May 22nd, 2012, 1:40 pm
QuoteOriginally posted by: foxkingdomQuoteOriginally posted by: Traden4AlphaYes, the design of the head-side and tail-side would affect three critical physical variables: 1) the center of mass of the coin; 2) the heights of the rims; 3) the signed rate of change of these variables as the coin stamping die wears down. Moreover, after the coin is made, the effects of everyday usage would also create p≠0.5 effects (e.g., a dent on the head-side rim that increases the chance of tails) so that the scatter of p would grow in time and virtually all coins would become increasingly unfair.Perhaps the only fair coins in the world are those that occupy statistics textbooks and brainteasers.This thread suddenly becomes ultra-realistic.Indeed! Given that the financial markets are "ultra-realistic" with the trillions of dollars/euros/drachmas and the lives of millions/billions at stake, that seems warranted.What's crucial here is the breaking of an unstated central assumption. In the academic world, all coins are fair unless stated or until proven otherwise. In the real world, no coins are fair until proven otherwise. And given the limits of finite sample sizes, one can never prove that a real-world coin is fair, only that it is unlikely to be unfair outside a confidence interval.
Last edited by
Traden4Alpha on May 21st, 2012, 10:00 pm, edited 1 time in total.