Re: Missing Digits Filter

On Tue, 13 Mar 2007 17:42:45 -0400, Stig Holmquist
<stigfjorden@xxxxxxxxxxx> wrote:

On Tue, 13 Mar 2007 11:24:31 +0000, Evil Nigel <useweb@xxxxxxxxxx>
wrote:

Stig Holmquist wrote:

A simple formula can predict how many digits are likely ,on average,
to be missing when sampling digits at random with replacement from
a table of random numbers or from an urn with all ten digits 0-9.

E.g. after 10 draws there will be on average 3.5 digits missing and
after 20 draws it will be 1.22, after 30 draws it will be 0.42, after
40 draws it will be 0.15 and after 50 draws it will be only 0.05.

These numbers can be verified by very large samplings of
digits from a random numbers table, where digits are arranged
in units ot ten with 2x5.

A manual count quickly shows there is a variation between tests,
which raises the question about standard deviation. Various formulas
have been proposed and need to be compared by computer simulation.

One formula in particular says the std.dev. for 10 draws with 3.5
missing on average will have a s.d. of 1, for 20 it will be 0.8, for
30 draws it will be 0.36, for 40 draws it will be 0.14 and for 50
draws it will be 0.05, similar to the missing number.

All this refers to the most ideal random set of digits. But how might
it apply to the digits drawn in pick 3 an4 type games?

Could it be used as a filter for picking digits in lottery games?

Ideas and opinions are invited as long as they are rational and
factual and free from nitpicking and personal attacks and innuendoes.
Violators will be responded to in kind.

Stig Holmquist

It's easy to construct a "Gambler's Fallacy" type argument - after 10
draws, if 5 digits are missing, surely the five missing digits are "due"
to balance out the statistics.

Evil Nigel

There are too many missing digits after ten draws so I would suggest
looking for the one digit missing after 22 draws. It would
be interesting to do a statistical study of how many draws it takes
for this digit to be drawn on average. I lack the ability to do such a
study. Maybe it will inspire somebody to do it.

Stig

Since nobody offered to test my suggestion to look for the missing
digit in 22 draws I decided to do a manual test for missing digits in
sets of 20 in a random numbers table and then count the number of
steps to find this digit again going up or down. Well, the result was
rather discouraging. It varied from 0 to 42 in a few tries. This
reminded me of a formula for "waiting time" or the geometric distr.
So this was not my brightest idea. Hope nobody is working on it.

Stig
.

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