It has been said that three is a magic number, but U.S. regulators seems to think it takes four carriers to make a competitive wireless marketplace. That’s the math that Sprint is going to run into if it goes forward with a bid for T-Mobile, which the Wall Street Journal recently reported the company to be considering.

Sprint and T-Mobile are the minor powers of the U.S. mobile industry. Combined, they would have 52 million post-paid customers, compared with AT&T’s 72 million and Verizon Wireless’s 95 million. The argument for merging the companies would be that they could compete better as one operator than they can on their own. This argument, however, is unlikely to pass muster in Washington.

While regulators don’t want to see Sprint or T-Mobile fail, both companies have managed to pull themselves back from the brink in recent years. Sprint, which has long been bedeviled by a lack of capital, was acquired by SoftBank in June. SoftBank, a Japanese telecom and Internet giant, said it would lay out $8 billion in capital expenditures in 2013 and 2014. In T-Mobile’s case, a failed 2011 merger with AT&T ended up being a boon. As part of its $39 billion bid, AT&T promised to give T-Mobile $3 billion in cash as well as some spectrum in major American markets if the merger didn’t go through. The breakup settlement became the foundation of T-Mobile’s rejuvenation in the U.S.

And what a rejuvenation it has been. T-Mobile added 648,000 postpaid subscribers last quarter. It has moved aggressively toward lower prices and is rethinking such standard industry practices as subsidized phones and unbelievably expensive international calling plans. It has driven larger carriers to follow suit, as AT&T did earlier this month with a discount for customers who aren’t on hardware contracts. The Federal Communication Commission has plenty of ammunition to argue that its skepticism of AT&T’s attempt to buy T-Mobile was well-founded.

If Sprint and T-Mobile can compete with the big boys on their own, why let them merge? Another argument was laid out by Tom Wheeler, the head of the FCC, in 2011 before he took his current position. Regulators, Wheeler said, could require serious conditions on a megamerger that they wouldn’t be able to put in place any other way. “Given the statutory paralysis preventing the Communications Act from keeping pace with new technology and market structures, a mutually-agreed-to set of merger terms could become the de facto regulatory template for the wireless industry,” he wrote in an article supporting the idea of AT&T’s purchase of T-Mobile.

But regulators are on the record arguing the other way, too. Both the Department of Justice and the FCC have said they think that having fewer than four national wireless carriers would pose a threat to competition. Also, Sprint and T-Mobile would end up with an enormous cache of spectrum rights, more than twice as much as Verizon or AT&T, estimates analyst Craig Moffett. This would keep the FCC from arguing that the larger carriers shouldn’t be allowed to acquire more of their own in planned auctions.

In an informal survey of former regulators and industry experts over the weekend, Moffett found a good deal of skepticism about the deal, with the consensus being that it had roughly a 25 percent chance of going through. With the deal facing those kinds of odds, it’s likely that Sprint would simply back away, since a lengthy review would carry high costs for both companies. In this case, skepticism may be a self-fulfilling prophecy.

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