The governor's office did not say Tuesday whether Corbett, a Republican, would seek to rewrite the contract with Camelot. In a statement, it said he is committed to a cautious approach to the introduction of any new games that are legally allowed.
"We are confident that Camelot shares the same commitment," the administration said.
It also said Camelot's management agreement does not include video poker, video poker-like games or video lottery terminals.
The deal has drawn heavy criticism from Democratic lawmakers, a lawsuit from the union that represents state lottery employees and a warning from Democratic state Treasurer Rob McCord that he may not approve payments to Camelot if he is not convinced that its plans to expand gambling are legal.
In the letter, the senators said their concerns escalated after watching testimony at a Jan. 14 Senate Finance Committee hearing on the matter and reading through recently released documents about the management agreement with Camelot.
Also signing the letter were Majority Whip Pat Browne of Lehigh County and Sens. Robert Tomlinson of Bucks County and Kim Ward of Westmoreland County.
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