vpFREE2 Forums

Bankroll question

#1

Thank you for this explanation which I could actually follow. But it brings up a question: in your example, if you could only afford to lose the amount OVER ($2895) the Kelly bankroll, then what's the other $17105 for? Are we never to risk the bankroll portion?

···

----- Reply message -----
From: "nightoftheiguana2000@yahoo.com [vpFREE]" <vpFREE@yahoogroups.com>
To: <vpFREE@yahoogroups.com>
Subject: [vpFREE] Re: Bankroll question
Date: Thu, Jan 22, 2015 12:35 PM

vtroy216 asked: "It would probably be an interesting poll about how many of us use risk-of-ruin calculations and concerns when we go on a trip or casino visits, vs. how many of us just play with whatever we can afford to lose."

I play with whatever I can afford to lose, but I use the Kelly criterion to tell me what I can afford to lose. If you know the betsize, edge, and variance of a gamble or "investment", you can estimate the Kelly bankroll in your head (betsize x variance / edge). That's the reserve, you can leave that in the bank, any EXTRA amount you can afford to gamble with. And that's the bleeding edge, if you want to be more conservative, double that amount.

Example: I find a dollar FPDW machine. Sweet. Estimated Kelly bankroll is $5 x 26 / .0076 = $17,105. My current bankroll is $20,000, the good news is I can play. I take $2,895 (the amount my bankroll is over the Kelly bankroll) out in cash and start playing, unfortunately my luck is bad and after playing for some time the $2,895 (the amount I can afford to lose from my bankroll) is gone. I stop, I can no longer afford to play. Maybe I can make some money selling this machine to someone? Or work some deal with someone who has a bigger bankroll?

If you want to be slightly more sophisticated, you can calculate Kelly numbers in advance, for FPDW the Kelly number is 2925, multiply by the betsize, in this case $5, to get the more accurate $14,625. Jazbo has some more numbers and a calculator here:

Kelly Betting for Video Poker http://www.jazbo.com/videopoker/kelly.html

Kelly Betting for Video Poker http://www.jazbo.com/videopoker/kelly.html 9/6 DB/DJ 9/6 Double Bonus with Double Jackpot. This game is appearing in Atlantic City. It is slightly positive even without cash back, but beware the variance! Pick'em

View on www.jazbo.com http://www.jazbo.com/videopoker/kelly.html

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#2

I want to throw a little cold water on this logic, since it's what I do.
First is the assumption that this bankroll is unreplenishable out to
infinity. This is the money you have, and you will never have a penny more
that you didn't win playing the game. For typical human beings, this is
kind of a silly assumption. Even if you're a pro, there are ways to add
money to the bankroll that don't involve playing FPDW.

Second, Kelly maximizes exponential bankroll growth. That's what it does.
If you bet slightly less than Kelly, your bankroll is likely to grow still
at an exponential rate, but slower than at Kelly. Same goes if you bet
slightly more than Kelly.

If you bet way more than Kelly, then your bankroll eventually completely
stops growing. But the Kelly number isn't some magical bright line across
which no bankroll shall survive. It is a maximum, and for practical
purposes, numbers slightly to one side or the other are also fine.

I'm not arguing that people should run around playing games for which they
are underbankrolled. Overestimating edge and underestimating variance are
the bane of many gamblers. But at some point if there's a machine you want
to play and you have a nice edge and your bankroll is close and you're
willing to accept some risk of ruin because, hey, you still have two hands
and a brain and these are not the last dollars you will ever see, just play
the darn game. This is particularly true if your plan is to play the game
for a weekend and not for every waking hour from here to infinity.

Ed

···

On Thu, Jan 22, 2015 at 2:04 PM, 'vtroy216@yahoo.com' vtroy216@yahoo.com [vpFREE] <vpFREE@yahoogroups.com> wrote:

Thank you for this explanation which I could actually follow. But it
brings up a question: in your example, if you could only afford to lose the
amount OVER ($2895) the Kelly bankroll, then what's the other $17105 for?
Are we never to risk the bankroll portion?

----- Reply message -----
From: "nightoftheiguana2000@yahoo.com [vpFREE]" <vpFREE@yahoogroups.com>
To: <vpFREE@yahoogroups.com>
Subject: [vpFREE] Re: Bankroll question
Date: Thu, Jan 22, 2015 12:35 PM

vtroy216 asked: "It would probably be an interesting poll about how many
of us use risk-of-ruin calculations and concerns when we go on a trip or
casino visits, vs. how many of us just play with whatever we can afford to
lose."

I play with whatever I can afford to lose, but I use the Kelly criterion
to tell me what I can afford to lose. If you know the betsize, edge, and
variance of a gamble or "investment", you can estimate the Kelly bankroll
in your head (betsize x variance / edge). That's the reserve, you can leave
that in the bank, any EXTRA amount you can afford to gamble with. And
that's the bleeding edge, if you want to be more conservative, double that
amount.

Example: I find a dollar FPDW machine. Sweet. Estimated Kelly bankroll is
$5 x 26 / .0076 = $17,105. My current bankroll is $20,000, the good news is
I can play. I take $2,895 (the amount my bankroll is over the Kelly
bankroll) out in cash and start playing, unfortunately my luck is bad and
after playing for some time the $2,895 (the amount I can afford to lose
from my bankroll) is gone. I stop, I can no longer afford to play. Maybe I
can make some money selling this machine to someone? Or work some deal with
someone who has a bigger bankroll?

If you want to be slightly more sophisticated, you can calculate Kelly
numbers in advance, for FPDW the Kelly number is 2925, multiply by the
betsize, in this case $5, to get the more accurate $14,625. Jazbo has some
more numbers and a calculator here:

Kelly Betting for Video Poker http://www.jazbo.com/videopoker/kelly.html

Kelly Betting for Video Poker http://www.jazbo.com/videopoker/kelly.html
9/6 DB/DJ 9/6 Double Bonus with Double Jackpot. This game is appearing in
Atlantic City. It is slightly positive even without cash back, but beware
the variance! Pick'em

View on www.jazbo.com http://www.jazbo.com/videopoker/kelly.html

Preview by Yahoo

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#3

vtroy216 asked: " if you could only afford to lose the amount OVER ($2895) the Kelly bankroll, then what's the other $17105 for? Are we never to risk the bankroll portion?"

The reserve portion is for games that require less reserve bankroll, for example quarter FPDW. The idea is to eliminate or at least minimize the chance of being completely busted out.

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#4

Ed Miller writes: "First is the assumption that this bankroll is unreplenishable out to
infinity. This is the money you have, and you will never have a penny more
that you didn't win playing the game."

You don't need to make that assumption, of course in the real world there are likely to be other sources that add to your bankroll, but more likely to leaks that deplete your bankroll. These should be accounted for as adjustments to EV, which is what they are.

Ed Miller writes: "But the Kelly number isn't some magical bright line across
which no bankroll shall survive. It is a maximum, and for practical
purposes, numbers slightly to one side or the other are also fine."

Somewhat correct, but be carefull where you take this. The Kelly number is a mathematical inflection point. On one side is a region where risk is proportional to gain, in other words the more risk you take the more gain you get. This is the rational region, this is the region rational people want to be in. On the other side of the Kelly number is the region where increased risk actually yields less gain, this is the looney side.

Ed Miller writes: "I'm not arguing that people should run around playing games for which they
are underbankrolled."

Define "underbankrolled". The Kelly criterion is one definition of "underbankrolled".

Ed Miller writes: "Overestimating edge and underestimating variance are
the bane of many gamblers."

Absolutely, also the bane of "investors".

Ed Miller writes: "But at some point if there's a machine you want
to play and you have a nice edge and your bankroll is close and you're
willing to accept some risk of ruin because, hey, you still have two hands
and a brain and these are not the last dollars you will ever see, just play
the darn game."

Define "bankroll is close". Close to what?

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#5

Ed Miller also wrote: "This is particularly true if your plan is to play the game
for a weekend and not for every waking hour from here to infinity."

Yes, the Kelly criterion is a good fit for someone who plans to take their gambling into the long term, long term defined as greater than the N0 number.

For the short term there are other approaches, for example perhaps your goal is to play until you hit a royal and then you plan to quit forever, or perhaps you just want to take your play one royal at a time. In this situation min-cost-royal strategies are the better fit, they are optimal for a royal cycle, but not so optimal for many royal cycles. Naturally this approach is not limited to royals, could be quad aces, or a filled parlay card, or whatever.

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#6

Or another way to look at this:

Any bankroll amount over 2925 x $5 = $14,625 is for dollar FPDW

Any bankroll amount over 2925 x $2.50 = $7,312.50 is for half dollar FPDW

Any bankroll amount over 2925 x $1.25 = $3,656.25 is for quarter FPDW

Any bankroll amount over 2925 x $.50 = $1,462.50 is for ten coin nickel FPDW

Any bankroll amount over 2925 x $.25 = $731.25 is for nickel FPDW

And this should be obvious, but just in case, I'm using FPDW as an obvious example, but any gamble is applicable, just substitute the appropriate Kelly number or estimate with variance / edge.

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#7

Actually, the min-cost-royal strategy is optimal for any number of royal
cycles. It minimizes the average drop in bankroll between royals. The number
of royal cycles played doesn't alter that average.

···

On Thursday, January 22, 2015 11:20:08 PM nightoftheiguana2000@yahoo.com [vpFREE] wrote:

Ed Miller also wrote: "This is particularly true if your plan is to play
the game for a weekend and not for every waking hour from here to
infinity."

Yes, the Kelly criterion is a good fit for someone who plans to take their
gambling into the long term, long term defined as greater than the N0
number.

For the short term there are other approaches, for example perhaps your
goal is to play until you hit a royal and then you plan to quit forever,
or perhaps you just want to take your play one royal at a time. In this
situation min-cost-royal strategies are the better fit, they are optimal
for a royal cycle, but not so optimal for many royal cycles. Naturally
this approach is not limited to royals, could be quad aces, or a filled
parlay card, or whatever.

#8

jacobs wrote: "Actually, the min-cost-royal strategy is optimal for any number of royal
cycles. It minimizes the average drop in bankroll between royals. The number
of royal cycles played doesn't alter that average."

Good point. Any strategy works with the Kelly criterion, it's just a matter of different Kelly numbers. And of course, there is a Kelly optimal strategy.

vpFREE FAQ Strategies http://www.west-point.org/users/usma1955/20228/V/FAQ_S.htm

vpFREE FAQ Strategies http://www.west-point.org/users/usma1955/20228/V/FAQ_S.htm 1 1038.6796 Royal Flush 2 48.8386 Straight Flush 3 24.7133 4/Kind 4 23.7749 4/royal 5 8.9654 Full House 6 5.9856 Flush 7 4.2856 trips 8 3.9942 Straight

View on www.west-point.org http://www.west-point.org/users/usma1955/20228/V/FAQ_S.htm
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#9

Ed Miller writes: "First is the assumption that this bankroll is unreplenishable out to
infinity. This is the money you have, and you will never have a penny more
that you didn't win playing the game."

Just to flesh this out a bit: Say every Friday you add $200 to your gambling bankroll, from your other side jobs. And you play during the weekend, then continue this every week. The safe way to play this is to consider your bankroll as it exists on a moment by moment basis. However, if you know for certain (but could also be probabilistic) that at say 5pm Friday you will always add $200 to your gambling bankroll, you could have played more aggressively the previous weekend. One way to estimate an appropriate level of aggression is to treat the $200 as cashback or rakeback. So, if your EV on the weekend is $20/hour, and you play 20 hours, the $200 due next Friday can be estimated as an additional $10/hour to EV. Variance is unchanged, as long as you know for certain the $200 is coming. Of course, the reverse is also possible, that is you take $200 out every Friday to fund your lifestyle, in which case you can estimate a leak of $10/hour, making your net EV $10/hour.

This topic is actually accounting, whether you use a cash basis of accounting or something else:

Basis of accounting - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Basis_of_accounting

http://en.wikipedia.org/wiki/Basis_of_accounting

Basis of accounting - Wikipedia, the free encycl... http://en.wikipedia.org/wiki/Basis_of_accounting A basis of accounting can be defined as the time various financial transactions are recorded. The cash basis (EU VAT vocabulary Cash ac...

View on en.wikiped... http://en.wikipedia.org/wiki/Basis_of_accounting
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#10

noti, please ground me a bit here ...

When Kelly is discussed in the context of advantage blackjack play (where the delightful circumstance presents itself of being able to adjust one's wager in small increments and a game having very low variance), Kelly is the nirvana that optimizes one's expected bankroll growth.

In advocating a Kelly threshold for video poker (with respective conditions of disproportionate betting increments, substantially higher variance, and a skewed distribution curve), do you contend that the betting scheme below also maximizes expected bankroll growth?

I'm dubious. For example, generally speaking, betting below Kelly is no more advantageous to bankroll growth than betting above Kelly. So, it's difficult for me to understand why your scheme (that sets a Kelly bet as a upper threshold) stands out as optimal in this respect.

If bankroll growth isn't what's being optimized, what is the target of your scheme?

---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote :

Or another way to look at this:

Any bankroll amount over 2925 x $5 = $14,625 is for dollar FPDW

Any bankroll amount over 2925 x $2.50 = $7,312.50 is for half dollar FPDW

Any bankroll amount over 2925 x $1.25 = $3,656.25 is for quarter FPDW

Any bankroll amount over 2925 x $.50 = $1,462.50 is for ten coin nickel FPDW

Any bankroll amount over 2925 x $.25 = $731.25 is for nickel FPDW

And this should be obvious, but just in case, I'm using FPDW as an obvious example, but any gamble is applicable, just substitute the appropriate Kelly number or estimate with variance / edge.

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#11

vp_wiz wrote: "For example, generally speaking, betting below Kelly is no more advantageous to bankroll growth than betting above Kelly. So, it's difficult for me to understand why your scheme (that sets a Kelly bet as a upper threshold) stands out as optimal in this respect. "

Sometimes there are two betsizes that yield the same average bankroll growth, but why would you take the higher betsize? It's possible there is a valid bet on the dark side that has a higher growth than the valid bet on the good side, but you're playing with fire. In the real world there are Rumsfeldian unknown unknows, and those are going to get you into trouble on the dark side. On one side of Kelly, the good side, there is always bankroll growth and growth is proportional to risk, the more risk you take, the more growth you get in return. You make a mistake and take a bit more risk than you wanted to, at least you get a better return for taking that risk, up to a point. Not true on the other side, the dark side, there the more risk you take the less growth you get and eventually the growth even turns negative. On this side there be dragons. Actually, a better analogy would be a black hole. The good side has some built in stability, the bad side is unstable and eventually turns ugly, faster than your expecting, that black hole will suck you in. Sure, if you're really really good and really really know what you're doing, you could play around on that dark side, but, as your mother told you, it's not safe, you could shoot your eye out kid. I'd recommend Poundstone's book "Fortune's Formula" for a non mathematical discussion of this topic and its real world implications.

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#12

vp_wiz asked: "If bankroll growth isn't what's being optimized, what is the target of your scheme?"

Optimized bankroll growth given the allowable choices available AND staying on the safe side of the Kelly criterion.

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#13

noti -- Not looking to try your patience, but on the surface this doesn't make sense to me ...

Kelly is about maximizing bankroll growth. ROR doesn't factor.

Now, I understand one can introduce ROR as an added factor in defining their own strategy, but there's nothing magic about the ROR at a kelly bet amount. So, I don't perceive an inherent advantage at adopting that ROR as a threshold. Given large discrete betting increments, I would think one would be best advised to bet as close to Kelly as possible (rather than limit to no more than Kelly).

If bankroll growth is a primary objective (and if it's not, then any discussion of Kelly is out the window), then I would generally see it more advisable to play a wager at 120% kelly then 60% (assuming these were the only increments available).

Your strategy suggests otherwise.

---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote :

vp_wiz asked: "If bankroll growth isn't what's being optimized, what is the target of your scheme?"

Optimized bankroll growth given the allowable choices available AND staying on the safe side of the Kelly criterion.

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#14

I need to respond to this since I read it after replying to your other related post.

Let me say first off, that when it comes to a largely quantitative science, I develop an inate distrust of anyone who'd be inclined to conjure "Rumsfeldian unknown unkowns".

Frankly, that's a bit of hand waving that I could scarcely tolerate that in the context of Iraq and WMD's (but, let's not stray there!).

And is it really necessary to involve black holes and dark (matter)?

Look, I truly applaud the cautionary nature of your post. A few around here seem to advocate wading into uncertain waters rather carelessly.

Bottom line, I'm suggesting that never exceeding a kelly bet (assuming that your primary goal is bankroll growth) isn't a sound strategy. Significant exercise of caution is warranted. But under that goal, I think playing 120% of kelly is advantageous over the alternate of 60%.

ftw, my comments are strictly limited to a stated goal of intelligently maximizing bankroll growth. Personally, this isn't a strategy that I'd adopt.

The prospect of entering a play at one given wager, where my strategy might call for me to drop denom in half after just $2k-$3k of incurred loss doesn't seem sensible (I can see it for others.)

Generally, I'm going to look to keep my wager at 40%-80% of kelly, where my own gut comfort of play volatily and ROR is a more important driver. I grasp what I sacrifice in exchange.

---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote :

vp_wiz wrote: "For example, generally speaking, betting below Kelly is no more advantageous to bankroll growth than betting above Kelly. So, it's difficult for me to understand why your scheme (that sets a Kelly bet as a upper threshold) stands out as optimal in this respect. "

Sometimes there are two betsizes that yield the same average bankroll growth, but why would you take the higher betsize? It's possible there is a valid bet on the dark side that has a higher growth than the valid bet on the good side, but you're playing with fire. In the real world there are Rumsfeldian unknown unknows, and those are going to get you into trouble on the dark side. On one side of Kelly, the good side, there is always bankroll growth and growth is proportional to risk, the more risk you take, the more growth you get in return. You make a mistake and take a bit more risk than you wanted to, at least you get a better return for taking that risk, up to a point. Not true on the other side, the dark side, there the more risk you take the less growth you get and eventually the growth even turns negative. On this side there be dragons. Actually, a better analogy would be a black hole. The good side has some built in stability, the bad side is unstable and eventually turns ugly, faster than your expecting, that black hole will suck you in. Sure, if you're really really good and really really know what you're doing, you could play around on that dark side, but, as your mother told you, it's not safe, you could shoot your eye out kid. I'd recommend Poundstone's book "Fortune's Formula" for a non mathematical discussion of this topic and its real world implications.

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#15

vp_wiz: "Kelly is about maximizing bankroll growth."

That's an overly simple summary of the Kelly criterion.

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#16

vp_wiz wrote: "Bottom line, I'm suggesting that never exceeding a kelly bet (assuming that your primary goal is bankroll growth) isn't a sound strategy."

There are plenty that would disagree with you.

vp_wiz wrote: "But under that goal, I think playing 120% of kelly is advantageous over the alternate of 60%."

Very few people would advocate overbetting Kelly. There is a reason.

vp_wiz wrote: "Generally, I'm going to look to keep my wager at 40%-80% of kelly, where my own gut comfort of play volatily and ROR is a more important driver. I grasp what I sacrifice in exchange."

Actually, you are playing Kelly and don't even know it. The use of half Kelly is pretty standard, again there are reasons.

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#17

You could reduce those levels I gave you a bit and get a bit more bankroll growth, if you know what you're doing. But I'm not going to advocate that, to me going up to the Kelly limit is aggressive enough. If anything, ADDING a bit of margin to the levels makes more sense and is safer, in that direction you will always get some growth. It's a mistaken understanding and a bit of a straw puppet to think that under the Kelly system you always have to go for maximum growth. The Kelly criterion is the solution to maximum growth, but you can always bet less, and get some safety margin in return. Very few people actually take it to the limit, even less beyond. For safety reasons. It's historical, you can read about all the wise guys who thought they knew what they were doing.

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#18

"Investopedia" resorts to the same type of simplification:

DEFINITION of 'The Kelly Criterion' A mathematical formula relating to the long-term growth of capital developed by John Larry Kelly Jr. The formula was developed by Kelly while working at the AT&T Bell Laboratories. The formula is currently used by gamblers and investors to determine what percentage of their bankroll/capital should be used in each bet/trade to maximize long-term growth.

---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote :

vp_wiz: "Kelly is about maximizing bankroll growth."

That's an overly simple summary of the Kelly criterion.

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#19

I'll suggest that most players who happen to target half-Kelly betting have no interest in Kelly at all.

It just happens that there's a direct correlation between Kelly numbers and ROR. Half Kelly comes out to about 2% ROR, which represents VERY comfortable risk for most people.

And I wouldn't be surprised that most casual active gamblers, with no knowledge of statistics, intuitively end up targeting their wagers at around half-Kelly as a consequence.

Still, when it comes down to it, the derivation of Kelly numbers is not sourced from ROR calculations.

---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote :

Actually, you are playing Kelly and don't even know it. The use of half Kelly is pretty standard, again there are reasons.

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#20

vp_wiz wrote: "Still, when it comes down to it, the derivation of Kelly numbers is not sourced from ROR calculations."

??? There is no ROR with the Kelly system. There is risk, perhaps that's where I lost you. Anytime you have a gamble there is risk. With the Kelly system there is no risk of RUIN (ROR).

The bottom line is that we hear all the time: "don't overbet your bankroll". But what does that mean in terms of hard numbers? You seem to be saying that several percent of risk of ruin is OK. How many percent? Many Kelly gamblers, but not all, consider betting more than the optimum Kelly bet to be overbetting. How is this applied to video poker? If you only gamble with the portion of your bankroll that is over the optimum Kelly bankroll (approximately betsize x variance / edge), you will never bet more than the optimum Kelly bet (approximately bankroll x edge / variance) and by this definition you will never overbet your bankroll, and your risk of ruin is zero. What do you do with the rest of your bankroll? You find a lower risk gamble that puts some of it into play. Or you wait until you can build it back up again with contributions from your day job.

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