But the rollout is not unfolding as anyone quite expected it to, from the seemingly unlikely businesspeople like Mr. Larson who are leading the charge to the downright odd pattern of where the first shops will open.

Seattle, for example, with a population of 652,000 the state’s largest city and perhaps most marijuana-friendly, will have only a single store initially, and a tiny one at that: 620 square feet, called Cannabis City. But Vancouver, about one-fourth Seattle’s size, in a largely conservative county that has tried to slow or stop marijuana businesses with strict land-use rules, could have three shops. Tacoma, also in a county that has tried to block marijuana businesses, may have four.

The pattern came down to chance and circumstance, said Mikhail Carpenter, a spokesman for the Washington State Liquor Control Board, which wrote the regulations and administers the system. With multiple inspections and requirements to meet, “a lot of people weren’t ready,” Mr. Carpenter said.

Only about 20 licenses out of 334 authorized by the regulations will be granted in this first wave, Mr. Carpenter said, with many would-be operators slowed by financing troubles, inspection questions or other issues. Mr. Larson, for example, applied for three licenses in three cities, and two were denied, in each case because state inspectors said the boundary line was too close to a licensed day care center.

He disagreed, but quickly gave up: “You can’t argue with the state.”

And even the shops that open will not have that much to sell, because marijuana growers got their licenses only in March, not enough time to produce a big crop. Mr. Larson expects to have perhaps two pounds, which he expects could be gone in hours, and no edible products at all, since no state-licensed marijuana food producers are up and running.