The Flat Earth Theory

Main Match 1: The Flat Earth Theory

In the Flat Earth Theory, it is commonly believed that the edge of the world consists of the continent of Antarctica, a ring that encircles Earth. You will be attempting to make that journey to prove that the Earth is flat, once and for all!

RULES

Setup

This game takes place on an infinite 2D Cartesian plane. Players can occupy any point on the plane, and will begin the game at (0, 0). Note that points are described with their x-coordinate first, followed by their y-coordinate. At the end of each round, all player coordinates will be rounded to the nearest hundredth.

At the beginning of the Main Match, there are 4 unit vectors, signifying the win conditions of the match. They are labeled A, B, C, and D, and initially are the vectors with angles of degree 0, 90, 180, and 270, respectively, corresponding to right, up, left, and down. They represent the win conditions of the Main Match; the players that traveled the furthest in those directions wins.

Rounds

There will be 8 rounds in this MM. In each round, there will be a set of movement options given. These movement options will be vectors. During each round, a player may make either a movement proposal, or a shift proposal.

A movement proposal consists of assigning distinct players to each movement option.

A shift proposal consists of one of the existing win condition vectors (labeled A, B, C, and D), a direction (either clockwise or counterclockwise) and a non-negative integer number of degrees, no greater than 30. This proposal may not cause a vector to cross over or coincide another vector.

At the end of the round, all proposals will be anonymously revealed, with identical proposals being combined into a single proposal.

Voting

You must vote on every movement proposal that you are a part of. If you don't vote, it is assumed that you accept it. A movement proposal passes if at most 1 person in the proposal rejects it. All players in the passed proposal who accepted will have that movement option contribute to their movement for that turn.

You may also vote for one shift proposal to be enacted. The shift proposal with the most votes will be enacted. If there is a tie, nothing happens. When a shift proposal passes, that win condition vector will change direction according to the proposal.

Movement

A player moves by a vector that is the average of all of their movements taken.

If all of your movement options taken are identical, you move an additional unit (in that direction) per additional movement option you took over one.

Results

The directions of the win condition vectors are revealed after every round. You will be privately told your location after every round, as well as your distance in each direction. Nothing else is revealed.

The winners of this MM are the players who have traveled the farthest unique distance in each of the four win condition vectors. To be precise, for a given vector, the distance traveled in a particular axis is the magnitude projection of that vector onto that axis, also known as the magnitude of the vector dot product the axis. Those winners stay in heaven; all other players all fall down into Hell. If there is a player with multiple ToLs, they must give them away to other (non-loser) players until they only have one.

The losers are the players with the smallest nonnegative distance in the four win condition vectors (that isn't a winner). They will gain a Mark of Elimination for the next MM.

At the start of the next episode, there will be 4 players in Heaven, and 9 players in Hell.

TIMELINE

Rules release: There is a 24 hour pre-game for players to discuss and ask questions.

Round 1 Start: The movement options for Round 1 are released. Submit your movement proposal or shift proposal.

Round 1 Voting, Round 2 Start: For every movement proposal you’re on, vote on it, and optionally vote for a shift proposal. Also, movement options for Round 2 are released; submit your movement proposal or shift proposal for Round 2.

Round 2 Voting, Round 3 Start: See above, except in addition, the results from Round 1’s voting phase are announced; players are told privately their location and any win condition vector change is revealed.

…

Round 8 Voting: Round 8's proposals are announced, and Round 7's results (your current location and the win condition vectors) are revealed. Vote for Round 8 movement / shift proposals.

End of Main Match: All player locations, and therefore the winners, are revealed.