Green’s Dictionary of Slang

ringie n.

(Aus./N.Z.) the keeper of the ring n. (3) in a game of two-up (a gambling game played by tossing two coins, bets being laid on the showing of two heads or two tails).

Press (Canterbury) 2 Apr. 18: A ‘boxer’ is a gratuity to the ‘ringie’ at two-up.
[Aus]Baker Popular Dict. Aus. Sl. 65: Ringie, the keeper of a two-up school.
[Aus]S.J. Baker in Le Courrier Australien (Sydney) 12 June 5/1: A ‘boxer’ is a forced contribution by players made to the ringie after each throw .
[Aus]Western Mail (Perth) 5 Sept. 11/4: A boxer is the sling made to the ringy by a successful punter in two-up.
[Aus]Newcastle Sun (NSW) 29 July 9/2-3: Players would have to rely more on the ‘ringie’ — the man who runs the game [...] A dishonest ‘ringie’ with hangers-on betting for him on the side, could rig the result with a slick turn of the wrist.
[Aus]N. Pulliam I Travelled a Lonely Land (1957) 38: The person (he’s a ‘ringie’) who runs the school takes a ten per cent cut. He deals with the Law, if it shows, bails out players who get caught, gets attorneys for them and pays their fines, if any.
[Aus](con. 1941) R. Beilby Gunner 297: ‘Wanna quid inna guts,’ the ringie chanted.