Place a disc so that one or more of your opponent’s discs sit in an unbroken straight line between your new disc and another disc of your colour. Every disc in that line flips. Moves that flip nothing are not legal, and the marked dots show you exactly which squares are.

The rules played here are the standard Othello rules — 8x8 board, four discs in the centre to start, dark moves first. Othello is a trademarked version of the older game Reversi; the play is the same.

Because discs are not points until the game ends. A disc you flip now can be flipped back, and holding many discs usually means you also hold many edges of the enemy shape, which gives your opponent more moves and you fewer. Strong play usually means owning few discs in the middle of the game.

A corner disc can never be flipped — flipping requires enemy discs on both sides of a line, and a corner has no second side. That makes corners permanent, and it makes the squares diagonally next to them the most dangerous on the board, because playing there hands the corner over.

They are different and they are also ordered, and both halves are measured rather than claimed. In the same position the four pick a different move between 56 and 92 percent of the time, because each one is reading a different feature of the board. Playing the wrong way against any of them costs between 28 and 55 percentage points of win rate. They do get harder in order: a fixed reference player beats the Glutton about 85 percent of the time and the Anchor about 45 percent. What is not true — and it is worth saying, because good Reversi advice is the same everywhere — is that each one needs a different strategy. Playing for the corners is the right answer against all four; the difference is how badly each one punishes you for not doing it.