Green’s Dictionary of Slang

one-on-one n.

1. (orig. US) a fight between two individuals (as opposed to a gang fight or an unequal competition); thus used of a two-person basketball game.

[US]Current Sl. IV:1.
[US]W.D. Myers Won’t Know Till I Get There 85: [W]e changed and went to the park and played two games of one on one.
[US]Simon & Burns Corner (1998) 254: Boo thought it was an invitation to a one-on-one, but when he started out the door of the shopping pavillion, he realized that the entire Stricker and Ramsay crew [...] was following him.
[UK]K. Sampson Outlaws (ms.) 21: Last day of school we had a big one-on-one right outside the gates.
[UK]G. Krauze What They Was 163: Up n coming youngers who can’t win a one-on-one.

2. see one-and-one n.2