YOU don’t need to be a mathematician or a Vegas card shark to know that, when all things are equal, the probability of flipping a coin and guessing which side lands up correctly is 50-50.
But what most people seem to forget, or so says Stanford math professor Persi Diaconis, is that things are almost never equal. In reality, the odds of guessing heads or tails correctly aren’t as even as you might think, and the reason has much more to do with physics than probability.
According to Diaconis, a natural bias occurs when coins are flipped, which results in the side that was originally facing up returning to that same position 51 per cent of the time. This means that if a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times.
Diaconis came to this conclusion after determining that no matter how hard a coin is flipped, the side that started up will spend more time facing up most of the time.
One way of thinking about this, as noted in an article from Coding Wheel, is to look at the ratio of even and odd numbers starting from one. What you’ll discover is that no matter what number you stop at, there will never be more even numbers than odd numbers in that sequence. The coin flips work in much the same way. Diaconis first realized that coin flips were not random after he and his colleagues managed to rig a coin-flipping machine to get a coin to land heads every time.       –DM