Is a coin toss fair ?
 

You may find the answer to be rather surprising ... no.
http://www.stat.berkeley.edu/~aldous...in_tosses.html
The mathematical proof is found:
http://comptop.stanford.edu/u/preprints/heads.pdf

A coin is more likely to land as it started (not accounting for you flipping it at the end, in which case it would be the opposite).

I think this is important because coin tosses are a popular and sometimes official method (sports) of "fairness".

But wouldn't the fairness be restored if no party knows the starting conditions? AFAIK, you decide for one side before the coin is tossed, before knowing the starting conditions.

I used to practice flipping coins so that I had a very good chance of getting heads or tails depending on the starting position. I'm sure a professional (ie magician) could do it nearly 100%. Just be careful who you flip with and how ;)

Yes, but can it be done ? Maybe decide the end state, put the coin in a box, shake it around, then without looking, pick it up and toss it.

Does the coin land on the ground or does one catch it and "flip it over" as some do?

Catching it may be the best thing to do. If it falls on the floor and bounces this is ok, but if it rolls or spins then that adds a huge amount of bias due to the uneven weight distribution of the coin.

At least in sports it is usually a referee that tosses the coin, not one of the players, so I would gues that comes pretty close to not knowing the starting conditions.

As long as the ref doesn't meet with the choosing team before the game, it should be ok.

As a side note, dice may also show bias if they have even small imperfections in manufacturing:
http://www.awesomedice.com/blog/353/...s-gamescience/

I would say that casino dice are better to use if you are actually gambling (like in a casino)
http://dicephysics.info/0107.htm

I particularly liked linked page since it gives lots of approaches to what data to gather. Also the main article tells what further analysis can be done with the data.
http://www.stat.berkeley.edu/~aldous...ugrad_res.html
OK

How many shuffles do you think it takes to randomize a new deck of cards ?
http://www.ams.org/samplings/feature.../fcarc-shuffle

I used to do that too and got pretty good at it.
I must try to teach myself again.

Half the time it is fair I'd guess.

The article notes that it hasn't been proven empirically, and mentions the time needed to do a useful number of flips. That sounds like a job for distributed experimentation to me - anyone for Flipping@Home?

A coin-toss is theoretically "fair," but no coin is fair, and coin tossers can certainly train themselves to cheat you. Just as can any dealer in a casino, no matter what precautions "the house" might take to prevent it. (As if "the house" actually would . . . ) Yes, they can cheat you, and no, you will not see it being done.