ARLINGTON HEIGHTS, Ill. - Campaigning Thoroughbred horses requires patience, and to win races on a regular basis requires either great luck or a vast arsenal of starters. But the gap between Mystery Giver's last two victories was extreme, even by this sport's standards. Some 27 months after he set a Fair Grounds turf course record when he won the Mervin Muniz Handicap in March 2004, Mystery Giver had his picture taken again after winning the seventh race here June 30 by a nose.