>mathematically prove I'll give it a rough swing. I probably overcomplicated the endgame I describe below, and maybe make some assumptions that aren't actually

>mathematically prove I'll give it a rough swing. I probably overcomplicated the endgame I describe below, and maybe make some assumptions that aren't actually how the mechanics work, but hopefully it's understandable. The balls are about the same size as the blocks. Lets say they are infinitesimally smaller, so they can still fit down a 1 block wide tunnel. Imagine the gameplay somehow gets into the condition that both balls are in tunnels, but white in the worst way (perfectly aligned, so it just bounces off the far ends) and black in the best way (barely zigzagging in a nearly straight line, killing all wall blocks, leaving a 3 block wide tunnel in it's wake). This would result in whites tunnel rapidly shrinking. Even if white exists in a 2x1 tunnel and is getting kills, black is still killing at almost 2x the rate. White will be in their 2x1 tunnel, make it into a 3x1 tunnel, but it will become a 2x1 tunnel again by the time it's bounced a little over a block. Now suppose black then reaches the (white) end of their tunnel, scoring 3 kills in almost the same instant. There's nowhere to spawn those three that doesn't clash. The app will either crash with a null value error, or some other result that qualifies as an end condition since it would break the fundamental rules of the game.