How random is a coin toss? - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when asked whether coin flips and dice are truly random, as an accessible summary of Diaconis's research.
Recommended by 3 people across 3 different months, 2015 to 2021.
What it is
A short Numberphile interview with Stanford professor Persi Diaconis about the physics and probability of coin tossing. He explains the research behind "Dynamical Bias in the Coin Toss" and why a flipped coin is not perfectly fair.
What people said
Recommends orlp · 2017-09 · Mathematics Stack Exchange · on “How can I compare randomness with flipping and spinning a coin?”
Persi Diaconis has studied exactly this problem. A nice introduction to his work can be found in this Numberphile video [this video] . It addresses exactly the questions you have. Also see this related video, also by Numberphile [LINK] . There he explains that spinning is significantly worse than throwing.
Recommends K.defaoite · 2020-07 · Mathematics Stack Exchange · on “When we toss a coin, there are equal chances for both heads and tails to turn up.”
It's not **totally** random, but is random enough so that we can *model* it as a binomially distributed random variable. The mechanics of coin tossing have actually been well studied: see this Numberphile video [this video] for a short explanation of a pretty cool paper. I believe robots have been built that can flip heads every time as well.
Recommends awkward · 2021-02 · Mathematics Stack Exchange · on “Is a dice more random than a coin?”
Along the same line as the comment by @RobertIsrael, you might be interested in this YouTube video: How random is a coin toss? [this video]
Cites kjetil b halvorsen · 2015-05 · Mathematics Stack Exchange · on “Impact of weight of the dice”
Well, statisticians have indeed published about this, so it could well stay here. Voting to not close! See, for instance [LINK] or [this video] (and then search youtube for Persi Diaconis)
Cites Martin Van der Linden · 2019-12 · Mathematics Stack Exchange · on “Can true randomness come out of mathematical rules?”
On the topic of "You might argue that the apparent randomness of a coin flip is really just a result of the fine details of the starting conditions being unknown and uncontrollable, which is (or could be argued to be) different from randomness in principle", see [this video]