Kelly Criterion explained

[coldhardfacts]

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.

Believe me, I understand where you're coming from. Just three points:

With a coin flip, I know exactly what the probabilities are. The probabilities of my winning any game are much less precise. Using this formula, it is inevitable that at least as often as not (and quite possibly more often, since when the hot streaks follow cold streaks my wagers will be lower, and vice versa), I'll be betting more on games that I have a lesser chance of winning.

Despite what Santo claims, there is no way I can or would want to establish a bankroll for myself. It's ridiculous to set the limit at the amount I'm willing to lose in a given year, because I am certainly going to wager many multiples of that throughout the year. If I bet an average of 5 games a day, $500 per game, then I guess technically I'm risking $912,500 - much more than I'm able to lose. I'm sure you're going to tell me to determine the number of bets I make in a year to come up with some sort of average, but that isn't practical, either. I bet what I like - sometimes it's 0 games a day, sometimes it's 10 games a day. In any case, I have no idea how many total bets I make in a year, but I'm sure it varies more than a little from year to year.

Along those lines, no one makes one bet at a time. As I said, some days I may make 1 bet, some days 10. If you're telling me to bet the same amount per day, then in the second instance I'd be betting technically 1/10 on each play as I did on day 1. Doesn't make much sense to me.

[tomcowley]

The idea of "expected growth" is based on the same principal.

Please define "expected growth" in your own words. Seriously.

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.

If you want to turn a positive-growth proposition into a negative growth proposition with a small chance of hitting it really big, that's a personal preference. It's like somebody coming up to you and giving you a choice: 1) Person will double your net worth, guaranteed. 2) roll 2 dice. If you don't roll 12, you give him 99.99% of your net worth. If you roll 12, he gives you 80x your net worth. Game 2 has higher expectation. Nobody acting remotely rationally would chose to play game 2. Please stop using EV as your tool for evaluating staking strategies. It's categorically stupid.

Despite what Santo claims, there is no way I can or would want to establish a bankroll for myself. It's ridiculous to set the limit at the amount I'm willing to lose in a given year, because I am certainly going to wager many multiples of that throughout the year

Not if you hit a really cold streak early. Then you'd bet through your "bankroll" about once, and it would be gone. How many games in a row can you lose (without adjusting your bet size) before you're stone broke or would quit gambling (whichever comes first)? Use that amount of money as your bankroll, and you'll come pretty close. That doesn't mean you can't add money to it later (from a job>expenses), or subtract from it later (for expenses>other income).

If I bet an average of 5 games a day, $500 per game, then I guess technically I'm risking $912,500 - much more than I'm able to lose.

No.. you'll only be risking that much if you ACTUALLY STILL HAVE ENOUGH MONEY after all your previous bets. People who are dedicated can risk millions in a year on a BR starting well under 100k.

Along those lines, no one makes one bet at a time. As I said, some days I may make 1 bet, some days 10. If you're telling me to bet the same amount per day, then in the second instance I'd be betting technically 1/10 on each play as I did on day 1. Doesn't make much sense to me.

Who ever suggested to bet the same amount per day? Believe it or not, kelly handles simultaneous events too, and it's not by betting 1/n on each of n individual plays.

[Art Vandeleigh]

With a coin flip, I know exactly what the probabilities are. The probabilities of my winning any game are much less precise. Using this formula, it is inevitable that at least as often as not (and quite possibly more often, since when the hot streaks follow cold streaks my wagers will be lower, and vice versa), I'll be betting more on games that I have a lesser chance of winning.

You should do this simple yet pain in the neck simulation anyway, to get a feel for the bankroll fluctuations better when using Kelly vs. flat betting.

The simulation can be adjusted later to accomodate the fact that you don't know the exact advantage you have for each and every game.

[donjuan]

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.

Seriously, I would love to hear you define expected growth. Have you even read Ganchrow's article on it? Kelly is pretty much the opposite of Martingale and is used precisely because you can't run exactly at your expectancy.

[RealSlimShady]

Justin, thanks for the highly informative video!

[Data]

I like the quantity of posts in this thread, it is unclear what the argument is about though. So I thought I would throw in something.

While I admire a beauty of Kelly staking approach and the framework that Ganchrow enlightened many of us with, I see it hardly applicable to sportsbetting. The reason being that the market is too thin. What that means is that no winning sports bettor actually uses Kelly as his staking method because he faces an unsolvable problem of betting limits. Trying from the other side and using fractional Kelly with multipliers of .01 or less can hardly be considered Kelly staking. So, Kelly is very much useful but only for a short period of time during an advantage bettor's career if and only if that bettor starts with a small bankroll.

[reno cool]

"If you want to turn a positive-growth proposition into a negative growth proposition with a small chance of hitting it really big, that's a personal preference. It's like somebody coming up to you and giving you a choice: 1) Person will double your net worth, guaranteed. 2) roll 2 dice. If you don't roll 12, you give him 99.99% of your net worth. If you roll 12, he gives you 80x your net worth. Game 2 has higher expectation. Nobody acting remotely rationally would chose to play game 2. Please stop using EV as your tool for evaluating staking strategies. It's categorically stupid."

The point is the person needs to decide what kind of risk he wants to take. Betting 1xK will often turn a winning year flat betting into a loser. Why should someone who has a winning handicapping system increase his risk of having a losing year?----- I guess its because he wants to give himself a chance at a bigger win.------Why do many Kelly proponents bet a fraction? Because they have found the full amount too risky. With good reason.
Lets admit the realities of our experiences. Instead of trying to shape the world around an antiqued theory.

[reno cool]

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 cannot afford to make less than 15000

[tomcowley]

What is a bet? A risk to make money. Criticizing kelly on that basis (that it's higher risk to make more money), which is the basis of all betting, is utterly moronic. Do what several of us have asked- define "expected bankroll growth" in your own words.

[reno cool]

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.

This is what I would suggest and what I have done. Obviously, much more than 5 times, and pertinent probabilities. Looking at such results is beneficial for a gambler trying to decide on his betting strategy.
This is basically what I suggested originally about the 100 gamblers.

[reno cool]

What is a bet? A risk to make money. Criticizing kelly on that basis (that it's higher risk to make more money), which is the basis of all betting, is utterly moronic. Do what several of us have asked- define "expected bankroll growth" in your own words.

I have addressed defining "expected bankroll growth" several posts back in response to Dazeez. If you don't like it why don't you tell me what you'd like me to say? Maybe you should read some of my posts with an eye towards understanding instead of dismissing.

I'm interested in what betting to win a percentage = to your edge does to your bankroll. Not what words you use to codify.

2. A second ago you were saying only moron would risk so much. Now your saying: "What is a bet?" Are you aware of your own hypocrisy.

[tomcowley]

You didn't discuss expected bankroll growth at all in response to dazzez- you discussed the effect of running near expectation on the growth of your bankroll. Do you think these are, roughly, the same concept?

[reno cool]

pretty much. Explain how they are different in an actual sense.

[reno cool]

I like the quantity of posts in this thread, it is unclear what the argument is about though. So I thought I would throw in something.

While I admire a beauty of Kelly staking approach and the framework that Ganchrow enlightened many of us with, I see it hardly applicable to sportsbetting. The reason being that the market is too thin. What that means is that no winning sports bettor actually uses Kelly as his staking method because he faces an unsolvable problem of betting limits. Trying from the other side and using fractional Kelly with multipliers of .01 or less can hardly be considered Kelly staking. So, Kelly is very much useful but only for a short period of time during an advantage bettor's career if and only if that bettor starts with a small bankroll.

so your saying your just maxing everything out anyway?

Thats the reality for many plays (outside sportsbetting)

[Art Vandeleigh]

I like the quantity of posts in this thread, it is unclear what the argument is about though. So I thought I would throw in something.

While I admire a beauty of Kelly staking approach and the framework that Ganchrow enlightened many of us with, I see it hardly applicable to sportsbetting. The reason being that the market is too thin. What that means is that no winning sports bettor actually uses Kelly as his staking method because he faces an unsolvable problem of betting limits. Trying from the other side and using fractional Kelly with multipliers of .01 or less can hardly be considered Kelly staking. So, Kelly is very much useful but only for a short period of time during an advantage bettor's career if and only if that bettor starts with a small bankroll.

Yes I see your point if you were trying to grow your bankroll to the moon, i.e. if your bankroll is at $5,000,000 and you have found a situation where your advantage is such that Kelly says to bet 4%, it may not be too easy to get down $200,000 at the number you need.

But in a more down to earth way, since Kelly grows your bankroll optimally, maybe one should think more in terms of acquiring a $250,000 bankroll (where the wager would now be $10,000, a more practical amount to get down or spread around town), growing the bankroll to $350,000, taking out the 100k from you bankroll and having fun for a couple of weeks, then re-grow your 250k back to 350k. Rinse, then repeat, up to the point where the market can support efficient growth. You don't have to attempt to build your bankroll to infinity to have fun in this world.

[Data]

But in a more down to earth way, since Kelly grows your bankroll optimally, maybe one should think more in terms of acquiring a $250,000 bankroll (where the wager would now be $10,000, a more practical amount to get down or spread around town), growing the bankroll to $350,000, taking out the 100k from you bankroll and having fun for a couple of weeks, then re-grow your 250k back to 350k. Rinse, then repeat, up to the point where the market can support efficient growth.

It seems you are not including one's net worth into his Kelly bankroll while you must do that.

You don't have to attempt to build your bankroll to infinity to have fun in this world.

Very true.

[tomcowley]

pretty much. Explain how they are different in an actual sense.

You've been directed to ganchrow's posts, which you obviously haven't read (or understood in the least if you did). You're discussing concepts (risk vs. reward, in a general sense) that can be modeled mathematically, but you refuse to use math at all, to the point of refusing to learn what THE MOST IMPORTANT term in the discussion even means. Seriously- read ganchrow's posts, play with the kelly calculator, demonstrate that you actually understand what expected growth means, and how different bet sizes affect it, and then we can talk.

[reno cool]

You've been directed to ganchrow's posts, which you obviously haven't read (or understood in the least if you did). You're discussing concepts (risk vs. reward, in a general sense) that can be modeled mathematically, but you refuse to use math at all, to the point of refusing to learn what THE MOST IMPORTANT term in the discussion even means. Seriously- read ganchrow's posts, play with the kelly calculator, demonstrate that you actually understand what expected growth means, and how different bet sizes affect it, and then we can talk.

Just make a damn point. If I'm wrong about something particular, point it out. I believe I have a good understanding of what betting a particular percentage does to your bankroll. You can call it expected growth or fried chicken for all I care.
It is your crew that makes ridiculous and misleading statements such as :
"If you overbet Kelly you will lose.

[tomcowley]

I've made a point. You can't understand it because you refuse to do any work of your own to learn the necessary background information, and I'm sure as hell not duplicating Ganchrow's posts in here when you're too lazy to follow one link to read them yourself. When you learn what expected growth is, and what a rational measure for "winning" and "losing" is, then come back and talk.

[donjuan]

It is your crew that makes ridiculous and misleading statements such as :
"If you overbet Kelly you will lose.

You can overbet Kelly and still make money. Kelly just maximizes your EG. However, there is a point at which overbetting will make your bets -EG.