In turn based games like chess, the player playing the first move has an advantage the whole game. One way to "remedy" this is to let the player starting the game make one move (and have the advantage) but after that, let the players make two moves in a row. The first move to "catch up" the other player's advantage and then the second move to her-/himself get an advantage. Rinse and repeat.
Is chess ever played like this? If yes, how does it differ from regular chess? Is it fairer (=black wins as much as white)? Any other interesting observations about a game like that?