What are the odds? New study shows how guessing heads or tails isn't really a 50-50 game



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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.

Beating the Odds: Stanford professor Persi Diaconis, pictured, has determined that a flipped coin is more likely to end up facing the same direction as when it was first tossed than not.

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.



Making a Bet: Specifically, a coin will land with its initial face up 51 per cent of the time.

He and his team then asked humans subjects do the same thing over and over, recording the results with a high speed camera. Though the results were a little more random, they still ended up with the 51-49 per cent margin.

Diaconis noted that the randomness is attributed to the fact that when humans flip coins, there are a number of different motions the coin is likely to make. For instance, he showed how coins don’t just move end to end, but also in a circular motion, like a tossed pizza.



He also found that there are ways to flip a coin where it looks like it is tumbling in the air, but in reality, it doesn’t move at all. Diaconis proved this by tying a ribbon to a coin and showing how in four of 10 cases the ribbon would remain flat after the coin was caught.

Still in the long run, his theory still held to be true. And while the margin is relatively small, it’s enough to maybe get you reconsidering using a coin toss to settle your next argument.

In another startling discover, Diaconis determined that the probability of guessing which side comes up of a spinning penny is also skewed more in one direction.



According to Diaconis’ research, a spinning penny will land tails side up roughly 80 per cent of the time.

This is because the heads side of the penny, the one with the portrait of Abraham Lincoln on it, is slightly heavier than the tail side., This causes the coin’s center of mass to lie more toward the head side than the tail.



So when it is spun, the penny will naturally fall toward its heavier size, which means there is considerably higher chance that it will land with the tail side up.

Diaconis did warn that an older penny may pick up dirt and oils over times that could sway the direction it lands in one way or another, but a relatively new coin should land tails side up more.

A magician in his spare time, Diaconis is well known for his work with probability. He was famous for discovering that it requires either five of seven shuffles, depending on the criteria, to get a deck of cards into a mathematically random order.