Parity & Mobility: Step-by-Step Guide

Prerequisites

Edge Stability

Core ideas

• Break the board into regions—track parity (odd or even empty squares) in each region separately.
• Forcing a pass gives you back-to-back moves; use it to claim corners or secure a final sweep.
• Maintain mobility—avoid positions where you have only one move that gifts a corner.

Regional parity walkthrough

1. Divide the board into four quadrants. Suppose the north-east pocket has five empty squares—an odd count.
2. Play F4, dropping the pocket to three empties. White must respond elsewhere, keeping the count odd.
3. After White fills the south-west, return to the pocket with H4; now only one empty square remains and you finish the region.

Whenever a region has an odd number of empties, you can force the last move there by playing elsewhere until your opponent is compelled to enter it first.

Why it works

Controlling parity lets you dictate who plays last in a region. Combined with safe edges, this often converts into a disc lead even if you were behind earlier.

Try it now

• Pause a hard game with ten empties remaining. Mark each region as odd or even before you move.
• Play sequences that force a pass—note how the parity labels change when you take two moves in a row.
• When the board reaches four empties, predict the final score before finishing the game.

Common pitfalls

• Winning parity in one region but losing it everywhere else—track the entire board.
• Forcing passes too early and giving your opponent a high-mobility midgame.

Evaluation drills