Heads or Tails? Flipping Real Coins in the Actual Universe

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:

    1. The coin lands heads up.
    1. The coin lands tails up.
    1. The coin lands on its edge.
    1. The coin lands in an ambiguous position that cannot be said to be heads, tails, or on edge.
    1. The coin is irretrievably lost.
    1. 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?

The coin ‘landing on its edge’ probably depends a lot on the surface in use.
In any case I’m sure it’s a really small chance.

You could add (if you want):

  1. The coin rolls under a table.

I’ve read that a couple of wealthy poker players bet a lot on a coin toss in a Vegas casino - and the coin rolled under a table!

  1. The coin is flipped with such force that it achieves escape velocity and never comes back down.

Fiendish_Astronaut: “8. The coin is flipped with such force that it achieves escape velocity and never comes back down.”

Yes. I think this outcome can be distinguished from the irretrievably lost outcome because even if it never comes back down we might still always know where it is so it is not entirely lost.

Edited to add: Great user name/response combination.

The coin is discovered to be something other than a coin.

Actually, no, if the flipping is done on the surface of the Earth, giving the coin enough momentum to achieve escape velocity would cause it to vaporize in the atmosphere, rendering its heads/tails outcome beautifully ambiguous!

  1. A bird in flight grabs the coin in the air and flies away with it.
  2. A high powered energy device, or just lightning, reduces the coin to molten metal so that it’s heads or tails state can no longer be determined.
  3. The coin falls through a hole in the floor into a clothes dryer and enters the alternate universe with the socks.
  4. You swallow the coin. Nobody wants to know what side is up when it comes out.

In the philosophy of science, this is a good illustration of the fact that there is ultimately no distinction between something being “unknowable” versus being “too disgusting to know”. Ultimately, in information theory, the result is the same.

Somebody steals the coin in mid air (saw that in a pirate movie when I was a kid, do not remember which one).
The coin gets stuck to the ceiling. There it can be either heads, tails or skewed, but one shoud agree in advance what counts as what: is it heads when the heads side is visible from below or is it when the heads side is up? I see arguments for both interpretations.

  1. You put the coin in a sealed box with a coin flipper. The flipper is activated by a Geiger counter which will activate if there is decay in a very tiny radioactive substance - an amount that makes the chances about 50/50.
  1. Joe and Bob toss the coin , which falls onto a table top, where it slides along the surface for a second, and is about to come to a rest. Everyone sees that it has, say, tails visible, and they all say so out loud" “Heads!! Bob wins!!”… But then it continues sliding–helped along by the cat,( whose job it is to slide things along table tops), and lands on the floor, where the visible side is now seen to be tails. Joe now says, “No, I win.”
    The cat jumps down from the table and continues to bat at the coin till it slides across the room and disappears down a heating vent.

If we’re granting this, then we also have to recognize a position in between this and the unambiguous positions: You could have a position where one gambler says “it’s not on heads or tails; we should re-flip”, but the other says “But it’s closer to heads than to tails, so I should win”.

Of course, once a position between the ambiguous position and the unambiguous position is recognized, and a resolution decided upon for that, then we have a position between that position and the one with a different resolution, and so on.

I forgot numbering, those in #8 could be 15. and 16.

  1. The coins lands on tails for the rest of your life. Then someone else flips it and it comes up heads.

Clearly this machine will be a lot more complicated to construct than the OP imagined. Unless all of these options listed so far, and those yet to be stated are outcomes designed into the machine it is not providing a useful model of real world conditions.

The dog ate my coin

How would one design an actual coin that avoids a heads or tails bias? There’s a classic answer that does not depend upon the design of coin, but upon how one plays the game:

Flip the coin twice. Discard any result of H-H or T-T. If the result is H-T or T-H, accept the result. Call a H-T result a head, call a T-H result a tail. (OF COURSE you could reverse what you call the two results.)

I actually had a quarter stand on the edge after a flip. It rolled in a curved path into the next room and stood there. I can’t remember if it was leaning on something.

  1. The coin is tossed, and while it is in the air, the Earth is destroyed to make room for a hyperspatial bypass route.
  1. Any of the above plus “heads and tails become reversed” - e.g. if coin is thrown into extremely hot space that melts the metal but it spontaneously and luckily recongeals with heads on the other side.