Check the actual player count
Some games are designed specifically for two people; others include a two-player variant. Read the relevant rules rather than assuming that removing players leaves the experience unchanged.
Choose the relationship to the game
You might enjoy direct competition, a shared puzzle or parallel choices with occasional interaction. Ask which kind of attention suits both people tonight.
Allow a learning game
A short first play can be about understanding the system. Agree how to handle questions and mistakes so that learning does not feel like an unexpected contest.
Change sides or roles thoughtfully
Different starting positions or roles can change a game. If the rules support swapping them, a second play may offer a fresh perspective. Do not invent a fairness claim for a game you have not checked.
Leave the rematch optional
A close result can make another game tempting, but either person can stop. Decide based on interest and time rather than an obligation to settle a score.