Who Goes First? A Riddle Hidden in Your Deck
Sitting down for a playtesting session with a friend, I reach for my dice bag: gone. Left at home.
Since we are running a known, specific matchup, I propose this procedure to decide who plays first:
My opponent calls Even or Odd.
I shuffle and cut my deck, then reveal a random card and look at the collector number of it.
If the parity matches his call, he goes first. Otherwise, I go first.
Neither of us knows the collector numbers of our cards by heart. The cut is genuinely random. The procedure is followed exactly and in good faith.
Here's the puzzle:
(a) Is this a fair coin flip?
(b) If yes, why? If no, how can my opponent exploit it for an edge?
Drop your answers and thoughts in the comments. No spoilers: full solution revealed in one week!
(Hint: you don't need to know a single collector number to crack this.)