User:4st/Graphomic

Initial Ruleset

Definitions

The Graph

The game is played on a matrix of discrete size. Each entity has a row and a column. The values in the graph can be integers from -10 to 10 inclusive, rules to the contrary notwithstanding.

Each player is an entity.

Edges

Each row represents the starting vertex, and each column represents the destination vertex for a connection. The value at this matrix element is the weight of the edge. A value of 0 represents no edge.

(This makes the matrix representative of a weighted, directed graph: See these links for more details:

https://en.wikipedia.org/wiki/Adjacency_matrix

https://en.wikipedia.org/wiki/Directed_graph)

Paths

A path from entity A to entity B is a list of edges where the first edge in the list has starting entity A, and the last edge in the list has destination entity B, and each edge in-between has a starting edge of the destination edge of the previous edge in the list.

Turns

Each phase, a player can make one move.

Moves

A move is one of the following actions:

Graph Adaptation

A graph adaptation consists of a player can modifying a value in the matrix that is neither in their row or column by adding or subtracting 1 to that value, and they can do such a move so by announcement in #game-actions.

Winning

A player wins if there is a path, whose edge weights sum to a positive value, from themself to each other player. Multiple players can win at the same time, but once a win exists, no more graph adaptations can occur.

bad? ideas (not part of initial rules, but serve to promote this initial ruleset)

Bonus entities

As long as a path with total positive value exists from themself to a bonus entity, that player can make an additional move each phase.

Power Bonus

If a path from a player exists with infinite value (ie a cycle), that player can make an additional move each phase.

Sad Bonus

If a path from a player exists with negative infinite value (ie a cycle), that player can make an additional move each phase.

Points revamp

Turns are now either one move or one firing. Winning is now the first player to 100 points.

Score

Each player has an integer called points.

Firing

A firing consists of a player traversing the directed graph, starting from their vertex, and adding up each traversal. A player adds up the points when the traversal finishes, or, if a traversal would never finish due to a cycle, then -10. This value is added to their score.

Shop

The shop is an entity. A player can buy items if the shop is connected to them. A player can sell items if they are connected to the shop.

Anti-cycle laws

If, after a move, a cycle exists, all positive edges in those cycles have their value decreased by 1, and all negative edges in those cycles have their value increased by 1.

Items

An item is stored on an entity. That entity may choose to give that item to any entity it is connected to by a path with a total positive value.