E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Discharged from an obligation, acquitted.
To John I owed great obligation;
But John unhappily thought fit
To publish it to all the nation
Now I and John are fairly quit.
Cry quits. When two boys quarrel, and one has had enough, he says, Cry quits, meaning, Let us leave off, and call it a drawn game. So in an unequal distribution, he who has the largest share restores a portion and cries quits, meaning that he has made the distribution equal. Here quit means acquittal or discharge.
Double or quits. In gambling, especially in a small way, one of the players says to the other, Double or quits?that is, the next stake shall be double the present one, or the winnings shall be returned to the loser, in which case both players would leave off as they began.