[s-b] Proposal: MathFlag

["Jamie Dallaire" <bad.leprechaun@xxxxxxxxx>]

Here's an attempt at a subgame. There are still several ndays before voting,
so please do suggest improvements to the subgame as I'm not sure where to
set the limits myself. E.G. should the list of operators include simple
logical ones like IF statements? That might get to be too ridiculously
difficult. E.G. how many characters sets a reasonable limit for each team's
secret expression?

Also, I'm not following the usual language of attributes and whatnot. I
don't think this needs to be so within a subgame as long as it is internally
consistent, right? Everyone ok with this?

I submit the following Proposal, entitled "MathFlag":
{
Create a Subgame named "MathFlag", described by the Game Document that reads
as follows:
{{
"MathFlag" is a team-based Subgame, described by this Game Document.

This Subgame, when it is Open, is always in one and only one of four Stages:
Preliminary, Selection, Active, or Challenge.

When this Subgame becomes Open, it is in the Preliminary Stage. During the
Preliminary Stage, Players (save for the Gamemaster) may join MathFlag by
announcement to the Public Forum. The Gamemaster may cause the Subgame to
move to the Selection Stage at a time of his choosing, provided at least 2
rdays have elapsed since the Preliminary Stage began, by announcing the
makeup of the two opposing teams to the Public Forum. These teams must
collectively include every Player who has joined MathFlag (and only those
Players), and these Players must be distributed randomly and as evenly as
possible between the two teams.

During the Selection stage, any Player may privately submit a Proposed
Secret Expression to the Gamemaster. The Gamemaster may cause the Subgame to
move to the Active Stage by announcement to the Public Forum at a time of
his choosing, provided at least 2 rdays have elapsed since the Selection
Stage began and at least one member of each team has submitted a valid
Proposed Secret Expression. When the Active Stage begins, the last valid
Proposed Secret Expression submitted by any member of each team becomes that
team's Secret Expression. The Secret Expression may never be changed.

A Proposed Secret Expression is valid if it fulfills the following
requirements:
- It includes no spaces.
- It consists of a maximum of 16 characters.
- It contains only characters from the following set: {- + / * ( ) 0 1 2 3 4
5 6 7 8 9 x p}
- If it contains the character "p", it is accompanied by an explanation of
which specific Attribute's Value this character represents. The Range of
this Attribute must only include finite numbers.

During the Active stage, any Player may submit (to the Public Forum) an
Input, which must be a single integer. The Gamemaster may, by announcement
to the Public Forum, Compute at any given time, provided that at least 1
rday has elapsed since he last Computed and since the MathFlag last entered
the Active Stage. The Gamemaster is obliged to Compute within 2 rdays of
receiving Inputs from members of both teams. When the Gamemaster Computes,
he evaluates the Result of each team's Secret Expression using the last
Input submitted by a member of the opposing team, as well as the current
Value of the Attribute represented by the character "p" for each team (if
relevant). The Gamemaster, when he Computes, must announce both the Input
used and the Result of each team's Secret Expression to the Public Forum.

During Computation, the Gamemaster must abide by the following guidelines:
- "-" represents subtraction, "+" represents addition, "*" represents
multiplication, and "/" represents division.
- mathematical order of operations must be followed, considering all above
operations and brackets.
- "x" is to be replaced by the last Input submitted by a member of the
opposing team.
- "p" is to be replaced by the current Value of the Attribute specified by
the team having submitted the Secret Expression being evaluated.

At any time during the Active Stage, any Player on either team may cause
MathFlag to move to the Challenge Stage by announcement to the Public Forum.
When this occurs, the Gamemaster must randomly compose a list of 3 integers
within the range [-1000,1000] and submit these to the Public Forum. These
integers are known as Queries. Any Player from each team may submit, to the
Public Forum, a Guess that corresponds to each Query. At a time of his
choosing, provided at least 2 rdays have passed since the Challenge Stage
was last entered, OR each Query has been met with a Guess from each team,
the Gamemaster may Compare the results.

When he Compares, the Gamemaster evaluates the result of each team's Secret
Expression (exactly as when he Computes) using each individual Query as an
Input. He then compares this result to the Guess submitted by the opposing
team from the corresponding Query, the difference being known as the Error
for each individual Guess.

If the sum of the three Errors for the team that caused the Challenge Stage
to begin is zero, all the Players on this team are Winners. The opposing
team's Players are Losers.

If this is not the case, but the sum of the three Errors for the other team
is zero, the Players on the other team are Winners, and the Players on the
team that caused the Challenge Stage to begin are Losers.

If neither team has a cumulative Error of zero, MathFlag re-enters the
Active Stage. If the cumulative Error of the team that last caused the
Challenge Stage to begin is greater than that of the opposing team, no
Player from the former team may submit an Input until the Gamemaster has
Computed once more.

If, at any time, the Attribute with a Value represented by "p" in a team's
Secret Expression ceases to be an Attribute, or if its Range ceases to
include only finite numbers, this team's Players are Losers. Unless they
simultaneously become Losers, the opposing team's Players are Winners.

Whenever Winners and/or Losers are declared, MathFlag ends.

When MathFlag ends, all Winners are awarded a Solar-Powered Pocket
Calculator as a Trophy.
}}
}

Billy Pilgrim
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