Originally, a dice game played in silence, though exactly how the game was played was poorly recorded. Many dictionaries specifically trace it to one played by mummers, or masked Christmas revelers, whose name is cognate to mumble or to be mum -- the game had to be playable silently because of the noise of the revel. Others, however, trace it not to Middle English but Middle German (possibly transmitted via Middle Dutch) mummenschanze, masked serenade or a game played as part of same, with Old French roots momen, mask + chance, game of chance. Either way, in England especially, there's a connotation of being silent because of stupidity, which even stronger when the word is used as a noun.
The two children stood mumchance, waiting for the sermon's end and their candy reward.