The Augusta National Golf Club in Augusta, Ga. (Rob Carr/AP)

That’s because the leaders of the all-male Augusta National Golf Club are in a pickle. Although they have always defended their right to invite whomever they want to join their ranks, and that means no women, they also have always had the smarts to extend an invitation to the CEOs of the handful of companies that bankroll the club’s legendary Masters tournament.

But this year, the CEO of one of those sponsors is IBM’s first female leader, Ginni Rometty. How very awkward.

Augusta National now has a choice -- change their tradition-bound all-male membership and admit IBM’s CEO, even if she isn’t a he, or reject the CEO of IBM-- precisely because she isn’t a he-- and risk losing millions in sponsorships for the tournament and a flood of negative publicity in the process. Picking an escape route from Sherman was probably easier.

History has shown that bad publicity doesn’t bother the members of Augusta National. All of Martha Burk’s chanting and protesting outside of the club gates in 2002 only strengthened the resolve of then-president Hootie Johnson to refuse to admit a woman “at the tip of a bayonet.”

He never changed the policy, and Billy Payne, the current president of the club, has not said whether he’ll change it either.

And why should they? Augusta National is a private club and has always had the legal right to do as it pleases and invite whomever it wants to join, even if those policies anger people.

They now admit African American men as members and occasionally invite women to play the course as guests. Even Hootie invited the women’s golf team from University of South Carolina to practice there.

The real question is what will IBM, IBM’s board, and IBM’s customers do if Augusta National does not extend an invitation to Ms. Rometty and the publicly-traded company subsequently chooses to sponsor the Masters again anyway.

Can you imagine the vice president of marketing going into Rometty’s office to recommend that IBM send more money to Augusta, even though the CEO herself is not welcome among the membership? I really can’t.

And I assume that the leaders of Augusta National really can’t either, because despite politicians’ recent and wrong assumptions about the South, nearly all of us have running water, horseless carriages and calculators that help an organization like Augusta National figure out the bottom line.

Although women are a tiny percentage of CEOs in America today, their numbers are growing and will continue to do so. Women are now the majority of the work force, the majority of consumers, and the majority of college students.

They will also eventually run a significant number of Fortune 500 companies and make all the decisions that CEOs currently make, including how to spend advertising dollars.

In that important way, change has already come to Augusta National, whether their all-male board approves it or not. Unlike 2002, when an unwelcome woman stood outside the gates of the Masters tournament yelling at the men inside to change their ways, another woman now sits atop a company that makes the Masters possible, and she has the power to decide if she’ll sponsor the tournament at all.

Ginni Rometty may not be invited to join Augusta National this year or any year. But for the first time ever, a woman is playing the game.

Patricia Murphy is an Atlanta-based writer. She is the founder of and a contributor to the Daily Beast. Previously, she covered Congress for Politics Daily.