No browser version required. At first I didn't really get it, but after doing the jump/roll to go up a ramp and seeing my character roll all the way back down the idea of a highly-committal "jump" like this in a 3d platformer became really interesting to me. I think you also found a way to nail the theme without any randomness. Not because your character is a die, but because each time you jump you're agency is briefly disabled and you just have to trust that you'll stop rolling before going off a ledge (though it still feels completely fair). So you basically can't completely predict how your jump/roll will end, but not thanks to randomness just thanks to the physics being too complicated to predict. Very well done.
My only minor point would be that it would be nice if the roll ended a little sooner, I don't think it works to let you move faster than walking only because of how long it takes once you've stopped to stand back up.