2 player local competitive games for mobile

My friend and I always play games on our commutes to college but it's hard to find games where: <br><br>- we can play on a single phone<br>- it's not a "pass the phone" back and forth <br>- it's not a game where the two characters have to work together <br><br>Any ideas to create games like that? <br><br>To clarify, we have a single phone and don't have any controllers. So the screen would be split in two and have to be played with our thumbs. <br><br>edit: I have a ton of simple ideas and I have a ton of complex ideas. Just looking for a "not simple, not complex" ideas. Ex: a fighting game could be complex, rock-paper-scissors could be simple.