Unholy Geometry

"Do not try the parallels in that way. I know that way
all along. I have measured that bottomless night, and
all the light and all the joy of my life went out there."
~Farcus Bulyai, regarding the Fifth Postulate
From now on, after each turn, active player flip
a coin until both have landed heads twice.
Opponent's attacks miss until they have one
head, and are double effective with two. Your
attacks are double effective once you
have one head, triple with two.