Hero Academy may be the first mobile game I really loved. It's reminiscent of one of my favorite PS1 games, Final Fantasy Tactics, and basically a more fantastical version of chess. Choose a class (trolls, humans, undead, etc.) and take turns, asynchronously battling friends. Each character has its own special abilities and the length of each game is perfect (usually 20-30 moves).
Robot Entertainment ported the game to Android and the Mac since I first started playing, and added tons of new content. cc @timithmcdoyle@kellymcgrath
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