Randomizing a sample by selected groups in R

In my dataset, 90 people (samples) must each play two types of game, of a total of four types: X, Y, Z and W. I would like to randomize in R which games each person will play, as well as the game order, so that it follows this way:

UA	First game	Second game
Person 1	Game X	Game W
Person 2	Game W	Game Y
Person 3	Game Z	Game W

Thus, each game must be played by the same number of people (i.e., 30 people per game), and game W must be played by everyone. Is there a simple way to do this in R?