A local multiplayer version of Battleships, to be played on the same phone.
You must place some divider (a folded up paper) halfway your phone screen. Both players get a secret base/layout and take turns shooting at each other (or do so simultaneously).
Take down all opponent ships to win!
You’d need a way to pick which square or which action without pressing the actual location, otherwise you give it away.
You could also use your hands to shield your part of the map, of course. But that would require a big part of the center to not register any taps or clicks or touches.