I would somewhat agree with Jumpin, But in my opinion a casual game is any game that can be picked up & put down without any requirement needed to get good at it.
For example I can pick up final fantasy or even demons & dark souls whenever I want & play them, & though I may not find them overly difficult (though monster hunter still kicks my ass often, as do some of the FF hunts, and bayonetta on climax difficulty) I dont have to 'train' or compete to stay good at them. These would be casual (to me) despite some (such as the souls games) being though of as hardcore by many reviewers. If I can beat every boss by playing an hour every other day for a few months, thats not that hardcore.
Hardcore games would be games like marvel v capcom 3 where if I wanted to be good & stay good I would have to put serious & concerted time in daily playing, training & generally competing with other users. The same applies with games like COD, halo & the other FPS's.
The first set of games I enjoy, the second set I avoid like the plague (normally) because I have neither the time nor inclination to do what it takes to get good at them, (outside of not enjoying the style on principle, but thats purely taste based) hence being a casual gamer. In my opinion this would be the difference between the two
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Favourite Games of 2013 1.Tomb Raider(PS3) 2.Atelier Ayesha(PS3) 3.Virtues Last Reward (Vita)







