For me personally, a great game is a game that I cannot stop playing. It's a game that keeps me playing all night until I either beat it, or I succumb to sleep. A great game makes me forget about eating, and drinking, and everything else in life. A great game keeps you focused on one thing, and one thing only...beating the game.
When a game captivates you so much, that you'll put everything else on hold just to beat it, you know it's great. Fortunately for me I have only played two games that fit my definition of greatness. Those games are KOTOR, and The Last of Us. Now I'm just focusing on single player games here, multiplayer is an entirely different beast. I've spent countless nights staying up for hours playing Halo 2 and Halo 3.
Well guys that's my definition of a great game. Now it's your turn. What makes a game great in your opinion?
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Any game that makes my keep thinking of it when Im not playing.