The former NFL quarterback, a two-time winner of this event, had three birdies and three bogeys to go with the eagle in accumulating 25 points in the modified Stableford system that puts a premium on birdies and eagles.
'I mean, I'm not Tiger Woods or anything. I know I'm going to have three or four bogeys a day,' said Tolliver, who shot a 2-under 70 in the opening round of the 54-hole tournament at Edgewood Tahoe Golf Course.
Sterling Sharpe, a five-time Pro Bowl wide receiver when he played for the Green Bay Packers, had 24 points, tied for second with Hockey Hall of Famer Grant Fuhr.
Another point back was a trio of past and present quarterbacks -- Chris Chandler, Trent Dilfer and Tommy Maddox.
Former major league pitcher Rick Rhoden, who has won the tourney a record six times, was tied with former quarterback Mark Rypien with 22 points. Defending champion Jack Wagner had 18 and four-time tournament winner Dan Quinn had 17.
An eagle is worth six points, a birdie three, a par one, a bogey zero and a double bogey or worse minus 2.
Rhoden, Wagner and Quinn have won five of the last six celebrity titles.
'On Sunday, they'll be there,' Sharpe said. 'It's like death and taxes. Rick is going to be there. Jack is going to be there. Dan's going to be there.'
Fuhr had the best round of the day -- a 3-under 69 -- but didn't have an eagle.
'It's fun to be in contention. Obviously this would be a lot more fun if it was Sunday,' the former goaltender said.
The field of 78 includes a variety of sports stars, entertainers and other celebrities.
Ray Romano, playing with former 'Saturday Night Live' star Kevin Nealon, enjoyed a lucky break when his shot wide right of the par-4 9th hit a Ponderosa pine in front of a greenside bunker and kicked directly in front of the green.
'My bad luck was drawing Nealon,' Romano said.
Nealon, who was next-to-last at minus 27 points, hit three consecutive shots back and forth across that same green into sand traps. He started by digging into the sand, approaching the ball and yelling, 'Fore!' before he swung.
The shot bounced off the grandstand and into the trap on the other side, where he again yelled, 'Fore,' before repeating the miscue back to the original bunker.
Nealon, who said before the tourney his goal was to finish in the middle of the pack, was followed by a group of friends and family members who wore bright orange T-shirts that read, 'Team Nealon' on the front and 'It could happen ...' on the back.
NBA forward Chris Webber, who in past years has made a wager for charity with Basketball Hall of Famer Charles Barkley about who would finish worse, pulled out of this year's event.
'Probably scared,' said Barkley, who was last at minus 30.
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