Having awoken in the middle of the night and unable to go back to sleep I began thinking about the probability of a coin landing heads up or tails up when flipped. Much has been written about the probability of heads or tails when randomly flipping a theoretical fair coin. None of that interests me at the moment. I am more interested in what happens when you flip an actual coin.
What are the possible outcomes when a coin is flipped? I can think of several:
- The coin lands heads up.
- The coin lands tails up.
- The coin lands on its edge.
- The coin lands in an ambiguous position that cannot be said to be heads, tails, or on edge.
- The coin is irretrievably lost.
- The coin is destroyed in the flipping process.
Can anyone think of some more possible outcomes?
I recall reading somewhere that most modern coins have a slight tendency to land tails up because the portrait on the heads side skews the center of gravity and this effect is especially true if the flipped coin is spinning on its edge prior to coming to rest. How would one design a real coin that avoids a heads or tails bias? I was thinking of a coin with uniform distribution of mass that only distinguishes heads from tails by color and also only flipping that coin in the dark. Does anyone have some other ideas? The probability that the coin lands on its edge could be reduced by making the ratio of edge area to head and tail surface area very small. Also, the heads and tails surfaces could be made convex to make the edge position less stable.
I would imagine that a skilled magician, after years of practice, could flip a coin and have it come up heads or tails at will. If one were to build a mechanical coin-flipping device with very controlled and precise initial conditions and flipping conditions then it would be expected that the outcome of the flips could be predicted. Indeed, it seems to me that the real challenge is to build a coin-flipping device that is not deterministic. What features would you include in your coin-flipping apparatus to ensure that the outcome is as close to random as possible?
Does anyone else with insomnia have additional thoughts on flipping real coins in the actual universe?