living of your bankroll using the Kelly criterion

[buby74]

I really enjoyed the recent (May 25th 2011) Behind the Bets Podcast on ESPN which featured handicapper Teddy Covers. He talked about many things including how to deal with losing streaks and bankroll management. But the thing that struck me was that he keeps his bankroll as his retirement fund and uses the income from his handicapping service for his living expenses.
This got me thinking about how to manage your bankroll while drawing an income from it. Or in other words how could you become a professional living solely off your winnings and not having any other source of income.
For example imagine you have developed a system which consistently generates positive EV bets so you use the Kelly criterion to size your bets in order to maximise the log of your bankroll growth. However as standard Kelly betting prohibits you from removing anything from your bankroll what happens if you start withdrawing a salary from your bankroll?
My approach is that instead of maximising the growth of your bankroll you would aim to keep your bankroll constant by withdrawing an amount before you bet of the correct size so that the average expected growth of your bankroll due to the bet will return your bankroll to its original level.
The key formula I am using is not the Kelly formula but the next step which is the average bankroll growth caused by a Kelly bet which is
Average bankroll growth per bet is (1+kd)^w*(1-k)^L
Where W and L are the probabilities of winning or losing the bet, k is the Kelly criterion percentage of your bankroll that you bet and D is the (fractional)odds you got on your bet.
For example if you are betting football and your system predicts 55% winners and you are getting odds of -110 (or 10/11 in fractional odds). Kelly says to bet 5.5% of your bankroll on each bet.
From the formula above the average growth per bet is 100.138% (or rather your bankroll will be 0.138% bigger on average after each bet). Therefore you can reduce your bankroll to the reciprocal of 100.138% which is 99.862% and your bankroll will be returned to its original size after the bet (on average). Therefore you can remove 0.138% of your bankroll as salary without leading to a long-term reduction.
This is 1/726th of your bankroll. So if you want to live off your bankroll with this system it depends how many bets you have a year what salary you want and what your bankroll is. If you have 50 bets a year your income is 50/726 of your bankroll so for a salary of 50,000 a year you need a bankroll of 726,000.
This seems like a very high bankroll requirement( although it is an annual income of 7.5%). So the key is to get a better system with a higher success rate and/or have more bets per year. For example If you had a system that generated twice as many bets your bankroll requirement would be halved for a given size of required salary.
If you had a system that won 56% of bets you could withdraw 1/380th of your bankroll per bet or if you expected to win 57% 1/233rd. Even a super duper 60% system allows only 1/86th withdrawal per bet.
So it looks extremely difficult to make a living solely of your bankroll unless you have a very good system with a lot of bets per year.
Are there any flaws in my logic? have I underestimated the risk of ruin? Has all of this been done before?

[sharpcat]

100 plays a year? Good Luck!!

[manutdlegend]

good luck with that

[wiffle]

lolwat

[That Foreign Guy]

However as standard Kelly betting prohibits you from removing anything from your bankroll

What is this I don't even.

Kelly tells you what to bet in this instance given your current bankroll. It doesn't care if your bankroll is smaller than it was last time or bigger or if that change is from a withdrawal or not.

[Dr.Gonzo]

Kelly is way to aggressive.

[Peregrine Stoop]

if you're building up any real bankroll, you'll be at casino limits long before quarter kelly

[maxvalue1]

Wow...would like to know what books you use??..this will require high limit books that wont cut you off

[buby74]

What is this I don't even.

Kelly tells you what to bet in this instance given your current bankroll. It doesn't care if your bankroll is smaller than it was last time or bigger or if that change is from a withdrawal or not.

Sorry but you are wrong. While the percentage of your bankroll you should bet is the same regardless of bankroll size Kelly assumes that all winnings are reinvested. For example if your bankroll is 10000 and Kelly requires a 2% bet that is 200. But if you plan on withdrawing 1000 next week to pay your mortgage then your bankroll is effectively 9000 and so 200 is too much and you should have bet 180.

[That Foreign Guy]

Kelly assumes that all winnings are reinvested. For example if your bankroll is 10000 and Kelly requires a 2% bet that is 200. But if you plan on withdrawing 1000 next week to pay your mortgage then your bankroll is effectively 9000 and so 200 is too much and you should have bet 180.

I'd love for you to show me where I am wrong.

In fact, I'd love it so much that if can you write a proof that a mutually agreed knowledgeable poster (I suggest Justin7) accepts is mathematically and logically valid I will give you 200 SBR points. Of course if you can't then I want 100 points for my valuable assistance.

Yes I am laying you 2-1. Do we have a bet?

Back to the topic at hand:

A recommendation for would be poker pros is to have 6 months living expenses saved up before attempting to go pro. I suggest you do something similar if you're worried about violating Kelly rules rather than trying to manage withdrawals on a per bet basis. Then take profits every month or season or whatever and refill your living expenses buffer. The rest you can spend on hookers and blow.

[buby74]

[quote=That Foreign Guy;10253533]I'd love for you to show me where I am wrong.

In fact, I'd love it so much that if can you write a proof that a mutually agreed knowledgeable poster (I suggest Justin7) accepts is mathematically and logically valid I will give you 200 SBR points. Of course if you can't then I want 100 points for my valuable assistance.

Yes I am laying you 2-1. Do we have a bet?




I accept the bet. 100 points at 2-1

[JustinBieber]

If you are to take gambling seriously you should probably keep your bankroll separate from your life roll in 99% of cases.

[That Foreign Guy]

I accept the bet. 100 points at 2-1

Excellent (I genuinely mean that as this is win win for me as I either get SBRpoints or a better understanding of Kelly).

[wiffle]

A Kelly bankroll refers to the entirety of all one's assets (financial and otherwise), including all mortgageable and stealable assets, as well as the present value of the future stream of one's income.

-Ganchrow

http://forum.sbrforum.com/handicapper-think-tank/60052-when-alright-go-all-p2.html

[Blax0r]

I think Bill Chen, a famous quant gambler/trader, visits this situation in the risk management section of his poker book.

I may be wrong, but I believe he states something like p(bankroll growth) = 0 if you don't reinvest your winnings. If this isn't resolved by the time I get home from work, I'll verify this and post the proof here.

[buby74]

Ok I was wrong even if you are taking way too much from your bankroll Kelly is still the best bet it will maximise your bankroll even if that just means you are slowing the decline. Mathematically adding a constant reduction factor to each bet to represent taking an income doesn't affect the calculation of Kelly when you do the calculus.
How do I pay you I tried to give you 100 points for your last post but it wouldn't let me. That error aside let me rephrase my original point. What size bankroll do you need to live solely off your winnings given a reasonably good system and how many bets a year would you need to make.

[wiffle]

a lot of pros make 10k+ wagers a year

[maxvalue1]

Where do most "pros" get there action ?

[buby74]

Wow 10000 bets a year there are 256 NFL regular season games 2500 MLB 1200 NHL and NBA games 750 college football (fbs) games and maybe 7000 d1 college basketball games every season. Are pros betting on almost every game every day?

I had assumed that the line is very hard to beat and a successful system will tell you not to bet most games as there is no value. Similarly how can you develop a good system for multiple sports?
Although if you can make 1000 positive ev bets a year then my original post about living off of your bankroll becomes much easier even if you switch to half Kelly to reduce variance and take less then the recommended fraction of your bankroll as income.

[Melloweitsj]

Wow 10000 bets a year there are 256 NFL regular season games 2500 MLB 1200 NHL and NBA games 750 college football (fbs) games and maybe 7000 d1 college basketball games every season. Are pros betting on almost every game every day?

There are possible to make several different types of wagers on the same matches (ML, spreads, totals, props, etc.)

[That Foreign Guy]

How do I pay you I tried to give you 100 points for your last post but it wouldn't let me.

I don't know, that's the only way I've ever transferred points. I just transferred you one so maybe it was just broken for a while or you don't have enough posts to send yet?

You seem like a decent fellow (admitting you were wrong is a sign of good character IMO) so I'm confident you'll pay me when it's possible.

That error aside let me rephrase my original point. What size bankroll do you need to live solely off your winnings given a reasonably good system and how many bets a year would you need to make.

The way I approach it is a little twisty:

Q1) How much do I want to make in a period?
Q2) What's a reasonable ROI? Half that to allow for run bad / bankroll growth.

Calculation 1) Income / expected ROI = how much you need to turnover during that period.

Q3) How much of my bankroll do I expect to get in play in total during that period? I estimate based on my own records so if a typical month during NBA I get 50% of my bankroll in play then I assume I can continue that, maybe adding a margin of safety depending on how much I hate my job at the time.

Calculation 2) required Turnover / expected fraction = bankroll requirement

It's a ball park figure at least and has enough of a margin of safety for my tastes.

[tukkk]

a lot of pros make 10k+ wagers a year

thats theoretically possible, if you have many partners + you sit in front of your screen 18h / day and you master basketball/football/soccer/baseball/tennis all together

in practice I dont think anyone achieves this

[durito]

10k is easy and it certainly doesnt take 18 hours a day. you know how many soccer games there are per year?

[donjuan]

soccer/tennis + derivatives + props + fun with push percentages (teasers, pleasers, etc.)

get to 10k pretty easy.

[tukkk]

10k is easy and it certainly doesnt take 18 hours a day. you know how many soccer games there are per year?

Soccer is the only sport i wager
If I get better betting sides, I think by my own i could get 3k soccer bets down in a year ... not more
10k by oneself with no teamwork is quite impossible imo

[Thremp]

You are delusional.

[chunk]

This is one of the better threads that I've run into during my short tenure. I'm not a jack of all trades, so I only make about 4 to 5 hundred plays/yr. Furthermore, I've always struggled with the definition of a "professional". When is that transition made from amateur to pro? Is it quantified in hours? Expertise? Dollars? Possibly the ability to support oneself solely on gambling income? Lots of gray area I suppose.

I realize that it's off topic, but still relates to some of the comments made here.

[buby74]

Chunk
My view is that a pro is someone who can make their living solely from gambling. if you cant afford to give up the day job then you are an enthusiastic amateur.
I would apply the same definition to an actor or musician (with apologies to all waiters in Los Angeles and new York).

[Arilou]

Kelly assumes the value of your bankroll is such that doubling and halving it have equal utility, and that losing all of it has infinite negative utility. Needless to say, this isn't true, as life goes on if one goes bust and betting has largely fixed time costs, although the fact that limits get in your way at the high end is also an issue. If you use Ganchrow's definition, which is the technically correct one, it's more true, but anyone who is going to run Kelly based on their projections of future income stream and what they can steal is clinically insane.

Here we see another basic reason why it isn't true, which is that a man's gotta eat. If there's a constant drain on your bankroll over time, then the value of a sufficiently small bankroll is obviously zero; having $100 in your bankroll and having $0 are not that different as either way you're going back to your day job, which will in turn inevitably offer the chance to rebuild your bankroll if that is what you want to do. Thus, losing money is *less bad* than we think it is, relative to bankroll size, which will inevitably encourage you to bet more rather than less compared to what you would have done otherwise.

A counterargument would be that betting more than Kelly will mean that you will probably go broke. That is true. But if you've got a bankroll you're draining over time, let's face it, you'll probably go broke anyway. The scenario where you just barely make ends meet for years on end is highly unlikely. If you have just enough Alpha to survive, you're going to go broke when you hit a downswing, and if you have more than enough and don't go bust quickly you will end up rich.

[solring]

10k by oneself with no teamwork is quite impossible imo

I made 4,700 bets last year and I took three months off. Most of the wagers (3,300) were made from September to December. I've made 1,000 bets this year and have already taken two months off... I'm not a pro...and I don't do this anywhere near full-time...

[tukkk]

I made 4,700 bets last year and I took three months off. Most of the wagers (3,300) were made from September to December. I've made 1,000 bets this year and have already taken two months off... I'm not a pro...and I don't do this anywhere near full-time...

If you blindly follow a basic model then its possible, but you will be making alot of 0EV bets for sure imo not to talk about several -EV bets ... I think that brings in less money than a more serious handicapping, if we are talking about handicapping not some kind of steaming
10k + bets a year will make you an instant millionaire IMO if 10k bets are +EV

[underthe total]

i cant believe i am reading this.....unreal

a few of you are delusional like he said

[luegofuego]

lots of people speaking with authority on issues they don't understand.

10k bets is completely doable. look at all the arbs/derivatives/props out there. you could probably do 10k bets using betfair alone.

[dendimurah]

If you are to take gambling seriously you should probably keep your bankroll separate from your life roll in 99% of cases.

Good advice Bieber. I'm listening to Biebers song right now. what a coincidence.

[necro]

you ll need luck.mujbh luck