Probability of head in coin toss is not exactly 1/2! I kinda heard that usual coins are not exactly fair.
The experiment done way ago and one done relative recently could reject the null
hypothesis of p=1/2 after maybe hundreds of thousands of coin tossing!
And I heard the probability of dice is not fair either.
The obvious reason is that the dot mark which is carved into the dice causes
some weight unbalance.
I am curious if anyone know the reference for the experiments I mentioned above?
 A: There was a pretty funny paper in The American Statistician a few years ago: You can load a die, but you cannot bias a coin. As far as I can recall, they flipped beer bottle caps or some other obvious non-coins, still producing results close to 50-50.
Given the publication bias towards significant results, of any 1000 studies that tossed a coin 1,000,000 times, the 50 that found a significant difference from 0.50 will be published. Meta-analysis can uncover though that 25 would find a positive bias, and 25, a negative bias.
Read about John Kerrich for the real reasons one would want to toss a coin for a few months.
As a class activity, I had my undergrad students sand-paper a few cubes, roll them and prove to me, using Pearson $\chi^2$ test, that they indeed produced a biased die. For the time limits they had (50 to 100 rolls), you had to basically reduce one of the sides to a half to see significant results.
A: Here is a link to a review Diaconis, P., Holmes, S. and R. Montgomery, 2007, “Dynamical Bias in the Coin Toss”, SIAM Review 49, 211–235.
A: Just as a personal note.  I was a graduate student at Stanford when Persi Diaconis was an assitant professor.  Michael Cohen and I were asked to run a dice tossing experiment to see if the dice were fair.  We rolled 6 dice on a felt cloth thousands of times. However after the experiment we learned that the dice were shaved and bias favoring two sides over the other four was to be expected.  I am not surprised that persi has done many such experiments of this type and published in the reference cited by simmmons.  I also remember the coin tossing experiment of Joe Keller (discussed in the cited article) being discussed by Keller and Diaconis back in the late 1970s.
