How to chose best coin flipping machine? How to chose best coin flipping machine ?
On job interview I was asked to solve the following problem.
There is some amount of different coins, some are fair and some are not. Also there are two coin flipping machines. As a result of several coin flipping experiments a table reflecting machine outcomes was created.
Also a person was asked to flip the same coins and his outcomes were added to the same table. Resulting table has the the following format:
Coin Id | Flip cnt | P hds | P tls | M1 hds | M1 tls | M2 hds | M2 tls

where:
P hds - count of heads flipped by Person
P tls - count of tails flipped by Person
M1 hds - count of heads flipped by Machine 1
M1 tls - count of tails flipped by Machine 1 
M2 hds - count of heads flipped by Machine 2
M2 tls - count of tails flipped by Machine 2
Question:
How to determine machine that is better to use for flipping coins using data in this table? 
As I understood at the interview a "better" machine in this context is the one that has coin flipping closer to normal distribution.
Any ideas how to solve this task?
 A: In order to comparatively evaluate two entities, we need an evaluation criterion. In general, we would want to check whether the two machines are "fair", and in comparative terms, which one is "fairer" than the other. So if the "optimal" would be that each machine functions as though giving 50-50 chance to heads/tails, we would compare the empirical relative frequencies, against the $(\frac 12 , \frac 12)$ ideal situation. Problem is, our coins are not all fair. So I suppose that the flippings by the person should now function as the evaluation criterion. Namely, we would obtain the empirical frequencies from the human flippings, accept them as representing "the" distribution implied by the fair and unfair coins together, and then compare pairwise the empirical frequencies from the two machines against the human ones, by some distance measure like for example the Hellinger distance. The machine with the smaller distance from the human flippings, could then be chosen as the one representing better the biased structure of the coins.  I don't see how the normal distribution fits the picture, the comments regarding limiting behavior notwithstanding.
