As random as a coin flip...

Apparently, not that random. [Link]

Here are the broad strokes of their research:

1. If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was launched. (If it starts out as heads, there's a 51% chance it will end as heads).
2. If the coin is spun, rather than tossed, it can have a much-larger-than-50% chance of ending with the heavier side down. Spun coins can exhibit "huge bias" (some spun coins will fall tails-up 80% of the time).
3. If the coin is tossed and allowed to clatter to the floor, this probably adds randomness.
4. If the coin is tossed and allowed to clatter to the floor where it spins, as will sometimes happen, the above spinning bias probably comes into play.
5. A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity.
6. The same initial coin-flipping conditions produce the same coin flip result. That is, there's a certain amount of determinism to the coin flip.
7. A more robust coin toss (more revolutions) decreases the bias.

The 51% figure in Premise 1 is a bit curious and, when I first saw it, I assumed it was a minor bias introduced by the fact that the "heads" side of the coin has more decoration than the "tails" side, making it heavier. But it turns out that this sort of imbalance has virtually no effect unless you spin the coin on its edge, in which case you'll see a huge bias. The reason a typical coin toss is 51-49 and not 50-50 has nothing to do with the asymmetry of the coin and everything to do with the aggregate amount of time the coin spends in each state, as it flips through space.
A good way of thinking about this is by looking at the ratio of odd numbers to even numbers when you start counting from 1.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

No matter how long you count, you'll find that at any given point, one of two things will be true:

• You've touched more odd numbers than even numbers
• You've touched an equal amount of odd numbers and even numbers

What will never happen, is this:

• You've touched more even numbers than odd numbers.

Similarly, consider a coin, launched in the "heads" position, flipping heads over tails through the ether:

H T H T H T H T H T H T H T H T H T H T H T H T H

At any given point in time, either the coin will have spent equal time in the Heads and Tails states, or it will have spent more time in the Heads state. In the aggregate, it's slightly more likely that the coin shows Heads at a given point in time—including whatever time the coin is caught. And vice-versa if you start the coin-flip from the Tails position.

I love this. My friends and I get in friendly arguments about the randomness of dice rolls every time the topic of computer dice rollers comes up. With this information, it appears the randomness we count on is not as straight with the odds (50/50) as we would like.
With dice, I would guess that the odds would be closer to even just because of more faces (possible outcomes). But this also means that electronic dice rollers are more fair even being pseudo random rather than truly random.