vpFREE2 Forums

CLT Steve, brumar, iggy, et al

#1

If you use only EV and Var, whatever you get out is very likely to
be an approximation, since you lose information by not including
any influence from higher moments.

The Normal distribution is completely defined by the first two
moments: mean and var...No information is lost by ignoring higher
moments.

> The "0.999346831403995" is a early warning sign that someone is

not

> following the convention of significant digits, and hence loses
> credibility.

Nonsense. All of the digits are significant.

>When you multiply two numbers together you have to
> truncate the result to the number of significant digits, otherwise
> you give the impression that you don't understand the output of

your

> calculator or computer.

Nonsense. Whether you say 2 x 2 = 4 or 2.0000000 x 2.000000 =

4.00000

makes no difference. The numbers are all exact, and the act of

multiplying

them together doesn't change that.

When you multiply a series of numbers with decimals together the
resultant number has many insignificant digits and must be truncated
accordingly... e.g. 5.26 x 7.38= 38.8188 but only the first two
digits after the decimal point are significant.

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:

#2

That's just fine, but no VP game will ever have a probability distribution
for a single play that is a Normal distribution. If you average a LARGE
number of VP outcomes, then what you get is a distribution that can
be closely APPROXIMATED by a Normal distribution. The key word
here is APPROXIMATED. The Normal distribution that you keep bringing
up is an approximation to the REAL distribution that describes the game.

Exact RoR can be computed directly from the REAL distribution of the
game. Approximate RoR can be computed from the (EV, Var) values
associated with the Normal distribution which approximates the game.

You keep going back to the Normal distribution as if it were the real
thing and the actual probability distribution of the game was the
approximation, but you've got that exactly backwards.

It is really a simple rule: if you are using a Normal distribution to
represent any _real_ game, you are automatically making an
approximation. Thus, any number you compute from the
(EV, Var) of that Normal distribution will be an approximation
of the corresponding number for the actual game.

The Normal distribution gets used so extensively that it is easy
to forget that it is only an approximation. The approximation gets
better and better as the sample sizes grows, but it is still an
approximation. Until you grasp that simple fact, further discussion is
pointless.

···

On Saturday 08 January 2005 01:47 am, jaydavidson118 wrote:

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
> If you use only EV and Var, whatever you get out is very likely to
> be an approximation, since you lose information by not including
> any influence from higher moments.

The Normal distribution is completely defined by the first two
moments: mean and var...No information is lost by ignoring higher
moments.