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Connecticut Lottery officials are hoping the odds are in their favor as lawmakers again consider legislation that would allow the agency to operate keno games in the state.

The bill, H.B. 7054, has been introduced by the Finance, Revenue and Bonding Committee, which will hold a public hearing on it and several other bills Wednesday.

If passed, it would allow Connecticut Lottery Corp. to operate keno games in restaurants and bars throughout the state. The Mohegan Tribe and Mashantucket Pequot Tribal Nation already have keno at Mohegan Sun and Foxwoods Resort Casino, respectively, through a compact with the state.

Keno is an electronic lottery game in which players guess which numbers will be drawn at random by a computer and are paid based on how many numbers they guess correctly. Numbers typically are drawn every several minutes.

The game has the potential to generate more than $5 million for the state in the first year it is legal, once some startup costs are incurred, said Rep. Jeffrey Berger, D-Waterbury, co-chair of the Finance committee.

After those initial costs subside, keno is projected to generate $20 million in the second year and $30 million in the third year, conservatively, he said.

The potential money maker is being proposed a time when lawmakers are grappling with a ballooning budget deficit. Comptroller Kevin Lembo earlier this month certified that under current spending projections the state would end the fiscal year with a deficit of $172.8 million, $40 million greater than the deficit predicted by Gov. Dannel P. Malloy’s administration March 20.

The keno legislation is important on two levels, Berger said. It will bring needed money to the state and it also will “support the business model and the competitiveness” of the state lottery, which competes in “a very tough market” with nearby Massachusetts, Rhode Island, and New York all offering keno, he said.

In Kentucky, whose population is similar to Connecticut’s, keno generated about $46 million for the state during its first year in 2013, he said.

If the bill passes, 600 to 700 restaurants and bars throughout the state likely would have keno games, said Anne Noble, president and CEO of Connecticut Lottery.

“We’re very supportive and excited about it,” she said. “It’s instrumental and excellent for the state because it will drive lottery growth in the short term and the long term.”

Keno would result in increased lottery sales, bring new players into the lottery system and generate revenue for the state and the retailers that have the game, Noble said.

Connecticut Lottery has paid nearly $9.6 billion collectively to the state and retailers since it launched in 1971, she said.

“We inject a lot of money into the economy,” she said. “This is a critical way for us to continue to play that important role in the state budget.”

This isn’t the first time legislation to legalize keno has been introduced.

Former Gov. Jodi M. Rell made a strong push to bring keno to Connecticut in 2010, but critics feared doing so would violate the state’s agreement with the casinos.

Several years later, in 2013, revenue from keno was included in a proposed state budget, but it was repealed in early 2014 before it was implemented.

In the past, the matter did not get a public hearing, according to Berger.

The lottery reached out to retailers in the past, when it looked like keno was on its way to being legalized. Retailers are again enthusiastic about the prospect this time around, Noble said.

“They’re excited about it and understand that it will help their business,” she said.

The lottery also previously had done preliminary work to launch the game, so if it becomes legal this time around, “Connecticut Lottery is ready to go,” she said.

The legislation also would give Connecticut Lottery more flexibility in its marketing efforts and clarifies that only Connecticut Lottery can operate and manage the sale of lottery games in places other than the Mashantucket Pequot Tribe and Mohegan Tribe reservations.

The Finance Committee public hearing is scheduled for 1 p.m. Wednesday in room IE of the Legislative Office Building in Hartford.