AUGUSTA (AFP) - Successful juggling of the risks and rewards of aggressive shot making at Augusta National has brought Phil Mickelson and Tiger Woods each three Masters titles in the past 10 years. While both American stars have struggled in the past year, each can claim the world number one ranking by capturing the green jacket symbolic of Masters supremacy after Sunday's final round of the 75th edition of the golf classic. "He and I both have some work to do on our games," Mickelson said. European rivals top-ranked Martin Kaymer, 2010 Masters runner-up Lee Westwood, England's Luke Donald and Northern Ireland's Graeme McDowell can also claim the top spot. Familiarity with the fabled course by Mickelson and Woods could offset form issues and bring about a long-sought fight between the two for a major crown with a host of Europe's best adding to the mix for a wide-open, intense drama. "It has been great for world golf that we have had so many non-Americans playing well and moving up the world rankings," Mickelson said. "Many of those players seem to be up there in every single major." Mickelson is defending champion and appears to have solved his woes by winning last week's Houston Open, his first triumph since last year's emotional Masters embrace of ailing wife Amy after the last hole of his final round. "That was a really special week for me and Amy," Mickelson said. "It was a really big emotional boost for us." Woods comes to Augusta National on an 18-month win drought since a sex scandal that led to a divorce. His share of fourth last year at the Masters in his first event after a five-month hiatus was the best he has done since his secret life with multiple mistresses was revealed. "I believe in myself," Woods said. "It's all about making the right decisions, plodding the ball along and more so this golf course than anything else, and missing the ball in the right spots." Left-hander Mickelson won last year by shaking off his caddie's suggestion not to make a risky shot from behind a tree on the 13th hole in the final round. His shot cleared Rae's Creek, found the green and made a birdie. Mickelson won his first major title at the 2004 Masters, added another green jacket to his wardrobe in 2006 and won again last year. Woods, a 14-time major winner chasing the all-time record 18 won by Jack Nicklaus, won his first major title at the Masters in 1997, completed a run of four major titles in a row at the 2001 Masters and also won in 2002 and 2005. "They are equally dominant, Phil obviously as of late and Tiger early," said American Nick Watney. "That is kind of like 1a and 1b. I would have a hard time picking one over the other." Westwood, still seeking his first major title, is expected to be a strong challenger. Mickelson, who spent years trying to shake the "Best Player Never to Win a Major" tag, expects his major breakthrough will come soon. "I understand where Lee is at," Mickelson said. "I think his game is at such a high level right now that I just think it's a matter of time."