It was game day at the District’s city hall, where lawmakers and their staff fiddled with joysticks and mashed buttons to capture dragons flying across the screen of a machine the size of a pool table.

The game caught the attention of policymakers because of the potential prize: cash.

Just don’t call it gambling.

Games such as Dragon’s Ascent have been sprouting across the nation, evading anti-gambling laws because the winnings depend on a player’s skill instead of Lady Luck.

Players can put as much as $100 into the machine and, with a lot of patience and a keen eye, turn a profit depending on how many winged beasts they snag. In Virginia, thousands of other purported games of skill, many of which closely resemble slot machines, have arrived at convenience stores and restaurants.

Critics blast these games as thinly veiled gambling devices trying to sneak into places where casinos are outlawed. But manufacturers say they are not games of chance, with preset odds, but are closer to video-game classics such as Pac-Man, where the best players can frequently win.

D.C. officials are trying to regulate the games before they reach the nation’s capital, while lawmakers in Richmond are trying to figure out what to do with the ones that have already taken hold.

Some state lawmakers in Virginia and elsewhere want to tax them or ban them outright, calling them gambling by another name and a drain on state-run lotteries.

A bill before the D.C. Council takes a more permissive approach. It would allow games of skill at bars and restaurants with liquor licenses, limiting them to players 18 and older and capping them at no more than three per establishment. Local prosecutors would have to sign off that they are not games of chance like slot machines and roulette.

“You are not winning $150 playing Pac-Man,” said Fred Moosally, the director of the D.C. Alcoholic Beverage Regulation Administration, which proposed the restrictions. “What we don’t want is to have illegal games that are unregulated that are actually gambling devices in the District of Columbia.”

The District has no casinos, but it has legalized sports betting, with the first wagers set to be placed later this year on a city-owned mobile app and at bars and arenas.

The proposal to regulate games of skill comes after the downtown bar Penn Social, which already boasts a collection of games including Skee-Ball, table tennis and shuffleboard, sought approval for Dragon’s Ascent.

The game’s manufacturer, Georgia-based Pace-O-Matic, wants Penn Social to be the first of many D.C. establishments with its games. From the bar’s perspective, it’s a chance to draw more customers.

“On a night, say, it is Sunday when we have football games and we have a lot of people there. In between the games, they play video games,” said Geoffrey Dawson, a co-founder of Penn Social’s parent company, during a liquor board hearing. “It’s an additional source of revenue for us that really helps us stay in an extraordinarily high-rent district.”

Regulators were intrigued. A representative in the attorney general’s office concluded that Dragon’s Ascent violated no gambling laws because it is not a game of chance. The liquor board also saw no reason to say no, but it wanted to put some rules in place.

Council member Kenyan R. McDuffie (D-Ward 5) is carrying the emergency legislation proposed by liquor regulators that would place limits on the machines before Penn Social can install the game in early February.

“We want to provide some assurance that these devices aren’t winding up in the hands of young kids, and that they are not proliferating in certain types of establishments,” McDuffie said in an interview. “Right now, Dragon’s Ascent is a legal game of skill. So it’s important for the consumer protections to be in place now rather than later.”

Other lawmakers questioned the rush to regulate just because one bar wants a game that’s already legal.

“I don’t see Dragon’s Ascent at the gates with 10,000 machines that are lined up on Eastern Avenue waiting to come into the District,” council member Elissa Silverman (I-At Large) said at a recent hearing. “My concern is we will create a regulatory scheme where there’s going to be winners and losers, and it doesn’t make sense, or there are unintended consequences.”

The bill before the council is a temporary measure that would remain in place until policymakers can come up with more detailed rules, including a tax rate.

Lawmakers in Richmond are already deep in discussion about how to regulate games of skill, part of the broader debate around gambling in a historically gaming-averse state. A House subcommittee on Tuesday advanced legislation to ban them, while more modest bills to rein them in are making their way through the state Senate.

Unlike Dragon’s Ascent in the District, the games in Virginia look like slot machines, with players trying to line up symbols. Their makers say the odds aren’t set like the slot machines found in casinos, and that players could win every time if they are able to press buttons with perfect timing.

Officials from the Virginia Lottery said they have noticed ticket sales declining at convenience stores that have the slotlike machines.

“We call it the invasion of the gray machines,” said Kevin Hall, executive director of the Virginia Lottery. “They came in uninvited, unregulated and untaxed, and they are cannibalizing established and regulated forms of gaming.”

Pace-O-Matic is fighting back against total prohibition. Officials say Pace-O-Matic is a reputable operator that sought to follow the rules by going to state liquor regulators with its slotlike game Queen of Virginia. They said the real problem was that other companies have sold slot machines masquerading as games of skill.

In Virginia, the company has hired lobbyists, given nearly $400,000 in campaign contributions to Republicans and Democrats, and touted donations to charitable causes.

“We don’t want to put machines on the street without some sort of approval,” said Michael Brantley, a spokesman for Pace-O-Matic. “There’s certainly some that would like to see no gaming whatsoever, but we feel the work we are doing to help small businesses and other folks helps to bring a great coalition.”