The Kelly criterion is actually somewhat complex, but I’ll take a shot at a simple explanation anyway. First off, everyone has a gambling bankroll, even those who claim they don’t or who claim their bankroll is infinite. That’s just a load of cacadevaca, everyone has a gambling bankroll and nobody has an infinite bankroll. With that out of the way, the question arises as to how much you should bet? You could bet it all, but it shouldn’t take much to realize that that is sheer lunacy. With one bet you’d be facing 50% risk of ruin (losing it all) or even worse. And if you keep on betting it all, the result will be that you will eventually lose it all, meaning 100% risk of ruin. As I said, sheer lunacy. Put that in the camp of people who claim to have infinite bankrolls. OK, with the preliminaries out of the way, then how much of your bankroll should you bet? Well, it turns out that the Kelly criterion is the mathematically optimal bet size for maximum average bankroll growth. You should bet that amount, or less, but never more. Don’t get stuck if the Kelly bet is $5.522589, yes you can bet $5 and no you can’t bet $6 or $10. It’s that simple. Just remember: Kelly bet or less, never more. Remember the raven. Now, you may not believe in the Kelly criterion or may not understand the math behind it, but that doesn’t matter, it still applies, always. It’s not a question of belief, it’s a mathematical truth. So there you have it, either follow the math, which leads to the Kelly criterion, or make up your own system for determining how much of your bankroll you should bet. And if you choose to violate the math of the Kelly criterion, all I can say is, good luck in crazy town.
Why you should care about the Kelly criterion
nightoftheiguana2000@yahoo.com wrote:
Don't get stuck if the Kelly bet is $5.522589, yes you can bet $5 and no you can't bet $6 or $10. It's that simple.
I think you're going too far here. It might depend on the situation,
since it's so close, but I believe there's more bankroll growth with a
$6 bet than $5.
But my main comment on a stress on the Kelly Criterion is skepticism
that stressing it is necessary. It's kind of like the situation with
Christians saying one has to accept Christ as their Lord and Savior or
spend eternity in hell, even if one was born into a country in which
no one is going to hear the name Christ. I happen to believe that
such people are not doomed to hell and will basically do all right,
even assuming that Christianity would have been a step in the right
direction, which I don't want to express an opinion about. What do
people without much understanding of the Kelly Criterion do? I doubt
if overbetting is generally much of a problem. Most gamblers can be
classified into the vast majority of losers, to whom Kelly would only
tell them to stop gambling, and professionals who, no matter how
unsophisticated their understanding of the Kelly Criterion is,
generally understand that they shouldn't bet more than a certain
amount and generally don't. I don't believe I've ever had much of a
sophisticated understanding of it, but I think I've done pretty well
in not overbetting my bankroll. And I'm skeptical that chronic
overbettors will be "cured" by understanding the Kelly Criterion.
Maybe they crave excitement so much that they wouldn't be affected by
such a cerebral approach. To make a case that the Kelly Criterion
needs to be propagated more, you'd have to show examples of people
whose failure had turned to success, not due to more positive EV, but
strictly due to not overbetting any more, with % EV held constant. It
wold have to be a professional who knows enough to have positive EV
but who is so blind to the danger of overbetting that s/he'll still
lose. I think that's rare. I don't think "Fortune's Formula" made
that case.
You are both wrong but in two different ways:
1 - you have to accept that the KC will only help winning players or help you at games with an edge. Period. If you apply it to a game with negative EV you will still lose. So its really not fair to talk about gamblers that do it for “excitement”. That’s a misapplication of KC
2 - to say that “you can bet below KC but not above” is also misguided. You must always wager at the KC number. You must recall that the KC number is also designed to optimize growth of your bankroll. Knowing how much to wager on an edge is relatively simple calculation and/or monte-carlo simulation - that’s just risk-of-ruin. But knowing how much to bet to grow your bankroll and get the most from any given EV, well, that’s a whole other number . . . in fact, that’s the KC 
···
On Sat, Apr 5, 2014 at 7:32 PM, 007 <…@…com> wrote:
nightoftheiguana2…@…com wrote:
Don’t get stuck if the Kelly bet is $5.522589, yes you can bet $5 and no you can’t bet $6 or $10. It’s that simple.
I think you’re going too far here. It might depend on the situation,
since it’s so close, but I believe there’s more bankroll growth with a
$6 bet than $5.
But my main comment on a stress on the Kelly Criterion is skepticism
that stressing it is necessary. It’s kind of like the situation with
Christians saying one has to accept Christ as their Lord and Savior or
spend eternity in hell, even if one was born into a country in which
no one is going to hear the name Christ. I happen to believe that
such people are not doomed to hell and will basically do all right,
even assuming that Christianity would have been a step in the right
direction, which I don’t want to express an opinion about. What do
people without much understanding of the Kelly Criterion do? I doubt
if overbetting is generally much of a problem. Most gamblers can be
classified into the vast majority of losers, to whom Kelly would only
tell them to stop gambling, and professionals who, no matter how
unsophisticated their understanding of the Kelly Criterion is,
generally understand that they shouldn’t bet more than a certain
amount and generally don’t. I don’t believe I’ve ever had much of a
sophisticated understanding of it, but I think I’ve done pretty well
in not overbetting my bankroll. And I’m skeptical that chronic
overbettors will be “cured” by understanding the Kelly Criterion.
Maybe they crave excitement so much that they wouldn’t be affected by
such a cerebral approach. To make a case that the Kelly Criterion
needs to be propagated more, you’d have to show examples of people
whose failure had turned to success, not due to more positive EV, but
strictly due to not overbetting any more, with % EV held constant. It
wold have to be a professional who knows enough to have positive EV
but who is so blind to the danger of overbetting that s/he’ll still
lose. I think that’s rare. I don’t think “Fortune’s Formula” made
that case.
There’s nothing catastrophic about betting slightly more than the Kelly Criterion would call for. So, as 007 correctly suggests, if you bet a few percent more than what the KC calls for, you’re going to have faster bankroll growth than if you bet, say, one-fourth the Kelly Criterion.
That said, if you consistently bet more than twice the KC, it IS catastrophic. Your bankroll will not grow at all and will in fact approach zero in the longrun. That’s why NOTI’s emphasis of the importance of understanding the KC is well taken, as well as his caution in betting over the KC.
I don’t agree with 007 that it’s a rare positive-EV player who would benefit from a better understanding of the Kelly Criterion. First of all, going broke isn’t the only bad consequence of ignoring Kelly. A stagnant or barely growing bankroll is also a negative consequence. A “gut” feel for how much to bet is going to be extremely inaccurate.
–Dunbar
—In vpF…@…com, <funny.young.guy@…> wrote :
You are both wrong but in two different ways:
1 - you have to accept that the KC will only help winning players or help you at games with an edge. Period. If you apply it to a game with negative EV you will still lose. So its really not fair to talk about gamblers that do it for “excitement”. That’s a misapplication of KC
2 - to say that “you can bet below KC but not above” is also misguided. You must always wager at the KC number. You must recall that the KC number is also designed to optimize growth of your bankroll. Knowing how much to wager on an edge is relatively simple calculation and/or monte-carlo simulation - that’s just risk-of-ruin. But knowing how much to bet to grow your bankroll and get the most from any given EV, well, that’s a whole other number . . . in fact, that’s the KC
···
On Sat, Apr 5, 2014 at 7:32 PM, 007 <007@…> wrote:
nightoftheiguana2000@… wrote:
Don’t get stuck if the Kelly bet is $5.522589, yes you can bet $5 and no you can’t bet $6 or $10. It’s that simple.
I think you’re going too far here. It might depend on the situation,
since it’s so close, but I believe there’s more bankroll growth with a
$6 bet than $5.
But my main comment on a stress on the Kelly Criterion is skepticism
that stressing it is necessary. It’s kind of like the situation with
Christians saying one has to accept Christ as their Lord and Savior or
spend eternity in hell, even if one was born into a country in which
no one is going to hear the name Christ. I happen to believe that
such people are not doomed to hell and will basically do all right,
even assuming that Christianity would have been a step in the right
direction, which I don’t want to express an opinion about. What do
people without much understanding of the Kelly Criterion do? I doubt
if overbetting is generally much of a problem. Most gamblers can be
classified into the vast majority of losers, to whom Kelly would only
tell them to stop gambling, and professionals who, no matter how
unsophisticated their understanding of the Kelly Criterion is,
generally understand that they shouldn’t bet more than a certain
amount and generally don’t. I don’t believe I’ve ever had much of a
sophisticated understanding of it, but I think I’ve done pretty well
in not overbetting my bankroll. And I’m skeptical that chronic
overbettors will be “cured” by understanding the Kelly Criterion.
Maybe they crave excitement so much that they wouldn’t be affected by
such a cerebral approach. To make a case that the Kelly Criterion
needs to be propagated more, you’d have to show examples of people
whose failure had turned to success, not due to more positive EV, but
strictly due to not overbetting any more, with % EV held constant. It
wold have to be a professional who knows enough to have positive EV
but who is so blind to the danger of overbetting that s/he’ll still
lose. I think that’s rare. I don’t think “Fortune’s Formula” made
that case.
007 wrote: “It wold have to be a professional who knows enough to have positive EV but who is so blind to the danger of overbetting that s/he’ll still lose. I think that’s rare. I don’t think “Fortune’s Formula” made that case.”
Of the professional gamblers that you know, how many have gone bankrupt at least once?
James Bean wrote: “You must always wager at the KC number.”
That’s a common misconception of the Kelly criterion. Most Kelly advocates bet less than the optimal Kelly bet, rarely if ever going to the very edge of full Kelly. The reason is that less than Kelly is less average bankroll growth but less risk, that’s always a reasonable tradeoff. More than Kelly is less average bankroll growth but more risk, that’s not a reasonable tradeoff for someone that values their bankroll.
There are three Kelly regions. Less than Kelly is less average bankroll growth than full Kelly but less risk. This is the region that Kelly advocates operate in, generally betting less than full Kelly and only rarely if ever going to the full Kelly limit. The second region is more than Kelly but less than double Kelly. This region has average bankroll growth, but it’s less than full Kelly with greater risk. Generally it’s not seen as a prudent idea to take on more risk while accepting less reward, but there is average bankroll growth in this nosebleed region. The third region is greater than double Kelly, in this region there is average bankroll shrinkage. There can be higher highs, but periods of bankruptcy are also likely. If you play long enough in this region, you will go bankrupt. So, pick a Kelly region, and have fun. Or just ignore the math and see what happens.
There are many ways to lose at gambling, but probably these two are the most common:
-
Gamble on negative expectation (negative EV)
-
Gamble on positive expectation (positive EV) but bet more than double Kelly
Everybody knows about #2, it is commonly called betting over your head or overbetting your bankroll, but not everyone knows there is a mathematical definition (Kelly) for the concept, and many are actually overbetting Kelly thinking they are not “over their head” when in fact they are from a mathematical standpoint.
nightoftheiguana2000@yahoo.com wrote:
007 wrote: "It wold have to be a professional who knows enough to have positive EV but who is so blind to the danger of overbetting that s/he'll still lose. I think that's rare. I don't think "Fortune's Formula" made that case."
Of the professional gamblers that you know, how many have gone bankrupt at least once?
Many may have, but I don't know to what extent it was due to
overbetting with positive expectation and to what extent it was due to
playing with negative expectation. An implication in your question is
another reason to place less emphasis on the Kelly Criterion, since it
operates in the vacuum of not being able to replenish a lost bankroll.