Yes, and that's decisive if the coin is stopped during that phase. It will be facing down for the second half of the spin, which is decisive if the coin is stopped in that phase instead.

Since coins can spin with different speeds and can be stopped after different periods of time, this should be somewhat random, once it's spinning.

I think I got your point that on average, the coin is facing more up than down, since it started facing up. But I think that's only relevant if the coin is stopped in that initial phase, before making at least half a spin.

Wait, are we approaching the same argument from different sides? If we assume a random distribution of spinning speeds and a random distribution of toss durations. Then there will be some coins which experience very slow rotation, and which are also caught early enough that they don't complete even half a spin. These have to face up.

All the other combinations of spin and toss produce random faces.

[–] [email protected] 2 points 1 year ago* (last edited 1 year ago)

It's not like rolling a die, the toss has to end at a point in time and time is linear. T=1 must happen before T=2. At any given time, the difference between the amount of time spent facing up and facing down will be between 0 and T/2n where T is the total time spent in the air and n is the number of spins completed in T. The more times it spins, the smaller the maximum difference between the two but there will always be a difference. It has more chances to land face up than it does face down.

Get your head around Benford's Law. It's a headfuck but it's true for certain data generating processes. A coin toss doesn't produce the same kind of data but it is the equivalent process for a binary outcome.

E2A: actually, it is a bit like rolling a die (because they come to rest at time T too). But that's a much more complicated problem because the die doesn't just land, it bounces around a bit. There's some stuff out there about this for craps and I guess it's why the dice have to hit the back wall. Any edge due to technique must be small enough for casinos not to care about it.