First prize is $1.2 million.
"In match play, you just have to be better than your opponent that particular day," Woods said at a news conference Tuesday."But it's fickle since on a given day over 18 holes, anybody can beat anybody. There's really no big upset."
Rollins said: "I just want to play well and at least give him a good match."
In last year's championship match, Woods defeated David Toms 2 and 1.
In some other first-round matches at the LaCosta Resort and Spa, Singh plays Shingo Katayama of Japan, Weir meets Rich Beem and Love take on Briny Baird. Mickelson plays Lee Westwood of England, Jerry Kelly meets Sergio Garcia, Jay Haas faces Loren Roberts and Charles Howell III plays Ben Curtis.