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Welcome to Bell's Casino. You and your partner will be playing our famous two-coin game today. We have hidden two coins under these two opaque cups. You and your partner are to guess the orientation, heads or tails, of both of the coins. Guess correctly and win $1. Guess incorrectly and lose your $1 bet.

In order to help you out, after you two have made your guess we are going to give you two a chance to back out and lose nothing. After your prediction we are going to reveal one coin to you and another coin to your partner. Together you and your partner will have an opportunity to back out, but the catch is that you two are not allowed to communicate!

Instead of communicating, you can raise either a red flag or a green flag after seeing your coin. Similarly, your partner can raise either their red flag or their green flag after seeing their coin. If you both raise the same colour flag, the game keeps going and we see if you win or lose. If you both raise different colour flags, the game stops and you lose nothing.

To ensure you don't cheat, we've separated you and your partner by 200 million kilometers and you have one minute to raise one of your flags after seeing your coin, otherwise you lose the game. (Alternatively you are your partner are separated by 400 meters and you have 100 nanoseconds to raise one of your flags.)

Good luck.

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The above casino game cannot be beaten using envelopes of marbles, but it can be beaten (i.e. positive expected value) using envelopes of entangled particles. See quantum pseudo-telepathy.