E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
By long odds. By a great difference; as, He is the best man by long odds. A phrase used by betting men. In horse-racing, odds are offered in bets on favourite horses; so, in the Cambridge and Oxford races, long odds are laid on the boat which is expected to win.
That makes no odds. No difference; never mind; that is no excuse. An application of the betting phrase.