How often should the same group play the same game?

Early plays teach the game, not skill
The first two to three plays are rule-learning. Players are too focused on mechanics to develop strategy. Plan on teaching plays being slower and less fun. This is normal.
Plays 4-8 build actual engagement
Once rules are automatic, players develop strategies and discover what they enjoy. Learning accelerates here because attention shifts from "what can I do?" to "what should I do?"
Beyond 8 plays, diminishing returns appear
After many plays, games can become predictable. Optimal strategies become clear, and novelty fades. Most groups benefit from rotating to new games before boredom sets in.
Exception: Genuinely open games
Some games stay fresh through variable setups or emergent strategies. These can sustain 15+ plays. Others hit a wall at five plays. Notice which is which in your group.
Spacing matters
Playing the same game three times in a row dulls interest faster than spreading plays across weeks. Spacing lets players forget enough details to feel fresh.
The sweet spot
Most groups get maximum learning and enjoyment from 4-8 well-spaced plays of any single game before moving on. This lets mastery develop without requiring endless repetition.