Massachusetts Lottery officials constantly tinker with their offerings and odds to try to attract players and haul in more money for the state.

Now they will have a new way to bring in cash, by selling ads on game tickets and monitors.

The Massachusetts State Lottery Commission approved a contract yesterday that will pay the Fenway Sports Group $10,000 a month plus a percentage of whatever advertising revenue the sports-marketing spin-off of the Red Sox is able to attract for the lottery.

Treasurer Timothy P. Cahill said he thought Fenway Sports Group would be more likely to attract advertising for Keno screens between games than for scratch tickets.

"I don't imagine there's a whole lot of space on instant tickets for advertising, but it would be an option if we could come up with something," Cahill said.

He added that this is a good way "to increase revenues without putting billboards on the MBTA right-of-way or anything like that."

The Legislature authorized the Lottery Commission to seek proposals from advertising solicitors last year, and only Fenway Sports Group responded.

The contract begins May 1 and lasts for one year, if the Legislature agrees to approve the funding for the fiscal year that starts July 1, covering the final 10 months of the contract.

The contract limits Fenway Sports Group's commissions to $360,000 for the year.

Lottery officials said they did not know which potential advertisers the firm is trying to sign up.