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Bob is right, but that doesn't matter!

Posted By: Timothy Chow
Date: Sunday, 3 April 2016, at 2:25 p.m.

In Response To: Bob is right, but that doesn't matter! (phil simborg)

Phil wrote:

I don't think there will ever be a way of generating dice that everyone will agree is random.

I agree. However, let me review a standard protocol for generating a coin flip when neither party trusts the other:

1. Each side brings his or her own coin.

2. They stand some distance apart in full view of one another, then simultaneously toss their own coin high into the air and allow it to fall to the ground near their feet.

3. They lean over and examine their own coin without touching or even getting too near it, and call out "heads" or "tails" accordingly.

4. Still not touching anything, they each walk over to the other person's coin and confirm that its value was correctly called.

5. If both coins have the same side facing up, then the overall coin flip is deemed to be heads (so for example if both coins come up tails, the overall flip is deemed to be heads). If the two coins have different sides facing up (one heads, one tails) then the overall coin flip is deemed to be tails.

The point of this protocol is that even though you might suspect your opponent of cheating and using a non-random coin (perhaps even a double-headed coin), the overall coin flip will be random as long as the part you control is random. For example, if your opponent's coin is double-headed but your coin is fair, then it will still be the case that both coins come up heads half the time, and the coins come up differently half the time.

Of course if you decide to use a biased coin then your opponent might out-Sicilian you and gain an advantage—but in that case you have only yourself to blame for not using a fair coin.

There are many ways to implement the above protocol electronically. The chief difficulty is not a theoretical one but a practical one—the protocol has to be carefully designed to minimize the possibility for dishonest manipulation. For example, a player's electronic proxy has to be prevented from waiting until learning the opponent's result before generating its own flip, and must also be unable to change or repudiate the value of its own flip once it is generated.

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