The paper linked was also based on 27 observable coin flips, all made with the same coin-flipping machine. Out of those 27, 18 were between .500 and .504 in pro

The paper linked was also based on 27 observable coin flips, all made with the same coin-flipping machine. Out of those 27, 18 were between .500 and .504 in probabilities - and the paper concludes by saying that the "the classical assumptions of independence with probability 1/2 are pretty solid". Edit: Actually, 21 out of the 27 flips were in the 0.5 - .505 range.