Parity in Reversi is the question of who makes the last move in each closed region of empty squares. The player who fills the final empty square in a region controls the last disc placement there — often a large flip. In the endgame (roughly the last 20 squares), correctly managing parity across all regions frequently determines who wins, even when both players are playing accurately.
What Is Parity?
Imagine the endgame board has a small isolated pocket of 3 empty squares. Two players will alternate filling these squares. Since there are 3 (an odd number), the player who enters the pocket first fills squares 1 and 3 — the last one. The player who enters second fills only square 2.
That last move in the pocket is often strategically powerful: it places a disc where the opponent cannot immediately respond within the same region. The result is frequently a disc swing in favour of the player making the last move.
Parity is the systematic analysis of this “last move advantage” across every closed region on the board.
Odd and Even Regions
A region in parity terms is a group of empty squares that form a connected pocket — squares that are accessible from each other but isolated from the rest of the board by played discs.
- Odd region (1, 3, 5, 7 empty squares): The player who moves first in this region makes the last move
- Even region (2, 4, 6, 8 empty squares): The player who moves second in this region makes the last move
The key insight: you want to be the player who makes the last move in as many regions as possible, and especially in the largest regions where the final placement has the biggest impact.
A Simple Parity Example
Consider an endgame with two isolated regions:
Region A: 3 empty squares (odd) Region B: 4 empty squares (even)
If it is your turn to move:
- If you enter Region A first, you make moves 1 and 3 in it — you get the last move in Region A (advantage)
- Region B has 4 squares — if your opponent enters it first, they make moves 2 and 4 — they get the last move (disadvantage)
Parity play: Enter Region B first (by moving there), forcing your opponent into Region A. Now:
- Your opponent enters Region A → they move 1st and 3rd, but since you forced them in, you enter the 3rd square from the outside?
Actually, the cleaner framing: when you enter Region B (even), your opponent will make the last move in Region B regardless. You want to enter Region A (odd) to claim its last move. But since it’s your turn, you enter the region of your choice.
The general rule: Move into even-sized regions to force your opponent to take the last move there; move into odd-sized regions to claim the last move for yourself.
Global Parity
Beyond individual regions, global parity considers the total number of empty squares remaining and whether the game’s overall parity favours you.
In a standard 60-move game:
- Black moves first → Black takes moves 1, 3, 5… (odd-numbered moves)
- White takes moves 2, 4, 6… (even-numbered moves)
- Move 60 (the last move) is taken by White (even)
This means White has a natural global parity advantage in a game with no passes. White always makes the final move. This is one reason White is sometimes considered slightly advantaged at high levels of play.
When passes occur, global parity shifts — the player who was forced to pass loses a turn, which changes who makes the final move. This is why forcing your opponent to pass can be strategically valuable beyond just gaining an extra turn.
Parity Regions in Practice
Identifying Regions
In a real endgame position, regions are identified by looking at clusters of connected empty squares surrounded by filled discs. Common region patterns:
- 1-square region (single empty): The player whose turn it is fills it (trivial — odd, first player gets it)
- 2-square region: The player who enters it fills the first, and their opponent fills the last — opponent gets parity (even)
- 3-square chain: First player fills 1st and 3rd (parity for the first player) — odd
- Corner cluster regions: Corners with adjacent empty squares form larger regions whose parity depends on their total empty count
Counting Regions
Experienced players count regions as the endgame approaches (roughly 15–20 empty squares remaining):
- Identify all isolated empty regions
- Count the number of empty squares in each
- Note which are odd and which are even
- Determine whose turn enters each region
- Plan move order to maximise the number of regions where you get the last move
This calculation is done mentally during play and is one of the core skills separating intermediate from advanced players.
Parity Errors: Common Mistakes
Entering the Wrong Region First
Playing into an odd region when you should be entering an even one (or vice versa) is the most common parity error. It hands your opponent the last move in a region you could have claimed.
Example: Two regions remain — one with 3 squares (odd) and one with 2 squares (even). It’s your turn. If you enter the 3-square region, you claim its last move. But if you enter the 2-square region, your opponent gets the last move in it — and then they enter the 3-square region and also get its last move. You lose parity in both regions.
Underestimating the Last Move’s Impact
In positions where both players’ options look equivalent, parity determines outcomes even when the immediate disc count looks equal. A parity mistake late in the game can reverse a 5-disc lead in a single move.
Ignoring Parity When Calculating Endgame Sequences
When calculating endgame sequences, always account for whose turn it will be when entering each region. A sequence that looks like it wins by disc count may be losing when parity effects are properly evaluated.
Parity and Mobility
Parity and mobility are related but distinct concepts:
- Mobility — how many legal moves you have (more is better throughout the game)
- Parity — who makes the last move in each region (critical specifically in the endgame)
In the midgame, mobility is the dominant consideration. As the board fills and regions become isolated, parity gradually becomes more important. In the final 15–20 squares, parity often outweighs all other factors. Read endgame strategy alongside this guide for the complete picture.
The transition between these phases — when to stop optimising for mobility and start optimising for parity — is a skill that separates intermediate from advanced players.
Parity in the Opening and Midgame
Parity is primarily an endgame concept, but experienced players keep it in mind throughout the game:
- Creating odd regions early — moves that leave isolated odd-count empty pockets can be advantageous later
- Edge play and parity — edge moves can create or isolate regions, with parity consequences 20–30 moves later
- Avoiding forced even regions — positions that inevitably create many even-sized regions for your opponent to control disadvantage you in the late game
For beginners and intermediates, the practical advice is: focus on parity from roughly move 40 onward (20 empty squares remaining). Before that, mobility and corner play are higher priorities.
Quick Reference: Parity Rules
| Situation | Parity Rule |
|---|---|
| Odd-sized region, you enter first | You get the last move (good) |
| Even-sized region, you enter first | Opponent gets the last move (bad) |
| Odd-sized region, opponent enters first | Opponent gets the last move |
| Even-sized region, opponent enters first | You get the last move (good) |
| Opponent forced to pass | Global parity shifts in your favour |
| Multiple regions remain | Enter even regions first, claim odd regions |
Practising Parity
The best way to develop parity intuition is endgame drilling:
- Set up a position with 12–18 empty squares (you can find these in recorded game databases or create them on a board)
- Identify all regions and their sizes
- Calculate the parity-optimal move order before playing it out
- Verify with a computer program (WZebra, Saio, Edax) whether your parity analysis was correct
After 20–30 such drills, recognising parity patterns becomes intuitive. This is one of the highest-ROI training activities for players at the intermediate-to-advanced transition.