I'm still looking for an intuitive or ELI5 explanation of the mechanism for this bias.
The original paper says:
The standard model of coin flipping was extended by Persi Diaconis who proposed that when people flip a ordinary coin, they introduce a small degree of precession’ or wobble—a change in the direction of the axis of rotation throughout the coin’s trajectory. According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up. Consequently, the coin has a higher chance of landing on the same side as it started.
Another coin toss experiment[1] site says this:
The basic reason is that, instead of rotating around a horizontal axis as one might imagine, a typical tossed coin is rotating around a tilted axis which is precessing in 3-space, and this entails a certain degree of "memory" of the initial parameters.
The Diaconis paper[2] has the definitive explanation but it's hardly intuitive. I got a feel for why it is, but I can't do an ELI5. The best I'm able to write is this: A human being is likely to introduce some precession in the coin toss. If there is precession, then the angular momentum vector is going to spend more time in the heads direction if starting from heads, and that accounts for the bias.
What I think would work well for an ELI5 is an animation of a coin toss showing the angular momentum vector sweeping out a region during its flight, and showing it spends slightly more time pointing toward heads.
Perhaps it helps to imagine someone had a "screwy thumb" and the coin only precesses when they "flip" it (in fact people can train themselves to do this, and its very difficult for you, the sucker, to see in the air that the coin is not rotating but just precessing!). Hopefully its obvious that whatever side is initially facing up will be the same one facing up when its caught?
The next step is not at all intuitive to me, namely that even someone trying to do a fair flip causes some precession, and that this isn't decoupled from the rotation.
The original paper says:
The standard model of coin flipping was extended by Persi Diaconis who proposed that when people flip a ordinary coin, they introduce a small degree of precession’ or wobble—a change in the direction of the axis of rotation throughout the coin’s trajectory. According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up. Consequently, the coin has a higher chance of landing on the same side as it started.
Another coin toss experiment[1] site says this:
The basic reason is that, instead of rotating around a horizontal axis as one might imagine, a typical tossed coin is rotating around a tilted axis which is precessing in 3-space, and this entails a certain degree of "memory" of the initial parameters.
The Diaconis paper[2] has the definitive explanation but it's hardly intuitive. I got a feel for why it is, but I can't do an ELI5. The best I'm able to write is this: A human being is likely to introduce some precession in the coin toss. If there is precession, then the angular momentum vector is going to spend more time in the heads direction if starting from heads, and that accounts for the bias.
What I think would work well for an ELI5 is an animation of a coin toss showing the angular momentum vector sweeping out a region during its flight, and showing it spends slightly more time pointing toward heads.
[1] https://www.stat.berkeley.edu/~aldous/Real-World/coin_tosses...
[2] http://epubs.siam.org/doi/10.1137/S0036144504446436