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== 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 has an entity. ==== Edges ==== Each row represents the starting vertex, and each column represents the destination vertex for a directed edge. The value at this matrix element is the weight of that 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 entity of the destination entity 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 (optional rule?: a value 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. (And then, preferably, updating the cycle's gamestate page.) === Winning === A player wins if there is a path, whose edge weights sum to a positive value, from themself to each other player's entity. Multiple players can win at the same time, but once a win exists, no more graph adaptations can occur.
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