Green’s Dictionary of Slang

1. to avoid, to ‘get out of’.

1914		R. Tressell Ragged Trousered Philanthropists (1955) 138: Well, I don’t see ’ow we can odds it. If the people wot’s got the money won’t spend it, the likes of me and you can’t make ’em, can we?
1958		F. Norman Bang To Rights 54: As if we could odds it if he says he wants us to stay we stay.
1977		G.F. Newman Villain’s Tale 20: Whispers about one you had planned were picked up all too easily as it was, there was no way to odds it, not when you were punting around.

2. to risk, to take a chance.

1970

G.F. Newman Sir, You Bastard 124: I can’t odds being mixed up in crime.