==============================  CFJ 1435  ==============================

    The method used by Goethe in the message with Message-ID
    <Pine.LNX.4.43.0302031253250.32726@hymn01.u.washington.edu> is
    reasonably close to the probability distribution required for the
    action e attempted to perform in that message (i.e. determine the
    Weather for February 2003).

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Caller:                                 Murphy
Barred:                                 G.

Judge:                                  Steve
Judgement:                              FALSE

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History:

Called by Murphy:                       04 Feb 2003 05:45:45 GMT
Assigned to Steve:                      05 Feb 2003 06:24:22 GMT
Judged FALSE by Steve:                  10 Feb 2003 04:49:40 GMT

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Caller's Arguments:

I note that the Judge would do well to review Rule 1079 (Definition
of "Random"), as well as the Nile Spice Black Bean Soup case, which
went roughly as follows:

* Method was "I need to choose randomly between Chuck and Steve.  I'll
  count the ingredients on this can of NSBBS; odd = Chuck / even = Steve".

* Judge's response was "if the number of ingredients was sufficiently
  close to random, *or* the method of assigning odd = Chuck / even = Steve
  was sufficiently close to random, then the whole method would be kosher;
  but neither is SCTR, so the whole method is not SCTR either".

I hereby quote the message identified in the statement.

> From: <kerim@u.washington.edu>
> To: "Agora Official" <agora-official@agoranomic.org>
> Sent: Monday, February 03, 2003 12:53 PM
> Subject: OFF: [Treasuror] Weather by Pi
>
> According to the Payroll Clerk, the Bank holds 495 Stems
> while non-Bank entities hold 1214 Stems.
>
> By Rule 2011 (Stems Weather) and the weather budget, the
> weather maps onto the following (0,1) probability
> distribution:
>
>  0.00000...
>    Foul
>  0.19298...
>    Plenty
>  0.66627...
>    Fair
>  0.83313...
>    Same (Foul)
>  1.00000
>
> Starting with the decimal point, I will select base-10 digits
> at random until the combined resultant number falls unambiguously
> into one of the above ranges.
>
> To do so, I intend to select the 1,000,001th digit of pi
> (following the decimal point) and read digits of pi in sequence.
> I state that (at this moment) I have no knowledge of the digits in
> at that point in the sequence.
>
> Selecting now...
>
> It is .3 (...3092756... to aid checking if desired) and falls
> in the Plenty weather range.
>
> The Weather is Plenty.
>
> If the Bank had enough Stems, 950 would be destroyed and
> 1425 created.  However, the Bank does not have enough Stems.
> So:
>
> 495 Stems in the possession of the bank are destroyed;
> 743 Stems are created in the possession of the bank.

I further note that Goethe later said the following:

> The above probabilities are incorrect due to a spreadsheet entry
> error.  The following probabilities are correct:
>
>  0.00000...
>    Foul
>  0.47323...
>    Plenty
>  0.66666...
>    Fair
>  0.83333...
>    Same (Foul)
>  1.00000
>
> As such, my selection of 0.3 makes the weather Foul.
> H. Payroll Clerk Steve, the following message is correct:
>
> 495 Stems are destroyed in possession of the Bank;
> 248 Stems are created in possession of the Bank.

but I do not believe that this changes the method itself, only its
input values.

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Gratuitous Arguments by G.:

A recent CFJ, judged by Judge Murphy I believe, found that
pseudo-random sequences are sufficiently random for the
purposes of the Rules (does someone have the #, with Eris'
firewall up I can't find it).

Best mathematical evidence on the randomness of base-10
Pi digits can be found at :
  http://www.lbl.gov/Science-Articles/Archive/pi-random.html

Since pseudo-random deterministic sequences are as controllable
by the user (through the seed) as selecting digits of pi with
an arbitrary starting point, all it comes down to is trust
that the selector does not have prior knowledge of the results.

As dice are considered fair by the Rules, and dice have the same
element of trust (there's no way to confirm that a player didn't
reroll until getting the desired quantity), all of these methods
should be acceptable.

Of course, *someone* had to calculate more than a million digits
of pi to call it random, but that someone was not me and the
same is true for other pseudo-random methods.

Judge Murphy wrote that pseudo-random sequences were acceptable
because "no one here understands how they work" or similar
wording.  If anyone here understand how pi "works" sufficiently
to know a digit without calculating it, I'd like to talk to
them: I'd like them to offer me two boxes, one with a million
dollars in it.

If Caller Murphy's arguments are due to the weighting of my
choice to the proper non-Uniform weights required by the Rule
Stems Weather, the math behind the weighting is left as an
exercise to the Caller...

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Judge Steve's Arguments:

"The method used by Goethe" to generate a random number was to pick an
arbitrary digit of pi (the millionth digit, in this case). Goethe
claims, and  I believe him, that e did not know in advance what the
millionth digit of pi was. This is equivalent to the use of any
deterministic, pseudo-random method of generating random numbers, where
the person making the selection does not know in advance what the
outcome will be.

As I see it, then, the question the Caller is trying to reach here is
whether the use of deterministic, pseudo-randomly generated numbers is
allowed by R1079, as long as the person making the selection does not
know in advance what numbers will be generated. We already have the
precedent of CFJ 1406 to guide us, but since the arguments were not
treated in any detail there, it is worth setting them out briefly.

Both common-sense and game custom would answer the question
affirmatively. We don't need to rely on quantum-mechanical processes
(assuming that these are at bottom non-deterministic). Rule 1079(d) also
strongly suggests, and perhaps even implies, that deterministic pseudo-
randomness is permissible: we are told that flipping a coin is a
permissible physical process, and flipping a coin can be modelled as a
deterministic, pseudo-random process.

What matters therefore is not that the outcome could in principle be
known in advance, but that (a) in practice it is not known in advance,
and that (b) the process is known to have the right statistical
properties in the long run.

The digits of pi are known to have the right statistical properties -
each digit is just as likely to appear as any other, and Goethe did not
know in advance what sequence of digits would appear from the millionth
digit of pi onwards.

However, the CFJ refers to "the method used... [to] determine the
Weather", and this includes not only the selection of a number but also
the assigment of numbers to the possible outcomes. In the message quoted
by the Caller, Treasuror Goethe used an assignment to the possible
Weather outcomes that was incorrect. E later corrected this assignment
(see <1>).

The CFJ is therefore trivially FALSE.

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Judge Steve's Evidence:

<1> Goethe's COE and correction of the Weather
    http://www.escribe.com/games/agora-official/m3358.html

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