Parity: getting the last move

Who moves last?

At the start, 60 squares are empty and Black moves first. If nobody passes, the players take turns until the board is full, and White fills the last square. That is why White is said to have parity at the start of the game.

Every pass switches it around. After one pass, Black is on course to make the last move – until the next pass.

Regions of empty squares

Near the end, the empty squares split into separate regions. Parity works region by region: try to make the last move in each one. In practice, that means:

• Move in regions with an odd number of empty squares.
• Leave regions with an even number alone, so that your opponent has to open them.

An example

Here is the end of a game, with Black to move and 3 empty squares in 2 regions.

• If Black plays g2, White has to move into the pair, and Black takes the last square. With best play, Black wins 36–28.
• If Black starts with g7 instead, White plays g2. Black has no legal move and must pass, and White also gets g8. White wins 37–27.

The same idea works with bigger regions: a region of 1 or 3 squares is a good place to move, a region of 2 or 4 squares is usually better left to your opponent.

A guideline, not a law

Parity helps you choose between moves that look equally good, but it doesn't beat everything else. A corner, or a move that leaves your opponent with no safe reply, can be worth more. Count the empty squares in each region, then check what each move allows.

Keep learning

The Daily challenge is endgame practice: every day there is a position that looks lost but can still be won, and thinking about parity often helps.

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