vpFREE2 Forums

Pressing your bet

#21

nightoftheiguana2000 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.

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

I like how the latter article points out that a valid alternative to
the Kelly Criterion is "utility theory" and that only if one's utility
function is logarithmic does it coincide with the Kelly Criterion.
That at least makes more sense, since I still don't see how, if
there's no diminishing marginal utility of money, betting one's entire
bankroll on any advantage, due to how it maximizes average bankroll,
doesn't outperform all other possible systems, including the Kelly
Criterion. A study of the extent to which human utility functions are
logarithmic might be interesting. I assume mine is. If you believed
your utility function were linear, so that you believed you had no
diminishing marginal utility of money, would you still prefer the
Kelly Criterion over betting your entire bankroll on any advantage? I
find the argument that betting one's entire bankroll on any advantage
might lose the entire bankroll to be an inadequate explanation of its
weakness, since that possibility is included in the calculation of
average resulting bankroll. It's like saying not to lay a big price
on a favorite in sports because it might lose when the possibility of
losing is already included in the estimate of expected value.

···

--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:

#22

Ed wrote:

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.

No it won't. B x ((.505 ^ T) * (2 ^ T)) > B x (1.01 ^ (T * .505) x
.99 ^ (T * .495)) (B being original bankroll and T being the number of
trials) for any positive T or B. The probability of the entire
bankroll bettor losing must be 1 in order for the Kelly bettor to
outperform him or her, but that's not the case for any finite number
of trials.

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.

Since it doesn't maximize average bankroll, for what purpose does it
matter?

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

Yes, a theory that deals only with an infinite number of trials has
limited use.

I'll try to understand his formulas later, but he does, as you say,
address my question. He agrees with me that average bankroll is
maximized by betting all of it on any advantage, no matter how many
trials there are, and he agrees with you that, eventually, the Kelly
bettor will outperform any other. At one point, he incorporates
utility function to explain why Kelly betting is preferred, but in his
conclusion, he seems to contradict that, which confuses me, since I
think the diminishing marginal utility of money is necessary for the
Kelly Criterion to be optimal. I assume that no one's utility
function is exactly logarithmic, but that everyone's approximates it,
which I believe is required for the Kelly Criterion to be in
contention as the optimal approach to gambling.

#23

Maximizing the arithmetic mean, which would involve betting it all every chance you get an edge, makes absolutely no sense if you value keeping a bankroll. Your risk of ruin approaches 100% with such a system. On the other hand if you have money to burn and are looking for a way to burn it, this is probably as good as any other, at least you get some value back in comps, until the casino figures out that you've burned all your money.

···

--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:

That at least makes more sense, since I still don't see how, if
there's no diminishing marginal utility of money, betting one's entire
bankroll on any advantage, due to how it maximizes average bankroll,
doesn't outperform all other possible systems, including the Kelly
Criterion.

#24

You find a nickel 50 play, including the card club and mailers and some secret promotions and employee greasing and back doors plus a fence for the casino swag, it's a 1% overlay. You guess your current bankroll would let you load up the machine about halfway, and the halfway variance is about 5. That would make the approximate Kelly number 5/.01 = 500. Each hand is five nickels = $.25, so the increment is 500 x $.25 = $125. Your current gambling bankroll is $2,612.21, divide that by 500 to get your Kelly bet of $5.22442 . Some nits would say you have to play exactly that amount but that's horse dookey, the rule is you can't bet more than that, less is perfectly ok, in fact even a good idea. So here we're talking 20 hands right? 20 x $.25 = $5. And you're off, but not to a good start, you have a bad run of cards and you're down $125. Hey, that's the increment, right, see above. What do you do? Down to 19 hands, that's right. You drop another $125, maybe this wasn't a good idea, maybe the machine is fixed, maybe that gypsy fortune teller was right, whatever, down to 18 hands. Finally you get a nice hand and win $200 (still a running loss of $50, right?), but you go back up to 19 hands, and so on. Hopefully you get the idea. $125 is your increment, you go up or down depending on where your current bankroll is.

http://www.youtube.com/watch?v=bg8lSyGavc4
http://www.youtube.com/watch?v=Mo0baknLDdU

#25

Does Kelly work the same way when the game does not have a normal
distribution (like video poker)?

Cogno

···

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com] On Behalf Of
nightoftheiguana2000
Sent: Thursday, September 22, 2011 9:26 AM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] example of kelly betting a multiplay

You find a nickel 50 play, including the card club and mailers and some
secret promotions and employee greasing and back doors plus a fence for the
casino swag, it's a 1% overlay. You guess your current bankroll would let
you load up the machine about halfway, and the halfway variance is about 5.
That would make the approximate Kelly number 5/.01 = 500. Each hand is five
nickels = $.25, so the increment is 500 x $.25 = $125. Your current gambling
bankroll is $2,612.21, divide that by 500 to get your Kelly bet of $5.22442
. Some nits would say you have to play exactly that amount but that's horse
dookey, the rule is you can't bet more than that, less is perfectly ok, in
fact even a good idea. So here we're talking 20 hands right? 20 x $.25 = $5.
And you're off, but not to a good start, you have a bad run of cards and
you're down $125. Hey, that's the increment, right, see above. What do you
do? Down to 19 hands, that's right. You drop another $125, maybe this wasn't
a good idea, maybe the machine is fixed, maybe that gypsy fortune teller was
right, whatever, down to 18 hands. Finally you get a nice hand and win $200
(still a running loss of $50, right?), but you go back up to 19 hands, and
so on. Hopefully you get the idea. $125 is your increment, you go up or down
depending on where your current bankroll is.

http://www.youtube.com/watch?v=bg8lSyGavc4
http://www.youtube.com/watch?v=Mo0baknLDdU

------------------------------------

vpFREE Links: http://members.cox.net/vpfree/Links.htm

Yahoo! Groups Links

#26

If you calculate the exact number, it doesn't matter. For FPDW, the exact number, using the wizard's hand probabilities, is 2925. The approximation (var/edge) is 3400. The approximation is more conservative, in this case.

···

--- In vpFREE@yahoogroups.com, Cogno Scienti <cognoscienti@...> wrote:

Does Kelly work the same way when the game does not have a normal
distribution (like video poker)?

Cogno

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com] On Behalf Of
nightoftheiguana2000
Sent: Thursday, September 22, 2011 9:26 AM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] example of kelly betting a multiplay

You find a nickel 50 play, including the card club and mailers and some
secret promotions and employee greasing and back doors plus a fence for the
casino swag, it's a 1% overlay. You guess your current bankroll would let
you load up the machine about halfway, and the halfway variance is about 5.
That would make the approximate Kelly number 5/.01 = 500. Each hand is five
nickels = $.25, so the increment is 500 x $.25 = $125. Your current gambling
bankroll is $2,612.21, divide that by 500 to get your Kelly bet of $5.22442
. Some nits would say you have to play exactly that amount but that's horse
dookey, the rule is you can't bet more than that, less is perfectly ok, in
fact even a good idea. So here we're talking 20 hands right? 20 x $.25 = $5.
And you're off, but not to a good start, you have a bad run of cards and
you're down $125. Hey, that's the increment, right, see above. What do you
do? Down to 19 hands, that's right. You drop another $125, maybe this wasn't
a good idea, maybe the machine is fixed, maybe that gypsy fortune teller was
right, whatever, down to 18 hands. Finally you get a nice hand and win $200
(still a running loss of $50, right?), but you go back up to 19 hands, and
so on. Hopefully you get the idea. $125 is your increment, you go up or down
depending on where your current bankroll is.

http://www.youtube.com/watch?v=bg8lSyGavc4
http://www.youtube.com/watch?v=Mo0baknLDdU

------------------------------------

vpFREE Links: http://members.cox.net/vpfree/Links.htm

Yahoo! Groups Links

#27

It doesn't need to be to the penny of course, but every controlled gambler needs a rigid stop loss limit and that limit needs to be set *before* you start gambling, not adjusted to the results. Your absolute stop loss limit is your "gambling bankroll", in other words money that you don't intend to lose but you are prepared for the possibility that you might lose it. If you don't have a rigid predetermined stop loss limit, you likely have a gambling addiction problem.

http://www.gamblersanonymous.org

···

--- In vpFREE@yahoogroups.com, Bob Dancer <bobdancervp@...> wrote:

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.

#28

will_gamble2 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?

A reality check prompts me to comment on a key limitation under which Kelly betting considerations have limited application to my optimal play choices ...

I can see Kelly coming into play were I looking at an "all you can eat" positive buffet; in other words, where my opportunity for an edge isn't limited.

However, it's generally the case that I am playing under constraints that restrict the amount of play that's appealing. The most frequent constraint is that I'm playing a negative expectation machine, where fixed promotional cash makes the play viable.

In such cases, there's a cap on the desirable total coin-in, and Kelly considerations go out the window. Instead, I'm left looking at options to play through that coin-in in a manner that best optimizes my goals re total play time and bankroll risk exposure.

I'll wistfully contemplate that someone has access to a 100-play FPDW machine (or otherwise has an opportunity with no bound on the positive ER) and can put this discussion into practice.

- H.

#29

The Kelly system is optimum geometric growth for one hand or infinite hands, the number of hands or events is irrelevant. Also, being able to vary the bet size is very useful, but not a requirement. However, optimum geometric growth is all it does. You could have other goals and those would require other systems. You could for example have a goal to keep your risk of ruin below 10% at all times. This would not be a Kelly system per se, but it would likely satisfy the Kelly requirement that your bet never be greater than the Kelly number.

FPDW Kelly number = 2925
FPDW 10% ROR number = 3525

···

--- In vpFREE@yahoogroups.com, "vp_wiz" <harry.porter@...> wrote:

will_gamble2 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?

A reality check prompts me to comment on a key limitation under which Kelly betting considerations have limited application to my optimal play choices ...

I can see Kelly coming into play were I looking at an "all you can eat" positive buffet; in other words, where my opportunity for an edge isn't limited.

However, it's generally the case that I am playing under constraints that restrict the amount of play that's appealing. The most frequent constraint is that I'm playing a negative expectation machine, where fixed promotional cash makes the play viable.

In such cases, there's a cap on the desirable total coin-in, and Kelly considerations go out the window. Instead, I'm left looking at options to play through that coin-in in a manner that best optimizes my goals re total play time and bankroll risk exposure.

I'll wistfully contemplate that someone has access to a 100-play FPDW machine (or otherwise has an opportunity with no bound on the positive ER) and can put this discussion into practice.

- H.

#30

I think if you had a linear utility function of money you would play maxEV strategy and max bet or bet it all on any edge, actually you don't even need an edge, you just need an acceptable win rate. If you're willing to play double or nothing for it all at 51 to 49, why not 49 to 51? Is that 2% really that significant in this case? Or how about 51 to 49 but if you win there's a 10% rake? A linear function would mean that you would fear losing it all no more than you would fear any other result, you would be indifferent to losing a dollar out of a million or your last dollar. Seems to me you would call that "someone who doesn't respect money." They would either be filthy rich from birth or have connections to unlimited amounts of cash or be an ascetic or wish to be one or simply a person who really doesn't understand money, what it takes to get it and what it means to lose it, a typical teenager?. It might also be some sort of psychological reaction, a person might be addicted to gambling and fear losing it all but would convince themselves they don't care to overcome their fear of losing. If Frank's still around that's probably right up his court.

···

--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:

If you believed
your utility function were linear, so that you believed you had no
diminishing marginal utility of money, would you still prefer the
Kelly Criterion over betting your entire bankroll on any advantage?

#31

I miss Frank and his participation here.

To: vpFREE@yahoogroups.com
Sent: Friday, September 23, 2011 4:19 PM
Subject: [vpFREE] Re: Pressing your bet

If you believed
your utility function were linear, so that you believed you had no
diminishing marginal utility of money, would you still prefer the
Kelly Criterion over betting your entire bankroll on any advantage?

I think if you had a linear utility function of money you would play maxEV strategy and max bet or bet it all on any edge, actually you don't even need an edge, you just need an acceptable win rate. If you're willing to play double or nothing for it all at 51 to 49, why not 49 to 51? Is that 2% really that significant in this case? Or how about 51 to 49 but if you win there's a 10% rake? A linear function would mean that you would fear losing it all no more than you would fear any other result, you would be indifferent to losing a dollar out of a million or your last dollar. Seems to me you would call that "someone who doesn't respect money." They would either be filthy rich from birth or have connections to unlimited amounts of cash or be an ascetic or wish to be one or simply a person who really doesn't understand money, what it takes to get it and what it means to lose it, a typical teenager?. It might also be some sort of psychological reaction, a

person might be addicted to gambling and fear losing it all but would convince themselves they don't care to overcome their fear of losing. If Frank's still around that's probably right up his court.

[Non-text portions of this message have been removed]

···

From: nightoftheiguana2000 <nightoftheiguana2000@yahoo.com>

--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:

#32

I think that's correct, assuming your primary goal is to grow your bankroll. It could be that you gamble for other reasons. If you were more risk-seeking you could "press your bet" beyond Kelly. If you were risk-neutral (linear function) the optimal would be to bet it all if possible. But when would you stop? If you continue with betting it all, wouldn't that be risk-seeking, since you would be increasing your odds of busting out? Does long term risk-neutral entail betting less than the full bankroll, perhaps a long term ROR of 50%? And if you were more risk-averse you could bet any fraction of Kelly since you would be getting a reasonable tradeoff of less risk for less reward. A lot of people recommend betting a fraction of Kelly, so perhaps a lot of people are a bit more risk-averse than log utility? Steve Jacobs if he's still around would know for sure.

···

--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:

I assume that no one's utility
function is exactly logarithmic, but that everyone's approximates it,
which I believe is required for the Kelly Criterion to be in
contention as the optimal approach to gambling.

#33

The more that I think about this question the more I think the answer is "it depends". I'm thinking if you have a linear function of money, and don't care about risk of ruin (as you put it it's factored into the EV already), the optimal one hand strategy would be to bet it all and walk with the results, never gambling again. What if you want to play more than one hand? Then it depends on what your acceptable risk of ruin is. If you go on betting it all, your risk of ruin approaches 100%, which is not a linear function of money, it's boom or bust with bust the likely result. If you want to play as long as possible, then you need a proportional betting system like Kelly, my guess is some multiple between 1 and 2 of the Kelly bet, since with a linear function you are more risk-seeking than Kelly. If you're willing to take some risk of ruin, then that defines your optimum bet size. The question of what risk of ruin is acceptable can also effect the optimum strategy for one bet.

···

--- In vpFREE@yahoogroups.com, 007 <007@> wrote:
> If you believed
> your utility function were linear, so that you believed you had no
> diminishing marginal utility of money, would you still prefer the
> Kelly Criterion over betting your entire bankroll on any advantage?

#34

What happened to Frank? I always appreciated his insights and humor.

···

Sent via DROID on Verizon Wireless

-----Original message-----
From: Bruce Cohen <brucedcohen2002@yahoo.com>
To: "vpFREE@yahoogroups.com" <vpFREE@yahoogroups.com>
Sent: Fri, Sep 23, 2011 23:25:43 GMT+00:00
Subject: Re: [vpFREE] Re: Pressing your bet

I miss Frank and his participation here.

From: nightoftheiguana2000 <nightoftheiguana2000@yahoo.com>

To: vpFREE@yahoogroups.com
Sent: Friday, September 23, 2011 4:19 PM
Subject: [vpFREE] Re: Pressing your bet

--- In vpFREE@yahoogroups.com, 007 <007@...> wrote:

If you believed
your utility function were linear, so that you believed you had no
diminishing marginal utility of money, would you still prefer the
Kelly Criterion over betting your entire bankroll on any advantage?

I think if you had a linear utility function of money you would play maxEV strategy and max bet or bet it all on any edge, actually you don't even need an edge, you just need an acceptable win rate. If you're willing to play double or nothing for it all at 51 to 49, why not 49 to 51? Is that 2% really that significant in this case? Or how about 51 to 49 but if you win there's a 10% rake? A linear function would mean that you would fear losing it all no more than you would fear any other result, you would be indifferent to losing a dollar out of a million or your last dollar. Seems to me you would call that "someone who doesn't respect money." They would either be filthy rich from birth or have connections to unlimited amounts of cash or be an ascetic or wish to be one or simply a person who really doesn't understand money, what it takes to get it and what it means to lose it, a typical teenager?. It might also be some sort of psychological reaction, a

person might be addicted to gambling and fear losing it all but would convince themselves they don't care to overcome their fear of losing. If Frank's still around that's probably right up his court.

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]