Is the "Choose Game" an actual game?
I've never seen odds and evens played in real life, but I have seen it several times presented in media. It appears to be a reasonably common method of resolving disputes, similar to rock-paper-scissors, with the advantage of draws being less of an issue. It does have the disadvantage, however, of the different options being less distinct; it is easier to switch two fingers into three as you see what your opponent is doing, than it is to switch paper into rock.