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A game that is 1-4 players has a multi-player mode that can support up to four players simultaneously.
On console games that use split-screen multi-player, four is the most commonly-seen limit on the number of players; this is due to the screen resolution (since each player has their own section of the screen, the more pieces you section off, the more detail you lose in each section) and the number of controller ports available. It should be noted that this is not a hard-and-fast rule as there are various ways to deal with these issues (e.g. networked consoles, single-screen gameplay, controller sharing, etc...).