Hi LB,
This is the last time I post on this subject. I was not going to
reply to your post, but I don't want to seem rude by not doing so,
since you took the trouble to make a comment.
Yes, you are right, my example of achieving the payback with one play
is extreme. I chose it purposely that way, it saves a lot of talk.
The point is that a gambler can achieve the return of a machine after
100 plays, 1000 plays, 1,000,000 plays, etc. It can happen with the
right combination of wins on those plays. Defining the long term as
the number of hands it takes for someone to achieve the return of a
machine then is wrong.
You can define the long term in any way you want. You mention a
number of hands that would give you a certain confidence level of
being within a certain percentage of the return. There are an
infinite number of ways here depending on the percentages and the
confidence levels you choose. It would not be a unique long term.
You see, the problem is that being vague with the term can and does
create confusion and misconceptions. On the other hand, the
phrase "long term" is constantly used. For example, people always say
a machine pays back 99.54% long term; people say that in 54% of the
plays you get nothing, average long term; they also say that the
cycle of royals is 40,000, but they add that is only valid in the
long term. Someone not familiar with probability theory -say, someone
who studied history and specialized in the French Revolution, LOL-
would like a quick idea of what the long term is. The simplest and
most useful thing to tell this person is that the long term is
infinity. Only after an infinite number of plays can you be
absolutely sure that the machine will pay exactly 99.54%, that 54% of
the plays will pay you nothing, and that you have on average a royal
per 40,000 games, besides all the multiple other assertions you make
about the long term.
I don't agree with your comment that the numerical example is
confusing. It is very enlightening, because it does clearly tell the
uninitiated reader the sorts of statements that are valid after
playing a machine a finite number of hands.
Given the way the "long term" is used colloquially and saying it is a
certain finite number of hands -no matter how you conventionally
define those- leads to practical misconceptions that can be
detrimental to the gambler.
I know, people hate infinity -well, not all people, Ben Casey seemed
to like it- but mathematics seems to always use it.
I do see what you mean in your post, perhaps. After one hand you have
a discrete probability distribution. For example, in JB you get paid
nothing with about 0.54 probability, your investment with 0.21, twice
your investment with 0.13 probability, 40,000 your investment with
0.00002 probability, etc. These numbers are sloppy and rounded, but
close enough. After two hands you can also construct a discrete
probability distribution, a little more complicated. As the number of
hands increases, the discrete probability suggests a continuous curve
and, if the number of hands is large enough, it is more practical to
talk about the curve. This probability curve, as the number of hands
increases, becomes narrower and narrower, centered on the theoretical
return. You want the "long term" to be defined as the point where
that curve "emerges", if I understand you correctly. I have two
objections with that. The first is that the decision on where that
point is -that is, after how many hands does the "curve" emerge-
would be entirely subjective. Sure, a convention might be adapted,
but then the long term will not be a simple concept but a complicated
one, such as "the number of hands after which you can with a
confidence of such and such, be within a such percentage of the
theoretical return". My other objection is that normal conversation
about VP would turn exceedingly complicated. The phrase "the royal
cycle is 40,000 hands in the long term" would become, "the royal
cycle is between 35,000 thousand and 45,000 hands with a certain
percent of confidence." Does one really want to burden a novice who
quickly consults the FAQs with such arbitrary and complicated
definitions?
Regards,
E
"I believe what really happens in history is this: the old man is
always wrong; and the young people are always wrong about what is
wrong with him. The practical form it takes is this: that, while the
old man may stand by some stupid custom, the young man always attacks
it with some theory that turns out to be equally stupid." Chesterton.
(I hope vppappy enjoys this one too,LOL.)
>
> The first phrase is wrong. Actual results can equal expected
results
> after just one hand. Take a machine that pays back 100%, play
five
> dollars, get a pair of Jacks, be paid five dollars, your actual
> results are exactly the expected results after one hand. As for
> approaching expected results, that applies only in statistical
terms.
I'm defending the FAQ explanation. It is clear--and if it isn't
the FAQ
explanation can easily be amended--that the meaning refers to
enough time
for the entire distribution to be reflected to a certain level of
confidence. In your example, breaking even on a paying pair is not
the
expected result of a game that promises, for example, 100.x percent
return...or for that matter one that promises 95.x return. The FAQ
assumes
the necessary time (or number of hands).
>
> The second part contains a Tom Ski calculation. I have not
checked
> it, but I assume it is correct. Nevertheless, for the gambler the
> important thing is the correct interpretation of the numbers. Let
us
> think of that 100% payback machine, and the 95% confidence
factor.
I agree that this is confusing. The main point, I think, is this:
If you
can narrow (or raise) the "confidence factor" in a specific game to
a
specific number of hands--which you can do--then you have defined
the long
···
--- In vpFREE@yahoogroups.com, "Lawrence Boxer" <ljboxer@e...> wrote:
term, at least for that game.
lb