Is it +EV to raise the number of hands you play on a multi hand machine as your winnings grow and then come back down at the same increments.
For example, you are playing quarters three hands with a buy in of $100 and go to 5 hands at $250 and 10 hands at $500.
Is this a better method than staying at 3 hands all the time?
How many credits you have in the machine doesn't affect your EV in any way.
Sent from my iPhone
On Sep 20, 2011, at 8:22 AM, "will_gamble2" <jchildress@sfbli.com> wrote:
Is it +EV to raise the number of hands you play on a multi hand machine as your winnings grow and then come back down at the same increments.
For example, you are playing quarters three hands with a buy in of $100 and go to 5 hands at $250 and 10 hands at $500.Is this a better method than staying at 3 hands all the time?
[Non-text portions of this message have been removed]
Varying number of hands played is EV neutral, but it does effect average bankroll growth. The approximate Kelly optimum is to bet edge/variance of your current bankroll.
http://members.cox.net/vpfree/Bank.htm
--- In vpFREE@yahoogroups.com, "will_gamble2" <jchildress@...> wrote:
Is it +EV to raise the number of hands you play on a multi hand machine as your winnings grow and then come back down at the same increments.
For example, you are playing quarters three hands with a buy in of $100 and go to 5 hands at $250 and 10 hands at $500.Is this a better method than staying at 3 hands all the time?
Thanks, this is what I was looking for.
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
Varying number of hands played is EV neutral, but it does effect average bankroll growth. The approximate Kelly optimum is to bet edge/variance of your current bankroll.
NOTI noted, with respect to multi-hand games: Varying number of hands played is EV neutral, but it does effect average bankroll growth. The approximate Kelly optimum is to bet edge/variance of your current bankroll.
This is true for many but not al multi-hand games. Games like Triple Play, Five Play, Ten Play, Fifty Play, Hundred Play, and Super Times Pay, plus others, are EV neutral. Multi-hands such as Multi Strike, Ultimate X, Wheel Poker Deluxe, and Extra Action Poker, plus others, are NOT EV neutral.
In most cases, whether you're winning or losing today should have nothing to do with your betsizing --- except in the probably rare cases that your gambling bankroll at the start of the day was barely enough to play a certain level (and you should move down if you're losing) or barely not enough to play at a certain level (and you can move up if you win.) Assuming we define bankroll as "the amount of money you can lose before you quit gambling," most players don't have an exact bankroll number for themselves anyway. Who among us can say, "If I lose $23,458.33 I'll quit forever and ever amen. Not one penny more!" We can say that BEFORE we begin that losing streak, but if and when that time actually gets there (assuming we can recognize the exact moment when our bankroll reaches such a level), many people will adjust their "drop dead' figure. Far more important than whether you are ahead or behind today is are you playing a game where you have the advantage? No stop-loss or bet-sizing strategy can make up for playing a bad game. When NOTI was talking about Kelly betting, this assumes a positive bet edge. A large number of players neglect the importance of this fundamental fact.
Bob
[Non-text portions of this message have been removed]
IMO, the Kelly Critereon is one of the most overused and misused concepts in
gambling.
Kelly Critereon is a mathematical method for maximizing the rate of bankroll
growth at a +EV game with a known edge and variance. It's not designed to
ensure you don't bust your bankroll. Also, the model assumes you can vary
your betsize at continuous increments (i.e., you can bet $0.27 a hand or
$0.09 a hand if the model asks you to) where real gambling usually involves
fixed tiers of stakes.
99%+ of people who gamble shouldn't even be thinking about Kelly. Why?
Because:
1. They don't play +EV games
2. They do play +EV games, but they can't really quantify their edge and/or
variance
3. They play +EV games with a fixed edge and variance, but they are more
concerned with making sure they don't bust their bankroll rather than
maximizing its growth rate.
Even professional gamblers typically aren't trying to maximize bankroll
growth rate because they are withdrawing a fixed amount from the bankroll
each month.
So the long answer to the original question is, no, there is essentially no
mathematical reason whatsoever to increase or decrease your wager size based
on your recent results. If it makes you happy to do so, then go for it. But
it's not "+EV" in any meaningful sense of that term.
Ed
On Tue, Sep 20, 2011 at 5:07 PM, Bob Dancer <bobdancervp@hotmail.com> wrote:
**
NOTI noted, with respect to multi-hand games: Varying number of hands
played is EV neutral, but it does effect average bankroll growth. The
approximate Kelly optimum is to bet edge/variance of your current bankroll.
This is true for many but not al multi-hand games. Games like Triple Play,
Five Play, Ten Play, Fifty Play, Hundred Play, and Super Times Pay, plus
others, are EV neutral. Multi-hands such as Multi Strike, Ultimate X, Wheel
Poker Deluxe, and Extra Action Poker, plus others, are NOT EV neutral.In most cases, whether you're winning or losing today should have nothing
to do with your betsizing --- except in the probably rare cases that your
gambling bankroll at the start of the day was barely enough to play a
certain level (and you should move down if you're losing) or barely not
enough to play at a certain level (and you can move up if you win.) Assuming
we define bankroll as "the amount of money you can lose before you quit
gambling," most players don't have an exact bankroll number for themselves
anyway. Who among us can say, "If I lose $23,458.33 I'll quit forever and
ever amen. Not one penny more!" We can say that BEFORE we begin that losing
streak, but if and when that time actually gets there (assuming we can
recognize the exact moment when our bankroll reaches such a level), many
people will adjust their "drop dead' figure. Far more important than whether
you are ahead or behind today is are you playing a game where you have the
advantage? No stop-loss or bet-sizing strategy can make up for playing a bad
game. When NOTI was talking about Kelly betting, this assumes a positive bet
edge. A large number of players neglect the importance of this fundamental
fact.Bob
[Non-text portions of this message have been removed]
[Non-text portions of this message have been removed]
Ed wrote:
IMO, the Kelly Critereon is one of the most overused and misused concepts in
gambling.Kelly Critereon is a mathematical method for maximizing the rate of bankroll
growth at a +EV game with a known edge and variance.
I must have a mental block about the phrase "maximizing the rate of
bankroll growth," since I can't get past the idea that maximizing
one's average bankroll requires betting one's entire bankroll on any
advantage. How is maximizing the rate of bankroll growth different
from maximizing average bankroll? In different words, can you explain
what the Kelly Criterion maximizes?
It's not designed to ensure you don't bust your bankroll.
I don't know if it was designed to do that, but, theoretically, it
will have that effect.
If you bet your whole bankroll on any edge, then X percent of the time you
will bust and then it's impossible to grow the bankroll. That severely
limits your average bankroll growth.
Kelly seeks to maximize the average rate of growth of a bankroll. In other
words, if you bet according to Kelly at a +EV game then you will experience
a greater average bankroll growth than if you bet any other way. If you bet
more than Kelly, then you will occasionally experience too large a loss and
have to waste a lot of time "grinding" back up. If you bet less than Kelly,
then you will see more consistent profits, but you won't grow as fast as
Kelly.
Indeed Kelly won't "bust" a bankroll if "bust" is defined as taking it to
literally zero.
The catch is that the Kelly model requires you to increase or decrease your
wager with every change in your bankroll. So if you were playing "according
to Kelly" then the moment you lost a hand at a $0.25 machine, you'd have to
try to find a $0.2497 machine to play the next hand. Obviously this is
impossible.
So the reality of gambling is that you play $1 for a while and if you lose
you still play $1 until your bankroll takes a significant hit. Then you drop
down to $0.25. If you continue to lose then you drop down to $0.05. But at
some point, dropping down and playing for ever lower stakes becomes a waste
of time and more lucrative ways to spend your time-like getting a
job-predominate. So there's a point at which your bankroll is effectively
busted even if it's not literally zero, because the bankroll can no longer
support Kelly betting that will provide an acceptable hourly winrate.
This is why most people recommend betting less than Kelly if you are doing
this for a living, because betting full Kelly will increase the risk that at
some point you'll have to drop down to nickels (or whatever stakes are too
small to continue playing).
Which is why, to me, Kelly is not a useful model for the vast majority of
gamblers. Most people who gamble aren't in the bankroll growing business.
Even pro players aren't. They are much more interested in bankroll
preservation than optimal bankroll growth.
On the other hand, if you're Warren Buffett and your goal is to grow your
$50 billion company as fast as possible, Kelly will certainly inform your
decisions well.
Ed
On Tue, Sep 20, 2011 at 7:21 PM, 007 <007@embarqmail.com> wrote:
**
Ed wrote:
>IMO, the Kelly Critereon is one of the most overused and misused concepts
in
>gambling.
>
>Kelly Critereon is a mathematical method for maximizing the rate of
bankroll
>growth at a +EV game with a known edge and variance.I must have a mental block about the phrase "maximizing the rate of
bankroll growth," since I can't get past the idea that maximizing
one's average bankroll requires betting one's entire bankroll on any
advantage. How is maximizing the rate of bankroll growth different
from maximizing average bankroll? In different words, can you explain
what the Kelly Criterion maximizes?>It's not designed to ensure you don't bust your bankroll.
I don't know if it was designed to do that, but, theoretically, it
will have that effect.
[Non-text portions of this message have been removed]
Are you the Ed Miller who writes a poker column?
Which is why, to me, Kelly is not a useful model for the vast majority of
gamblers. Most people who gamble aren't in the bankroll growing business.
Even pro players aren't.
Maybe they are but they don't know it. Bankroll growing is kinda important in gambling, it allows you to move up to bigger EV games, and it allows you to cash out some for that big wish expenditure. But you do have to watch the cashouts, they effectively reduce your EV. If your EV is $100/hr, but your nut (cost) is $10/hr, your real EV is only $90/hr and you need to adjust to that.
They are much more interested in bankroll
preservation than optimal bankroll growth.
Kelly supports that. You can bet the optimal ratio, or some fraction, which reduces gain but also reduces risk, which is a valid tradeoff. Of course the ultimate is not to gamble at all, they you have full bankroll preservation. The no-go zone in Kelly betting is to overbet the optimal Kelly fraction, because then you are taking on more risk (more threat to your bankroll) in exchange for less bankroll growth.
If you want a book to read on Kelly, try "Fortune's Formula".
--- In vpFREE@yahoogroups.com, Ed Miller <ed.miller@...> wrote:
Ed wrote:
If you bet your whole bankroll on any edge, then X percent of the time you
will bust and then it's impossible to grow the bankroll. That severely
limits your average bankroll growth.
Do you understand that average bankroll is maximized by betting it all
on any advantage?
Kelly seeks to maximize the average rate of growth of a bankroll. In other
words, if you bet according to Kelly at a +EV game then you will experience
a greater average bankroll growth than if you bet any other way.
I was hoping you'd use different words. I still don't understand what
the Kelly Criterion maximizes.
Ed wrote:
If you bet your whole bankroll on any edge, then X percent of the time you
will bust and then it's impossible to grow the bankroll. That severely
limits your average bankroll growth.Kelly seeks to maximize the average rate of growth of a bankroll. In other
words, if you bet according to Kelly at a +EV game then you will experience
a greater average bankroll growth than if you bet any other way.
I've heard the phrase that the Kelly Criterion maximizes average
bankroll growth for decades. I understand the formula of the Kelly
Criterion and how to use it. Since I understand that average bankroll
(and, as far as I understand what it means, average bankroll growth,
also) is maximized by betting it all on any advantage and that the
Kelly Criterion is much more conservative than that, I don't
understand what that phrase means. I suspect that no one who uses it
understands it, either, and that it needs revising. If you understood
it, I believe you could express it in different words. You only
repeated the phrase.
Ed wrote:
If you bet your whole bankroll on any edge, then X percent of the time you
will bust and then it's impossible to grow the bankroll. That severely
limits your average bankroll growth.Kelly seeks to maximize the average rate of growth of a bankroll. In other
words, if you bet according to Kelly at a +EV game then you will experience
a greater average bankroll growth than if you bet any other way.
Maybe an example would clarify. Let's say there's a gambling
proposition, similar to blackjack, that pays even money and has a
50.5% chance of winning and a 49.5% chance of losing. That's a 1%
advantage and the Kelly Criterion says to bet 1% of one's bankroll on
it. Let's say, for ease of use, that one's bankroll is $10,000.
After 1 $100 bet, one's average bankroll has grown by 1% of 1%, or $1,
and is now $10,001. If one bets $10,000, after 1 trial, one's average
bankroll is (maximized at) $20,000 x .505 = $10,100. How does the
Kelly Criterion maximize average bankroll growth? The same comparison
can be made after the next trial, and so on, forever, the fact that
betting one's entire bankroll on any advantage runs the risk of losing
all of it notwithstanding.
Betting a fixed fraction of your bankroll repeatedly on a +EV event causes
your bankroll to experience exponential growth. As the number of trials
approaches infinity, the rate of exponential growth is the only thing that
matters.
Kelly maximizes the rate of exponential growth.
You have maximized average bankroll growth for a finite, N, number of
trials. Eventually Kelly betting will overtake repeated full bankroll
betting because Kelly's exponential growth rate is higher.
By choosing a small number of trials, you're allowing a fixed term, the
initial bet size, to dominate. But over an infinite number of trials, only
the exponential growth rate matters.
Kelly addresses your specific question in his original paper:
http://www.racing.saratoga.ny.us/kelly.pdf
Though this discrepancy between exponential growth rates at infinity and
average bankroll growth over a finite number of trials is one of the many
reasons I think Kelly is utterly unsuited to enter most average gambler's
decision-making.
Ed
On Tue, Sep 20, 2011 at 11:18 PM, 007 <007@embarqmail.com> wrote:
**
Ed wrote:
>If you bet your whole bankroll on any edge, then X percent of the time you
>will bust and then it's impossible to grow the bankroll. That severely
>limits your average bankroll growth.
>
>Kelly seeks to maximize the average rate of growth of a bankroll. In other
>words, if you bet according to Kelly at a +EV game then you will
experience
>a greater average bankroll growth than if you bet any other way.Maybe an example would clarify. Let's say there's a gambling
proposition, similar to blackjack, that pays even money and has a
50.5% chance of winning and a 49.5% chance of losing. That's a 1%
advantage and the Kelly Criterion says to bet 1% of one's bankroll on
it. Let's say, for ease of use, that one's bankroll is $10,000.
After 1 $100 bet, one's average bankroll has grown by 1% of 1%, or $1,
and is now $10,001. If one bets $10,000, after 1 trial, one's average
bankroll is (maximized at) $20,000 x .505 = $10,100. How does the
Kelly Criterion maximize average bankroll growth? The same comparison
can be made after the next trial, and so on, forever, the fact that
betting one's entire bankroll on any advantage runs the risk of losing
all of it notwithstanding.
[Non-text portions of this message have been removed]
Yup, I write about poker.
Again, I think the overwhelming majority of gamblers tend to be much more
concerned about minimizing their risk of ruin at a given stakes without
having to move down (or allowing for maybe one or two drops in stakes) than
they are about optimal bankroll growth rates at infinity. I don't want to
speak for Bob Dancer, but I'm pretty sure he would forgo optimum exponential
bankroll growth if it meant he never had to play nickels or hustle coupons
again.
Now you could call that "fractional Kelly" betting, but I would argue that
one needn't even know anything about Kelly at all to functionally manage and
grow a working professional gambling bankroll. Ok, you're betting a fraction
of Kelly's optimum. So what?
Which brings me full circle back to the original poster's question about
adding hands as he wins for the day. This question has zero to do with Kelly
betting. It's not a question about optimizing exponential bankroll growth
rates, and it's not a question that involves an infinite number of trials.
So, IMO, the word "Kelly" should never have entered this thread.. and the
fact that it did, in my view, supports the idea that Kelly is widely
overused and misused.
Ed
On Tue, Sep 20, 2011 at 10:17 PM, nightoftheiguana2000 < nightoftheiguana2000@yahoo.com> wrote:
**
Are you the Ed Miller who writes a poker column?
--- In vpFREE@yahoogroups.com, Ed Miller <ed.miller@...> wrote:
> Which is why, to me, Kelly is not a useful model for the vast majority of
> gamblers. Most people who gamble aren't in the bankroll growing business.
> Even pro players aren't.Maybe they are but they don't know it. Bankroll growing is kinda important
in gambling, it allows you to move up to bigger EV games, and it allows you
to cash out some for that big wish expenditure. But you do have to watch the
cashouts, they effectively reduce your EV. If your EV is $100/hr, but your
nut (cost) is $10/hr, your real EV is only $90/hr and you need to adjust to
that.> They are much more interested in bankroll
> preservation than optimal bankroll growth.Kelly supports that. You can bet the optimal ratio, or some fraction, which
reduces gain but also reduces risk, which is a valid tradeoff. Of course the
ultimate is not to gamble at all, they you have full bankroll preservation.
The no-go zone in Kelly betting is to overbet the optimal Kelly fraction,
because then you are taking on more risk (more threat to your bankroll) in
exchange for less bankroll growth.If you want a book to read on Kelly, try "Fortune's Formula".
[Non-text portions of this message have been removed]
Totally useless example. "Let's say" there is an 11-8 JOB machine or a standard BJ game that pays on ties. All useless hypotheticals that will never exist.
Let's say there's a gambling
--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:
proposition, similar to blackjack, that pays even money and has a
50.5% chance of winning and a 49.5% chance of losing. That's a 1%
advantage and the Kelly Criterion says to bet 1% of one's bankroll on
it.
Ed, I absolutely loved Professional No-Limit Hold'em. It's basically my poker bible next to Mathematics of Poker.
Could you comment on the trade-off between rate of bankroll growth and expected hourly rate? I'm actually concerned with the latter but this thread has made me realize that I'm barely rolled for quarter VP when I've been playing dollars all this time. Hourly rate is a function of EV, bet size, and hands/hour, and as many others can probably relate, my time is valuable so the easiest way to immediately maximize hourly rate is to increase bet size. Since this variable is EV neutral, the OP's question on increasing bet size with respect to session bankroll growth could be construed (or misconstrued) as a topic in Kelly betting so a segue into that discussion is not entirely moot. And since the OP confirmed that it was "what he was looking for" I think a few posts on Kelly betting and bankroll growth could add value to some readers. I know in my case it did.
I think my question is a matter of relative utility like you said before, but I just want to confirm it with knowledgeable people such as yourself. If you increase your bet size beyond the optimal Kelly bet (but no more than twice the Kelly bet) you'll experience higher volatility and slower bankroll growth for a given bankroll. Increasing your bet size beyond twice the Kelly bet results in bankroll decline. Similarly, as Jazbo's article points out (http://www.jazbo.com/videopoker/kelly.html), you have a certain bet and if you're bankroll is less than half the Kelly "optimal bankroll" then you should not take the bet. Now the variable of bet size on whether or not you want to increase it beyond Kelly could be a question of "Do I want to increase my hourly rate or preserve my bankroll?" I think therein lies the problem because you can't have both, unless you have an infinite bankroll.
--- In vpFREE@yahoogroups.com, Ed Miller <ed.miller@...> wrote:
Yup, I write about poker.
Again, I think the overwhelming majority of gamblers tend to be much more
concerned about minimizing their risk of ruin at a given stakes without
having to move down (or allowing for maybe one or two drops in stakes) than
they are about optimal bankroll growth rates at infinity. I don't want to
speak for Bob Dancer, but I'm pretty sure he would forgo optimum exponential
bankroll growth if it meant he never had to play nickels or hustle coupons
again.Now you could call that "fractional Kelly" betting, but I would argue that
one needn't even know anything about Kelly at all to functionally manage and
grow a working professional gambling bankroll. Ok, you're betting a fraction
of Kelly's optimum. So what?Which brings me full circle back to the original poster's question about
adding hands as he wins for the day. This question has zero to do with Kelly
betting. It's not a question about optimizing exponential bankroll growth
rates, and it's not a question that involves an infinite number of trials.
So, IMO, the word "Kelly" should never have entered this thread.. and the
fact that it did, in my view, supports the idea that Kelly is widely
overused and misused.Ed
As the thread has progressed, I have found more of what I was looking for.. thoughts and opinions.
I appreciate all the feedback
--- In vpFREE@yahoogroups.com, "csantos84" <drumbandit@...> wrote:
And since the OP confirmed that it was "what he was looking for" I think a few posts on Kelly betting and bankroll growth could add value to some readers. I know in my case it did.
One trick is that it's the geometric mean that counts, not the arithmetic mean. Taking the arithmetic mean assumes you can just go on forever averaging a series of outcomes, but in the real world you can not. Once you bust out, that's it, you're busted, game over, no more chances and it doesn't matter how well you were running before you busted out. Having a zero in a list that is arithmetic meaned just lowers the mean. Having a zero in a list that is geometric meaned sets the mean to zero, irregardless of how great the other results were. Kelly optimizes the geometric mean of bankroll growth, which is why a Kelly better would never bet it all, unless there was no risk of losing. Under the Kelly system, if you bust out once, that's it. You have not only not optimized bankroll growth, you have in fact committed bankroll suicide.
http://en.wikipedia.org/wiki/Mean
http://en.wikipedia.org/wiki/Kelly_criterion
--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:
How does the
Kelly Criterion maximize average bankroll growth? The same comparison
can be made after the next trial, and so on, forever, the fact that
betting one's entire bankroll on any advantage runs the risk of losing
all of it notwithstanding.
In order to bet a fraction of Kelly, you have to know what the Kelly value is. Otherwise most likely you will eventually overplay your bankroll. You have to know what Kelly is to know whether or not you are over or under Kelly betting. It's just math, but if you're "trying to grow a bankroll", you are constrained by the math of Kelly. Even if you don't even know what Kelly is, you are still constrained by the math. Even if you deny Kelly, you are still constrained by the math.
The poker world is full of top players who overbet Kelly and bust out as a result, even though they are top players. Since they are top players, they can get someone (a sucker) to stake them and take the risk. But the end result is the same, overbet Kelly and bust out. If there are suckers who will take this risk, and there are, then it is they who suffer the consequences.
Here's a video poker example: FPDW has a Kelly number of 2899 (I think, someone else can double check that number). You spot a quarter FPDW machine, five coins max bet, so $1.25 a pull. Your current bankroll is $5,242.69. Can you play this game? Under Kelly, yes, as long as your bankroll remains over 2899 x $1.25 = $3624. If your bankroll is under $3624, the Kelly answer is no, if you played this you would be taking too much risk to your bankroll and getting less than optimal growth in return for taking that risk.
--- In vpFREE@yahoogroups.com, Ed Miller <ed.miller@...> wrote:
Now you could call that "fractional Kelly" betting, but I would argue that
one needn't even know anything about Kelly at all to functionally manage and
grow a working professional gambling bankroll. Ok, you're betting a fraction
of Kelly's optimum. So what?
Mike apparently does not grasp that you can learn things from hypothetical
examples that can be applied to or help you understand more complicated
real-world/practical examples.
On Wed, Sep 21, 2011 at 6:39 AM, mike <melbedewy1226@hotmail.com> wrote:
--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:
> Let's say there's a gambling proposition, similar to blackjack, that
> pays even money and has a 50.5% chance of winning and a 49.5% chance
> of losing. That's a 1% advantage and the Kelly Criterion says to bet
> 1% of one's bankroll on it.Totally useless example. "Let's say" there is an 11-8 JOB machine or a
standard BJ game that pays on ties. All useless hypotheticals that will
never exist.