Silence, Mumchance was a game of chance with dice, in which silence was indispensable. (Mum is connected with mumble; German, mumme, a muffle; Danish, mumle, to mumble.)
And for `mumchance,' howe'er the cehane may fall, You must be mum for fear of spoiling all.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Mumchance from Infoplease: