Stop the Presses! All mathematics books must be changed. All intuitions must be reprogrammed.
For eons, we have assumed that flipping a coin is a fair experiment, with Prob(Tail) = Prob(Head) = 0.50. But is it true?
Three mathematicians--Persi Diaconis (Stanford), Susan Holmes (Stanford), and Richard Montgomery (UC-Santa Cruz)--decided to test this assumption. They built a mechanical coin flipper and used high-speed photography to carefully analyze the phyics and mathematical model underlying a coin flip.
They concluded that "vigorously-flipped coins are biased to come up the same way that they started." For those who care about the science aspects, the key factor was the angle between the normal to the coin and the angular momentum vector. Their final conclusion was that for normal flips, the probability for a coin coming up with the same face it started with is 0.51.
How will this affect life? Probably not too much...but football teams deciding starting possessions of the ball, politicians deciding tied elections, and people fighting over who has to do the dishes...they need to be aware of this result.
If you want to do some additional reading about this earth-shattering result, consider a preprint of the research results and an interesting article by Ivar Peterson about the issues involved. I should add that Persi Dioconis is a magician-turned-mathematician, and it is reported that he has "trained his thumb to flip a coin and make it come up heads 10 out of 10 times."