> ## Documentation Index
> Fetch the complete documentation index at: https://docs.pcm.game/llms.txt
> Use this file to discover all available pages before exploring further.

# Euclidean Math & Combat

> The 3D vector space and the esoteric win conditions.

# Euclidean Math & Combat

PCMTG is engineered with a strict Anti-Meta Philosophy, utilizing hidden variables to ensure ideological intuition triumphs over mathematical calculation\[cite: 114, 115].

## The Objective

The objective is to pull a News Stub's vector toward the absolute neutral center of the compass\[cite: 117, 241]. The winner is the player who achieves the smallest squared Euclidean distance to the origin after all cards are played\[cite: 118].

The mathematical engine calculates the distance using the formula:
$d = \sqrt{(x_{final})^2 + (y_{final})^2 + (z_{final})^2}$ \[cite: 791]

## The Hidden Z-Axis

The Z-Axis is a hidden third dimension representing Populism (positive Z) versus Elitism (negative Z)\[cite: 122, 123, 124]. Because the exact magnitude is hidden by the server, players cannot perfectly calculate the distance\[cite: 130]. They must rely on their ideological intuition\[cite: 78].