BWE wrote:With the coin flip the question is why does the average hover around 50%?

Let me try a partial explanation. I expect someone else will be able to improve on it.

Flipping a coin is not random like radioactive decay is random.

When you flip a coin, you apply a torque, it spins the coin, the kinetic energy dissipates against air resistance, and then it stops spinning. If you could do that exactly the same every time, in still air, it would stop in the same way every time.

But you can't reliably apply the same flip force every time. Every time, the force is a little different, and tiny differences make the difference between it stopping on H or T. It's no more likely that you'll add a little more force next time, and it'll stop on T rather than H, or a little less, or the same, or whatever.

The difference needed to change the outcome is way smaller than the amount of control you can exercise, so the outcome seems random.

Contrast coin flips with knife flips. Table knives, that is - they aren't sharp enough to cut myself if I catch it with the blade. If I'm flipping one, I can reliably flip a half rotation 100% of the time. I can flip a whole rotation about 95% of the time. Two rotations, about 70% of the time, but the rest is either 1.5 or 2.5 rotations. The point is, I can control the flip force well enough to predict the outcome, so it's not random.

Does this help?