Green’s Dictionary of Slang

May-game n.

In phrases

make a May-game of (v.) [the trad. Mayday pastimes]

to play games with, to trick or deceive.

1687
16901695
c.1698
J. Phillips [trans.] Cervantes Don Quixote 175: [I]f I cannot accomplish my ends, can she have a greater hatred, then for the Person, on whom she had bestow’d such marks of her favour, merely to make a May-game of her Credulity? [ibid.] 448: I’le pay my Barbers I’le warrant yee—if they think to make a May-game of Me: but let ’em fairly bring a Comb.
[UK]B.E. Dict. Canting Crew.