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you need permission of the author before you can do a verbatim
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vpFREE Administrator
On 22 Mar 2010 at 8:49, BANDSTAND54 wrote:
Heavy duty stuff. May I forward this to another forum? Grumpy
I posted an article in the files section a while ago about long term play.
Every hand is independent and if you play long enough your results will be 'close' to the expected value. Both of these statements are true. I should add the qualifier that your long term result will be within x amount a certain percent of the time ( determined by the number of hands played).
All this really says is that if you play a million hands, your result from last Tuesday's 2000 hand session is not a very big factor in your overall results.
In engineering, it is transient response and steady state response. If you look at the waveform generated when you turn on a lamp in your house , the signal bounces all over the place for the first few milliseconds. After a second, the response is pretty steady. If you base your findings on the transient response, you will see wedely varying results. If you base it on the steady state response, the results are very predictable.
Same thing in video poker. A couple thousand hands and anything can happen. Play 5 million hands and I can predict pretty well what your results will be.
--- In vpFREE@yahoogroups.com, "vpFREE Administrator" <vpfreeadmin@...> wrote:
On 22 Mar 2010 at 8:49, BANDSTAND54 wrote:
> Heavy duty stuff. May I forward this to another forum? Grumpy
My understanding of copyright law and Yahoo policies is that
you need permission of the author before you can do a verbatim
re-post of their post.vpFREE Administrator
Every hand is independent and if you play long enough your results will be 'close' to the expected value.
"Close" in percent of action, but not at all "close" in dollars, and in the real world it's dollars that counts. If you play a breakeven game against an opponent with a much larger bankroll (the "casino"), you will eventually have one of two results: either busted out (50% chance) or doubled up (50% chance). You will eventually have no chance of breaking even. The casino breaks even because on average half the gamblers bust out and half double up. The more you play, the less likely is your individual chance of breaking even. Not even "close".
Same thing in video poker. A couple thousand hands and anything can happen. Play 5 million hands and I can predict pretty well what your results will be.
Not quite correct. Actually, you can exactly predict the outcome of one hand, and two hands, and a couple of thousand hands ... up to 5 million hands, and more.
Jazbo did it here for 1,000, 5,000 and 10,000 hands:
http://www.jazbo.com/videopoker/curves.html
--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@...> wrote:
I waive any copy rights.
--- In vpFREE@yahoogroups.com, "vpFREE Administrator" <vpfreeadmin@...> wrote:
On 22 Mar 2010 at 8:49, BANDSTAND54 wrote:
> Heavy duty stuff. May I forward this to another forum? Grumpy
My understanding of copyright law and Yahoo policies is that
you need permission of the author before you can do a verbatim
re-post of their post.vpFREE Administrator
But advantage gambling is based on theory, not facts. But for the
theory that results tend to approximate expected value in percentage
terms as the number of trials increases, they're irrelevant. What
action are you suggesting by saying that "it's dollars that counts?"
--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@...> wrote:
Every hand is independent and if you play long enough your results will be 'close' to the expected value.
"Close" in percent of action, but not at all "close" in dollars, and in the real world it's dollars that counts.
Isn't it obvious? At the end of the day, or year, or whatever, it's the dollars that are either in my pocket or not that counts. An accountant might claim that I got close to 99.99% of the expected return of my total action, but if that -0.01% "close" represents my entire bankroll, that's little consolation. At least to me anyway. To me, bankroll is what counts. The other statistics are just statistics, maybe interesting, but at the end of the day, it's the money, or lack of, in my pocket that counts.
Husband to Wife: "before you pull the trigger, yes I know I lost it all, but at least I got back 99.99% of my total action before I busted out, hey I got close!"
You seem to claim that there is some "theory of advantage gambling" and that this theory depends on another theory that an individual's "results tend to approximate the average value when expressed in percentage terms as the number of trials increases". I don't follow that logic at all. Sorry.
There is a concept called N0, but that's very different from what you are claiming, and it's not a theory, it's simply the result of using mathematical laws:
http://members.cox.net/vpfree/Bank_NO.htm
http://www.youtube.com/watch?v=kn481KcjvMo
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
>--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@> wrote:
>> Every hand is independent and if you play long enough your results will be 'close' to the expected value.
>
>"Close" in percent of action, but not at all "close" in dollars, and in the real world it's dollars that counts.But advantage gambling is based on theory, not facts. But for the
theory that results tend to approximate expected value in percentage
terms as the number of trials increases, they're irrelevant. What
action are you suggesting by saying that "it's dollars that counts?"
>> Every hand is independent and if you play long enough your results will be 'close' to the expected value.
>
>"Close" in percent of action, but not at all "close" in dollars, and in the real world it's dollars that counts.But advantage gambling is based on theory, not facts. But for the
theory that results tend to approximate expected value in percentage
terms as the number of trials increases, they're irrelevant. What
action are you suggesting by saying that "it's dollars that counts?"Isn't it obvious? At the end of the day, or year, or whatever, it's the dollars that are either in my pocket or not that counts.
That doesn't answer the question. No, it's not obvious to me. What
action are you suggesting? If results are all that matter, how do you
approach gambling?
An accountant might claim that I got close to 99.99% of the expected return of my total action, but if that -0.01% "close" represents my entire bankroll, that's little consolation. At least to me anyway. To me, bankroll is what counts. The other statistics are just statistics, maybe interesting, but at the end of the day, it's the money, or lack of, in my pocket that counts.
Let's say you are deciding whether to play a million hands on a 5 coin
$1 machine at a 1% advantage or not. Your expected value would be a
certain amount. Your standard deviation would be a particular amount.
You're a certain favorite to be ahead. How, if results are all that
matter and all this "theory stuff" is irrelevant, would you decide?
Husband to Wife: "before you pull the trigger, yes I know I lost it all, but at least I got back 99.99% of my total action before I busted out, hey I got close!"
You seem to claim that there is some "theory of advantage gambling" and that this theory depends on another theory that an individual's "results tend to approximate the average value when expressed in percentage terms as the number of trials increases". I don't follow that logic at all. Sorry.
There is a concept called N0, but that's very different from what you are claiming, and it's not a theory, it's simply the result of using mathematical laws:
http://members.cox.net/vpfree/Bank_NO.htm
How is that different from what I'm saying? How is "using
mathematical laws" different from believing that results tend to
approximate expected value in percentage terms as the number of trials
increases?
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
>--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@> wrote:
>> Every hand is independent and if you play long enough your results will be 'close' to the expected value.
>
>"Close" in percent of action, but not at all "close" in dollars, and in the real world it's dollars that counts.But advantage gambling is based on theory, not facts. But for the
theory that results tend to approximate expected value in percentage
terms as the number of trials increases, they're irrelevant. What
action are you suggesting by saying that "it's dollars that counts?"Isn't it obvious? At the end of the day, or year, or whatever, it's the dollars that are either in my pocket or not that counts. An accountant might claim that I got close to 99.99% of the expected return of my total action, but if that -0.01% "close" represents my entire bankroll, that's little consolation. At least to me anyway. To me, bankroll is what counts. The other statistics are just statistics, maybe interesting, but at the end of the day, it's the money, or lack of, in my pocket that counts.
Husband to Wife: "before you pull the trigger, yes I know I lost it all, but at least I got back 99.99% of my total action before I busted out, hey I got close!"
You seem to claim that there is some "theory of advantage gambling" and that this theory depends on another theory that an individual's "results tend to approximate the average value when expressed in percentage terms as the number of trials increases". I don't follow that logic at all. Sorry.
There is a concept called N0, but that's very different from what you are claiming, and it's not a theory, it's simply the result of using mathematical laws:
http://members.cox.net/vpfree/Bank_NO.htm
This says:
"As you play more hands, results are expected to more closely
approximate the ER"
It's also full of vagueness and arbitrariness. Maybe that's what you
don't like about what I'm saying. It says "The long term could be
defined as the point where the delta of one standard deviation is
equal to the average return"
The "long term" could be defined as anything. There's no magic number
that determines an acceptable level of confidence that one will be
ahead after a certain number of trials. NO is just one of many
possible ways of looking at the general idea that "As you play more
hands, results are expected to more closely approximate the ER"
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
>--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@> wrote:
Tom Robertson wrote:
The "long term" could be defined as anything. There's no magic
number that determines an acceptable level of confidence that one
will be ahead after a certain number of trials. NO is just one of
many possible ways of looking at the general idea that "As you play
more hands, results are expected to more closely approximate the ER"
Actually, NO is a unique way at looking at play expectation that handily demonstrates that a recreational player who sticks to moderate advantage, low variance games stands a very strong likelihood of coming out ahead over the course of their play.
It eliminates the misconception that lifetimes of play are necessary for any such assurance ... 10 hrs/mo handily puts one in the running for strong profit expectation over the course of 10 years in many cases.
I see a lot of hand wringing over the course of this thread. I read into that some people like to wring their hands than that there's something warrants struggling with in the concept.
Tom Robertson wrote:
The "long term" could be defined as anything. There's no magic
number that determines an acceptable level of confidence that one
will be ahead after a certain number of trials. NO is just one of
many possible ways of looking at the general idea that "As you play
more hands, results are expected to more closely approximate the ER"Actually, NO is a unique way at looking at play expectation that handily demonstrates that a recreational player who sticks to moderate advantage, low variance games stands a very strong likelihood of coming out ahead over the course of their play.
It eliminates the misconception that lifetimes of play are necessary for any such assurance ... 10 hrs/mo handily puts one in the running for strong profit expectation over the course of 10 years in many cases.
It's hardly the only measure that does that.
I see a lot of hand wringing over the course of this thread. I read into that some people like to wring their hands than that there's something warrants struggling with in the concept.
I agree. After I read the article about "NO," I decided that I think
ego explains it.
NOTI, you are correct. I forgot to include that footnote that even though the percentage deviation from expected gets smaller, the absolute deviation ( in terms of dollars) increases.
It is very possible to play a positive game for a lot of hands and still lose money. There is no getting around that except to play at a high enough advantage with a big enough bank roll.
I quoted a number for playing 10 million hands of 10/7 double bonus. You can lose a lot of money even though your percentage deviation is small.
Nothing earth shattering here. It is possible to lose money on a positive play even if you play a lot of hands.
--- In vpFREE@yahoogroups.com, "nightoftheiguana2000" <nightoftheiguana2000@...> wrote:
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@> wrote:
>
> >--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@> wrote:
> >> Every hand is independent and if you play long enough your results will be 'close' to the expected value.
> >
> >"Close" in percent of action, but not at all "close" in dollars, and in the real world it's dollars that counts.
>
> But advantage gambling is based on theory, not facts. But for the
> theory that results tend to approximate expected value in percentage
> terms as the number of trials increases, they're irrelevant. What
> action are you suggesting by saying that "it's dollars that counts?"
>Isn't it obvious? At the end of the day, or year, or whatever, it's the dollars that are either in my pocket or not that counts. An accountant might claim that I got close to 99.99% of the expected return of my total action, but if that -0.01% "close" represents my entire bankroll, that's little consolation. At least to me anyway. To me, bankroll is what counts. The other statistics are just statistics, maybe interesting, but at the end of the day, it's the money, or lack of, in my pocket that counts.
Husband to Wife: "before you pull the trigger, yes I know I lost it all, but at least I got back 99.99% of my total action before I busted out, hey I got close!"
You seem to claim that there is some "theory of advantage gambling" and that this theory depends on another theory that an individual's "results tend to approximate the average value when expressed in percentage terms as the number of trials increases". I don't follow that logic at all. Sorry.
There is a concept called N0, but that's very different from what you are claiming, and it's not a theory, it's simply the result of using mathematical laws:
http://members.cox.net/vpfree/Bank_NO.htm
Well, you seem to be saying that one should just assume that a million hands is enough so that one can assume that the actual return will be "close" to the "average value".
I think that's another gambler's fallacy.
The question I would ask of this gamble, is: what is the NO? How does a million hands compare to the N0? And note that N0 does not mean that you can expect results "close" to the "average value". N0 means only that you can expect to come out ahead about 84% of the time. 4 times N0 means you can expect to come out ahead about 98% of the time. 9 times N0 means you can expect to come out ahead about 99.9% of the time, and so on. Do you see the difference between these two approaches?
More specific: I wouldn't play this unless a million hands represented at least N0. That means the variance would have to be under 100. There are other considerations, for starters I would have to have at least the Kelly bankroll for this game.
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
Let's say you are deciding whether to play a million hands on a 5 coin
$1 machine at a 1% advantage or not. Your expected value would be a
certain amount. Your standard deviation would be a particular amount.
You're a certain favorite to be ahead. How, if results are all that
matter and all this "theory stuff" is irrelevant, would you decide?
A good example. 10 million hands of FPDB has a 2SD of about 17,000 bets. A proponent of the percentage deviation method would say that's 17,000/10,000,000 = 0.17%, which is declared to be "close". I would point out that 17,000 bets on a dollar machine represents $85,000 and that plus or minus $85,000 does not represent "close" in my book. Maybe if I had a billion to play with, it would be "close", but personally, I can tell the difference between +$85,000 and -$85,000. If $85,000 fell out of my pocket, I would definitely notice the loss. If you think plus or minus $85,000 is "close", I would like to be your personal shopper.
Comparison:
Method 1: The "close" method: Assume 10,000,000 hands is enough to assume that results should be "close" to the average. In this case, the average result is about +17,000 bets, so you should assume that your results should be "close" to this result. If they aren't you must have done something wrong.
Method 2: What the math actually says: In this case, if your starting bankroll is sufficient and you don't make significant playing errors, you can expect to get a final result somewhere between 0 and +34,000 bets about 95% of the time. In dollar terms this is of course no where near "close" to the average result of +17,000 bets.
--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@...> wrote:
I quoted a number for playing 10 million hands of 10/7 double bonus. You can lose a lot of money even though your percentage deviation is small.
Let's say you are deciding whether to play a million hands on a 5 coin
$1 machine at a 1% advantage or not. Your expected value would be a
certain amount. Your standard deviation would be a particular amount.
You're a certain favorite to be ahead. How, if results are all that
matter and all this "theory stuff" is irrelevant, would you decide?Well, you seem to be saying that one should just assume that a million hands is enough so that one can assume that the actual return will be "close" to the "average value".
I didn't do that any more than you did in your example below.
I think that's another gambler's fallacy.
I agree. Setting up concrete boundaries between the long run and the
short run is based on a fallacy.
The question I would ask of this gamble, is: what is the NO? How does a million hands compare to the N0? And note that N0 does not mean that you can expect results "close" to the "average value". N0 means only that you can expect to come out ahead about 84% of the time. 4 times N0 means you can expect to come out ahead about 98% of the time. 9 times N0 means you can expect to come out ahead about 99.9% of the time, and so on. Do you see the difference between these two approaches?
No, I don't. I don't see how analyzing the standard deviation,
expected value, and chance of being ahead significantly differs from
analyzing the NO. Unless I misunderstand, the NO is just one
particular way of looking at potential fluctuation.
More specific: I wouldn't play this unless a million hands represented at least N0. That means the variance would have to be under 100. There are other considerations, for starters I would have to have at least the Kelly bankroll for this game.
We both gave examples for what we'd consider an acceptable level of
confndence You characterized mine as "assum[ing] that a million
hands is enough so that one can assume that the actual return will be
"close" to the "average value". How are you not doing the exact same
thing? For what purpose, if not that you want your percentage return
to be acceptably close to the expected return, did you say that you
wouldn't play a certain game unless it represented at least N0 and you
had at least the Kelly bankroll? How is it "very different" from what
I'm claiming? Over the years, I've used the concept that you call
"NO" (or is it "N0?") without caring what anyone else called it, but
I've also used many other measures of potential fluctuation, none of
which I regard as sacred. None of them are sufficient for the job
they attempt to do, since an acceptable level of confidence depends on
many factors that can't be quantified. You seem to be going out of
your way to characterize "N0" as something unique, special, and sacred
and somehow independent of a way to measure how close results can be
expected to vary from the expected return. I don't see how it is.
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
Is your objection to the word "close" simply that it's not a number
and therefore too vague and intuitive? Assuming it is, that implies
that a method that is more strictly mathematical necessarily does "the
job" (of defining an acceptable level of fluctuation) better than
"close" does. I disagree. It's similar in principle to the concept
of significant numbers. You probably know what that is, but in case
not, I'll give an example. To a number that has been rounded to, say
24.9, add 2.6385. The "385" isn't significant because the 24.9 would
have had numbers in those places had it not been rounded more
"roughly." In the same way that 24.9 isn't suited to contribute to a
total that's to 4 decimal places, any strictly mathematical way of
measuring an acceptable level of fluctuation can only go so far
because of the many factors involved that aren't quantifiable. Every
example you've given, and every example you or anyone else could give,
about how you'd approach a gambling proposition has included all kinds
of arbitrariness. Someone else approaching the same problems might
come up with very different levels of desired confidence. He might be
right in his situation and you might be right in yours. You seem to
be implying that your way is the best way for everyone because it uses
more mathematics. I've been doing this for many years and I'm
basically educated about standard deviation, etc., but I don't have
the slightest idea what my acceptable level of fluctuation is. It
still constantly varies. I like how Bob Dancer wrote that he didn't
even know what his bankroll is, not, unless I recall incorrectly, just
because he might have trouble calculating it, but more because he
doesn't know how much he's willing to risk. In a way, it would be
easier to have a more definite standard, but I also like it "loose,"
since I know that the factor of arbitrariness can't be eliminated.
You don't seem to be aware of that. I've always seen having such a
definite standard as a "cop out" and a lazy way to avoid using my
intuition. "Close" is usually good enough for me and I'm skeptical
that more mathematics is an improvement.
--- In vpFREE@yahoogroups.com, "johnnyzee48127" <greeklandjohnny@...> wrote:
I quoted a number for playing 10 million hands of 10/7 double bonus. You can lose a lot of money even though your percentage deviation is small.
A good example. 10 million hands of FPDB has a 2SD of about 17,000 bets. A proponent of the percentage deviation method would say that's 17,000/10,000,000 = 0.17%, which is declared to be "close". I would point out that 17,000 bets on a dollar machine represents $85,000 and that plus or minus $85,000 does not represent "close" in my book. Maybe if I had a billion to play with, it would be "close", but personally, I can tell the difference between +$85,000 and -$85,000. If $85,000 fell out of my pocket, I would definitely notice the loss. If you think plus or minus $85,000 is "close", I would like to be your personal shopper.
Comparison:
Method 1: The "close" method: Assume 10,000,000 hands is enough to assume that results should be "close" to the average. In this case, the average result is about +17,000 bets, so you should assume that your results should be "close" to this result. If they aren't you must have done something wrong.
Method 2: What the math actually says: In this case, if your starting bankroll is sufficient and you don't make significant playing errors, you can expect to get a final result somewhere between 0 and +34,000 bets about 95% of the time. In dollar terms this is of course no where near "close" to the average result of +17,000 bets.
The difference is that I'm not making the claim that "results will be close to the average value". In fact, I stated that the more you play, the less likely are your chances of getting the average value. The claim of "close to the average value" seems to be based on the so-called "Law of Averages", which is a gambler's fallacy. The purpose of N0 is to define the point where you can expect to come out ahead about 84% of the time. That's not the same thing as "expect to be close to the average value". In dollar terms, the more you gamble, the more you deviate from the expected value. According to the math, there is no convergence to the expected value, instead there is convergence to a normal distribution around the expected value. And the normal deviation (square root of number of hands times the variance) increases (not decreases) with number of hands played.
http://en.wikipedia.org/wiki/Law_of_averages
http://en.wikipedia.org/wiki/Gambler's_fallacy
http://www.bjmath.com/bjmath/refer/N0.htm
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
We both gave examples for what we'd consider an acceptable level of
confndence You characterized mine as "assum[ing] that a million
hands is enough so that one can assume that the actual return will be
"close" to the "average value". How are you not doing the exact same
thing?
I understand very clearly, and have expressed, that in absolute terms,
results diverge more from expected value as the number of trials
increases and I think you understood perfectly well, since I also
expressed it probably three times in this thread, that I was referring
to how results converge to expected value in percentage terms, not
absolute terms, as the number of trials increases and I know you agree
with that. You're going out of your way to set up a strawman. Do you
not like the word "close" because you think it can only be referring
to absolute terms, not percentage terms?
--- In vpFREE@yahoogroups.com, Tom Robertson <madameguyon@...> wrote:
We both gave examples for what we'd consider an acceptable level of
confndence You characterized mine as "assum[ing] that a million
hands is enough so that one can assume that the actual return will be
"close" to the "average value". How are you not doing the exact same
thing?The difference is that I'm not making the claim that "results will be close to the average value". In fact, I stated that the more you play, the less likely are your chances of getting the average value. The claim of "close to the average value" seems to be based on the so-called "Law of Averages", which is a gambler's fallacy. The purpose of N0 is to define the point where you can expect to come out ahead about 84% of the time. That's not the same thing as "expect to be close to the average value". In dollar terms, the more you gamble, the more you deviate from the expected value. According to the math, there is no convergence to the expected value, instead there is convergence to a normal distribution around the expected value. And the normal deviation (square root of number of hands times the variance) increases (not decreases) with number of hands played.
http://en.wikipedia.org/wiki/Law_of_averages
http://en.wikipedia.org/wiki/Gambler's_fallacy
http://www.bjmath.com/bjmath/refer/N0.htm