TRENTON, N.J. — Gov. Chris Christie’s administration agreed to lower how much the private firm running part of New Jersey’s lottery had to bring in when state officials nixed a keno-style game two years ago. Now the state is allowing the game, but the company doesn’t have to promise more money.

The reworked 2015 contract between the state and Northstar New Jersey — dropping 15-year revenue projections for New Jersey by about $1 billion — has not been altered since the state last month announced its new Quick Draw game, a New Jersey Treasury Department spokesman said.

That means the lowered income targets the state agreed to will remain in place as Northstar rolls out the new game that is expected to bring in up to $20 million in the year ending June 30, 2018. As a result, while the public stands to benefit if Quick Draw increases lottery revenues, gains may not be as high as they could have been.

The treasury, which oversees the lottery, reversed itself on keno-like games because “the lottery regularly assesses the marketplace and responds with relevant product offerings,” said Will Rijksen, a department spokesman.

Even with the lowered income targets, Rijksen said, taxpayers benefit when lottery revenues increase “so the addition of Quick Draw is a positive development.”

Democratic Senate Majority Leader Loretta Weinberg said the changes don’t look like a good deal for the state and the next governor should raise the targets.

“It’s inattentive. By giving them reduced marks, they should very quickly rewrite the contract to where it was,” she said.

The New Jersey Lottery has brought in $25 billion for the state since its founding in 1970 as a public benefit to help pay for schools and higher education. Its annual sales now total about $3 billion, with about $1 billion going to the state.

The reworked deal not only dropped overall revenue targets but also lowered how much Northstar could get if it exceeded those targets, from 5 percent of net income to 3 percent. Christie touted the fact that he won certain new guaranteed revenue levels if targets are not met, but those guarantees last only through the Republican governor’s term, which ends in January.

Quick Draw is a keno-style game in which numbers are electronically drawn and displayed on TV screens at 400 retail locations. Drawings are held every five minutes.

The game has helped buoy other states’ budgets. In Michigan, where lottery sales are similar to New Jersey’s, keno was responsible for about 20 percent of sales in fiscal year 2015, according to figures compiled by Michigan’s Bureau of State Lottery.

Northstar’s track record running state lotteries overall is mixed. In Illinois, Republican Gov. Bruce Rauner fired Northstar after years of missing revenue projections. Northstar also missed targets in New Jersey. But instead of firing the company, the Christie administration reworked its contract, citing both the state’s denial of keno-style games and a national downturn in lottery revenues.

The governor signed legislation into law this year that made the lottery, valued at about $13 billion, an asset of the state’s troubled public pension fund. The move was designed to lower the pension’s unfunded liability, which the Christie administration estimates at around $50 billion. The move means that the lottery is indirectly helping public pensioners.

Steve Baker, a spokesman for the New Jersey Education Association, the state’s biggest teachers’ union, said the labor group is neutral on Christie’s transfer of the lottery and the keno authorization.

“The state has an obligation to fund the pension. How the state does that is up to the state,” he said.

Anti-gambling groups have raised concerns about the effects of the fast-paced game — drawings are every five minutes — and the potential effect on addiction rates.

But the leaders of the Council on Compulsive Gambling of New Jersey and the National Council on Problem Gambling say that as far as they know, no studies have been done specifically on keno and it’s unclear whether the game affects addiction rates.