Green’s Dictionary of Slang

1. a (game of) dice.

1931		‘William Hatfield’ Sheepmates 72: There’s too big of a mob fer one man to shout the house on his pat at a zac a pop, so you shove in a deaner a nob and flip the rats an’ mice, see? [Ibid.] 73: I think you know somethin’ about throwin’ them rats an’ mice.
1938		(ref. to 1910s) F.D. Sharpe Sharpe of the Flying Squad 170: We used to play dice with them for coppers or sixpence; Rats and Mice the game was called.
1960		J. Franklyn Dict. of Rhy. Sl.
1969		S.T. Kendall Up the Frog.

2. rice.

1967		‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxix 4/4: rats and mice: Rice.
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 14: The tucker in the bayne marie looked like it was the Michael Rodent, and he settled on a portion of rats and mice with a chow style loop the loop.