# Rithmomachia Quick Start Guide

**The Philosopher's Game** — Win by using math to capture pieces and build harmonies in enemy territory.

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## Goal

Arrange 3 of your pieces in enemy territory to form a **mathematical progression**, survive one opponent turn, and win.

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## The Board

- **8 rows × 16 columns** (columns A-P, rows 1-8)
- **Your half:** Black controls rows 5-8, White controls rows 1-4
- **Enemy territory:** Where you need to build your winning progression

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## Your Pieces (24 total)

Each piece has a **number value** and moves differently:

| Shape | Symbol | Movement | Count |
|-------|--------|----------|-------|
| **Circle** | ○ | Diagonal (like a bishop) | 8 |
| **Triangle** | △ | Straight lines (like a rook) | 8 |
| **Square** | □ | Any direction (like a queen) | 7 |
| **Pyramid** | ◇ | One step any way (like a king) | 1 |

**Pyramids are special:** They have 4 face values. When capturing, you choose which face to use.

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## How to Move

1. **Click your piece** to select it
2. **Click destination** to move
3. Pieces cannot jump over others — path must be clear
4. You can only move to an empty square OR capture an enemy

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## How to Capture

You can capture an enemy piece **only if your piece's value relates mathematically** to theirs:

### Simple Relations (no helper needed):
- **Equal:** Your 25 captures their 25
- **Multiple/Divisor:** Your 64 captures their 16 (64 ÷ 16 = 4)

### Advanced Relations (need one helper piece):
- **Sum:** Your 9 + helper 16 = enemy 25
- **Difference:** Your 30 - helper 10 = enemy 20
- **Product:** Your 5 × helper 5 = enemy 25

**Helpers** are your other pieces still on the board — they don't move, just provide their value for the math.

The game will show you valid captures when you select a piece.

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## How to Win

### Victory Condition #1: Harmony (Progression)

Get **3 of your pieces into enemy territory** forming one of these progressions:

- **Arithmetic:** Middle value is the average
  - Example: 6, 9, 12 (because 9 = (6+12)/2)
- **Geometric:** Middle value is geometric mean
  - Example: 4, 8, 16 (because 8² = 4×16)
- **Harmonic:** Special proportion (formula: 2AB = M(A+B))
  - Example: 6, 8, 12 (because 2×6×12 = 8×(6+12))

**Important:** Your 3 pieces must be in a straight line (row, column, or diagonal), and all 3 must be in enemy territory.

When you form a harmony, your opponent gets **one turn to break it**. If it survives, you win!

### Victory Condition #2: Exhaustion

If your opponent has no legal moves, they lose.

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## Key Rules

1. **White moves first**
2. **No jumping** — paths must be clear
3. **Can't capture your own pieces**
4. **Helpers can be anywhere** on the board (not just adjacent)
5. **Harmonies must survive one turn** to win

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## Quick Strategy Tips

- **Control the center** — easier to invade enemy territory
- **Small pieces are fast** — circles (3, 5, 7, 9) can slip into enemy half quickly
- **Large pieces are powerful** — harder to capture due to their size
- **Watch for harmony threats** — don't let opponent get 3 pieces deep in your territory
- **Pyramids are flexible** — choose the right face value for each situation

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## Common Progressions to Know

**Arithmetic** (easiest to spot):
- 4, 6, 8
- 6, 9, 12
- 5, 7, 9

**Geometric** (same ratio between values):
- 4, 8, 16
- 9, 27, 81

**Harmonic** (trickiest):
- 6, 8, 12
- 3, 4, 6

Practice spotting these patterns in your pieces!

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## Ready to Play?

1. Start by moving pieces toward the center
2. Look for capture opportunities using the math relations
3. Push into enemy territory (rows 1-4 for Black, rows 5-8 for White)
4. Watch for harmony opportunities with your forward pieces
5. Win by forming a progression that survives one turn!

**Remember:** This is a game of mathematical warfare. Every number matters!
