Probably comes from the card game which is usually actually called NAP (short for Napoleon) where to go NAP means to bid that you are going to win all the tricks i.e. the best possible bid (Used to play it with my grandma).
The clue in your answer being Etymology, the origin and development of a word.

Hmm, my dictionary says: 2. Racing a tip. supposed to be a certainty to win.
Guess dictionaries are like punters, some have more confidence than others. :-)
I reckon the derivation probably supports your 'best bet' view though.

KV