Each of the two sides corresponds to one player; we will call them light and dark after the sides of Othello pieces, but "heads" and "tails" would identify them equally as well, so long as each marker has sufficiently distinctive sides.
Originally, Reversi did not have a defined starting position. Later it adopted Othello's rules, which state that the game begins with four markers placed in a square in the middle of the grid, two facing light-up (indicated by o in our diagrams), two pieces with the dark side up (indicated by x). The dark player makes the first move.
ox xo (one of the possible starting positions)
Dark must place a piece with the dark side up on the board, in such a position that there exists at least one straight (horizontal, vertical, or diagonal) line between the new piece and another dark piece, with one or more contiguous light pieces between them. In the above situation, dark has the following options indicated by dots:
. .ox xo. .
After placing the piece, dark turns over (flips, captures) all light pieces lying on a straight line between the new piece and any anchoring dark pieces. All reversed pieces now show the dark side, and dark can use them in later moves -- unless light has reversed them back in the meantime.
If dark decided to put a piece in the topmost location (all choices are strategically equivalent at this time), one piece gets turned over, so that the board appears thus:
x xx xo
Now light plays. This player operates under the same rules, with the roles reversed: light lays down a light piece, causing one or more dark pieces to flip. Possiblities at this time appear thus (indicated by dots):
.x. xx .xo
Light takes the bottom left option and reverses one piece:
x xx ooo
Players take alternate turns. If one player cannot make a valid move, play passes back to the other player. When neither player can move, the game ends. This occurs when the grid has filled up, or when one player has no more pieces on the board. The player with more pieces in the board at the end wins.
One difference between Reversi and Othello involves the supply of pieces. In Reversi each player owns 32 pieces at the start of the game. Once a player has placed 32 pieces (including the initial 2 pieces placed on the centre squares) that player may not make any further moves. He/she may not use any of the opponent's pieces. In Othello all the pieces belong to both players equally; they come from a pool, from which both may draw in order to make a move.