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Comment by etskinner | Hacker News Reader

Something about the evens/odds heads/tails comparison the author makes doesn't sit right with me. If you're confident that the coin will make more than one flip, then how much cumulative time it has spent in 'heads' position doesn't matter (gambler's fallacy), since the 'catch' timing is effectively random after that first flip.

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I think I figured out whats bothering me about it. We need to figure out at what point in the rotation of the coin it can be determined to have changed to the next face. Is it when the coin is perfectly vertical? Maybe even a few degrees before because the rotational velocity will likely carry it over to the next face after making contact with your hand?

It seems that in any case the coin does spend more time statistically on the face that it was initially flipped from, but it's not exactly (num_rotations/2)+1

The actual paper linked from the article does a great job explaining this. They mention that the side facing up at any moment is a reasonable approximation for how it would land. The time each side faces up is significantly affected by the angle at which you flip, as the coin precesses during the flip. Page 4 has an excellent pair of graphs illustrating this.

Imagine that the differences were magnified, say heads 90% of the time. Would the randomness of the catch erase that difference?

Think about it as randomly picking (catching) from a bag that is 49% heads and 51% tails (time spent in that position in air).

And additionally...for the purpose used, it is "random enough".

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