Reversi is played with discs that are dark on one side and light on the other. Every move flips a straight line of the opponent's discs, so the board can swing from one colour to the other in a few turns. It rewards patience: the player with fewer discs in the middle of the game is often the one who wins.
Rules
The game starts with four discs in the centre, two of each colour placed diagonally. Dark moves first. A move places one disc on an empty square so that at least one straight line of opposing discs, across, down or diagonally, lies between the new disc and another of your own. All discs in every such line are flipped to your colour.
If you have no legal move, you pass, and the opponent plays again. A pass is announced and played for you here. The game ends when neither player can move, usually when the board is full.
Whoever owns more discs at that point wins. Squares left empty are credited to the winner, so even an early finish is scored out of 64.
Strategy
A corner disc is permanent. Nothing can flip it, and it anchors the edges that meet there. Keep off the diagonal squares next to an empty corner: a disc there usually opens that corner for the opponent.
Fewer discs, more moves. In the middle game, count your legal moves rather than your discs. Quiet moves that flip one or two inner discs keep the opponent short of options until they are forced into a bad square.
Stay away from the frontier. Discs next to empty squares give the opponent something to flip. Try to keep your discs inside the mass and let the opponent build the long walls.
Last word in each region. Late in the game the empty squares break up into small pockets. Aim to make the final move in each; a pocket with an odd number of empties usually favours the player who enters it first.
Questions
Who moves first in reversi?
Dark. The starting position has light discs on d4 and e5 and dark discs on e4 and d5.
What happens when I have no move?
You pass and the opponent moves again. If neither side can move, the game is over and the discs are counted.
Do empty squares count at the end?
Yes: they are given to the player who won, so the final score always adds up to 64.
Is it bad to have many discs early?
Often, yes. A big disc count in the middle game usually means few moves and many discs that the opponent can flip later.
How strong is the Master level?
It searches several moves deep with a careful evaluation of corners, mobility and edges, and it plays the last dozen or so moves perfectly.