The Card Game

Each player picks one of their two piles at random and turns over one card. One player is Odds and the other is Evens for the whole game. If the two arrows are different, Odds scores. If they match, Evens scores.

Each pile carries an angle. The line between two piles shows how often the arrows come out different when those two piles are picked. Play a few hundred rounds and the percentages settle.

Now put a wall between the two players so nothing can pass between them, and play again.

PLAYER 1

✓
Wall: nothing can pass
between the two sides

PLAYER 2

✓
 
Odds (arrows differ)0–
Evens (arrows match)0–
Arrows different, by pile pairing
Player 1 pilePlayer 2 pileRoundsDifferentQuantum target
Model details

How the quantum deck is made: each round, one card goes to each player. A hidden 50:50 direction is set. One player's card shows that direction and the other shows the opposite. One of the two cards then flips with chance (1 − cos gap)/2, where gap is the angle between the two piles picked. Pile angles: Player 1 = 0° and 90°, Player 2 = 45° and 135°. The shuffled deck is a fair coin for every card.