Coin Toss Fairness…
Should we go out tonight to a movie or rather stay in and get DVD’s? Not being able to decide we pull out our lucky coin and flip it saying heads we go out and tails we stay in. Tails it is! We stay in… we watch our DVD’s with the comfort that the choice was purely based on of fairness. 50/50 odds … think again.
Coin Flip
A three person team from Stanford University and UC-Santa Cruz decided the coin toss needed more research and in doing so have thrown conventional thought on its head. They have shown using a high speed camera that the coin toss is biased according to which side is on top before it is flipped. This bias is communicated as a minimum of a 51/49 odd but depending on the person flipping the coin and their technique it can be as much as a 60/40 odd. Here is how:
When one flips a coin the coin not only rotates around its own axis but also rotates in much the same way a frisbee does. Mechanics plays a large role in determining this and the degree to which the frisbee spin occurs is dependant on the technique used in the thumb to toss the coin.
It was found that the greater the frisbee spin the longer the side facing up remains facing up in each individual major axis rotation. This naturally translates into the coin being biased to its initial side facing up as the longer that side faces up the greater the chance of it still facing that direction will be when it lands. Please note that this is true as long as the surface it lands on does not materially change the outcome such as a wooden floor would.
With this new information I am curious as to why sport teams are not paying more attention to it and applied mathematics in general. In cricket for instance the toss is vitally important and if the captain can better his chances and does indeed see the initial side facing up with the landing material being grass, why then does he not employ this rule?
