After Bret bests Bimbo at a hand of poker - thus securing Bimbo's confinement in jail for the night - he looks skyward and says, "Forgive me, Mr. Hoyle." This is a reference to Englishman Edmond Hoyle (1672-1769), who wrote a series of treatises and books establishing, and thus helping to standardize, the rules of many common card games of his day, including whist (a precursor to bridge). The card game rules he helped to standardize eventually extended to poker, although that game did not yet exist in Hoyle's lifetime. The phrase "according to Hoyle" has come to mean proper card play, according to established rules. Bret's comment presumably indicates that the "sealed" card deck the poker game had been played with was not quite as pristine as he had led Bimbo to believe.
The plot point where the town leaders force Maverick to become the town's Sheriff would be used again in one of his movies ten years later in Support Your Local Sheriff! (1969).