The frequentists' definition of a "fair coin" is a coin that, tossed a million times, converges toward an equal number of heads and tails.
But what is meant by converges? We might imagine a plot of heads minus tails, in which an erratic line gradually smoothes into right-infinity, hugging the x-axis ever tighter.
But how many tosses is truly enough? How do the frequentists know that after 25 happy lightyears, the plot won't suddenly divorce its beloved and shoot upwards to y-infinity?
Let us design a coin to confound these quasi-intellectuals and run their casinos out of business. Create a coin that at first exhibits convergence, but after many, many flips, gradually biases completely in favor of one side.
- No external forces, e.g. magnets.
- The coin must work anywhere with Earth-like gravity.
- The coin must work 1,000 years from now, i.e. no batteries or disintegrating materials.
- The coin may be as intricate as desired, but throwable by a human, and must land only on one of two sides (provided the ground is solid enough e.g. a thin edge won't pierce the ground).
I have ideas that may produce such a coin, but so far nothing elegant enough to consider an answer. Might be off-topic, but I thought it might be interesting enough to inspire Puzzling.