Chess and backgammon, how you've changed. Once fancied only by intellectuals and Englishmen, you are now the trensdiest games in town. If you don't want to play matches at the local discos, new highs in gamesmanship can be found at a small Georgetown row shop at the foot of Key Bridge. Even if you know the rules, Your Move may be the place to brush up on your strategy. Don't be misled by all the chess and backgammon sets for sale in the front of the store: the action is in the back. There, at five long tables, players take part in rated tournaments, pit their wits in fast-moving, five-minute speed chess games, or just drop in for a leisurely game or two at lunchtime, which fifty cents an hour ($1 minimum) is cheaper than eating, and less caloric, too. For those whose idea of real games includes dice and a doubling cube. Thursday night amateur backgammon tournaments begin at 7:30. The entry fee is $2 but you might win that back in the evening's cash prizes. Tuesday night, same time and entry fee, five-minute speed chess matches are on the boards, with players punching moves on a time clock to start an opponent's turn. He who runs out of time first is known as the loser. Biweekly Swiss intramural chess rounds, comprised of four-player teams, are held Saturday 11:30 a.m. to 11:30 p.m. (next ones March 18, April 1), but late night kibitzing is in session every weekend. You might want to brush up for all of this, so owner Walter Stromquist will teach you the rules free, on a drop-in basis, or you may learn chess's warlike strategy from Sam Greenlaw, the only American player to defeat current world champion Anatoly Karpov, who will give you a series of ten lessons for $55. That's inexpensive if you consider it learning a new way to channel aggression. Checkmate.

Your Move, 3409 M St., NW, Every day 11 a.m. to 11 p.m. (Friday and Saturday till 1 a.m.). 338-0560.