Under a $365 billion agreement, the tobacco industry has promised to sharply curtail advertising. Even though the settlement still must be approved by Congress - and despite criticisms from President Clinton - Blenckstone said he believes it is only a matter of time before the billboard comes down.
Blenckstone said the economic impact on the Suns will be small. It's only one of 71 advertisements in the stadium, and Blenckstone said the sign generates about $2,500 a year.
The aggregate impact throughout the minor leagues will be greater, though, Blenckstone said.
"It's been a staple of minor league baseball for a long time," he said, adding that the team has two years left on its contract with the cigarette ad.
The billboard has become a fixture in Municipal Stadium, both because of its longevity and its unique appearance. Blenckstone said it has undergone minor changes over the years, both to replace worn out materials and to tweak the design.
At one time, he said, the Marlboro Man was a more realistic cowboy. Now, it is more of a silhouette.
Fans at Thursday's game against the Cape Fear Crocs had mixed views of the Marlboro Man.
"Leave it up," said Scotland, Pa., resident Wayne Mader. "That's the parents' responsibility, not the public's."
But his wife, Joan, said she thought the sign was a bad influence.
"I think they ought to take it down. What's the sense of having a symbol like that up there?" she said.
Mader, who used to teach third grade, said she worried about the children.
"They don't need that kind of influence," she said.
Others took a dimmer view of the Marlboro Man's demise.
"They advertise everything else. I don't see any harm in it," said Martinsburg, W.Va., resident George Seubert, 73. "It think it's a little too much on the smoking deal - making people go out of buildings. They don't even want them to smoke outside now."
Pulling a pack of Marlboro cigarettes out of his shirt pocket, Robert Dietz, 73, made no apology for his habit. He said smoking helped get him through World War II and Korea.
"That looks good up there, as far as I'm concerned. It don't say anything. It just says `Marlboro,' period," he said. "I always admired it, myself."
Paul Mason and Kimberly Spiker, of Cumberland, Md., said they saw no harm in the Marlboro Man. Spiker said she doubted it would have any effect on children's smoking habits.
Mason's 11-year-old son, Scott, was too busy watching the game to jump into the debate about cigarette advertisements.
"I ain't looking at the signs," he said.
Anti-smoking activists have long targeted advertising that can be seen by large numbers of children. The campaign clearly has had an impact. Lawsuits and public opinion forced the tobacco industry into negotiations and R.J. Reynolds on Thursday agreed to scrap its controversial Joe Camel character.
Blenckstone said that ballparks have gone through similar changes. Baseball banned smokeless tobacco - and its advertisements - about five years ago, he said. And at one time, ballparks sported whiskey signs, he added.