The rubber stamps stayed packed away on Tuesday.

University leaders, once expected to wield them to expand the College Football Playoff, had already scrapped their trips to a Hilton hotel near Chicago. Instead, after top leagues spent the summer undercutting one another, the playoff’s future remained in flux on the very day some had hoped would include college sports’ equivalent of a treaty signing.

Just how long the playoff’s direction will be unsettled is difficult to predict. The hunch among many executives, though, is that the most probable outcome is the one they have been contemplating for months: expansion, eventually.

For as monolithic as college sports can sometimes appear, tribalism can carry the day for a while in the industry. Last year, the Power 5 conferences briefly split over whether to play football during the coronavirus pandemic. Now, the debate over expanding the money-printing playoff from its four-team format is sparking more parochial posturing and shape-shifting as college football eyes an even richer future.

There is no guarantee of a deal. But history and math suggest that this interlude may ultimately go down as an untidy run toward an accord for more football and more money, even if there are lingering concerns about the demands on athletes’ health and time.

There have been arguments over everything from automatic qualifiers to where playoff games should be played. Executives have weighed at least 63 different scenarios, with much of the focus lately being on a 12-team format that would invite hundreds of millions of dollars more in television money every year.

“I don’t think there’s a conference that has said it doesn’t favor expansion; the question is expanding to what and working through the issues,” said Mike Aresco, the commissioner of the American Athletic Conference, whose 2021 headliner is seventh-ranked Cincinnati.

“Could you end up at four and not expanding?” he added. “It’s possible, but I think there’s momentum.”

Aresco’s league, which will lose Central Florida, Cincinnati and Houston to the Big 12 Conference before the end of 2024, has reason to hope as much. Although Bill Hancock, the playoff’s executive director, always cautioned that expansion was not certain, many other executives spent weeks suggesting the playoff was on a glide path toward a 12-team format.

Then came the surprise round of conference realignment, including the planned movements of Oklahoma and Texas from the Big 12 to the Southeastern Conference by July 2025, and all manner of acrimony. Still, many executives believe that three factors — cash, competition and the calendar — tilt the odds toward the playoff field growing sometime this decade.

The crassest and most conspicuous of those considerations, of course, is rooted in arithmetic: A 12-team format would almost certainly make the College Football Playoff a mightier financial force than the N.C.A.A.’s Division I men’s basketball tournament. Although the N.C.A.A. is so discombobulated that it has a former Pentagon chief, Robert M. Gates, leading an effort to rewrite its constitution, it is still scheduled to pull in more than $870 million from television rights tied to the coming season’s men’s basketball tournament.

ESPN’s existing college football deal, a 12-year agreement for more than $5.6 billion that ends following the 2025 season, covers three playoff games per season. Executives have figured that a refashioned playoff with 12 teams and 11 games a season would fetch more than $1 billion a year in television rights. Navigate, a sports business consultancy, has gone as far to predict that such an expanded format would give the playoff more than $2 billion in annual income, including ticketing and sponsorships.

There is an element of on-field competition in the minds of the sport’s leaders, too.

Just 11 universities have appeared in the playoff since it replaced the Bowl Championship Series in the 2014 season, and most conferences have always or regularly been shut out of college football’s biggest games. No team from the so-called Group of 5 leagues — the American, Conference USA, the Mid-American Conference, the Mountain West Conference and the Sun Belt Conference — has appeared in the playoff.

“Having only four teams in the C.F.P. is a broken system,” George Kliavkoff, the first-year Pac-12 commissioner, said in an interview this month at Ohio Stadium, hours before Oregon upset Ohio State, which played in last season’s national title game after it won the Big Ten championship.

“Just the way it’s set up, it’s designed — and I don’t think it was on purpose or malignant — but it was designed for the rich to get richer,” added Kliavkoff, whose reservations about the expansion proposal that became public in June helped slow its approval. “If you got invited to the C.F.P. in one of the first few years, it makes it easier to recruit, which makes it easier to get back to the C.F.P., which makes it easier to recruit, and it’s a self-fulfilling prophecy.”

(Oregon, now ranked No. 3 in the Associated Press Top 25 poll, reached the debut playoff championship game, but a Pac-12 team has not been in even a semifinal since the 2016 season.)

But Kliavkoff is right that plenty of fans complain about repeatedly seeing the same teams, even if the closest Clemson Coach Dabo Swinney might come to this season’s playoff is as a pregame commentator. And at day’s end, the conferences are juggernauts of marketing and event planning that respond to focus groups and the prospect of bigger television ratings.

The executives also have time on their side — months, at least — to sort out a strategy and soothe hurt feelings and barter themselves back onto the glide path they envisioned in June. A format change taking effect after the ESPN deal’s conclusion could be hashed out a year or two from now; a deadline is still months off even if playoff leaders want a quicker shift, Hancock said.

Indeed, depending on the yardstick and the spinmeister, the power brokers could still act quicker than they did in 2012 to replace the B.C.S. Back then, commissioners, many of whom now watch from retirement as their successors work at the negotiating table, spent six months formally bickering over what became the playoff.

The very same playoff just about everyone is now looking for ways to expand.