Recently, I pulled out a penny from my pocket, and as I looked at it, I almost startled myself as I realized that a penny is indeed not a fair coin at all. In fact a penny is most unfair. Most of us seem to think that a penny has two sides with probability = 1/2, 1/2. But as I ran this penny through my fingers, I realized that there is a forgotten, always neglected third side, usually called the edge. Well, it is easy to see that this edge has dimension. It is not a "zero!" I even have a memory of a flipped coin rolling around on the floor, almost ending up on edge, until it finally went into an Archimedes spiral and landed on... Well, it wasn't the edge. Still, I think I have made my point that a penny is a most unfair coin. The forgotten, always neglected third side doesn't have a chance.
The question then arose, "Just how can I turn one of these three-sided unfair coins into a fair coin? It seemed the only proper thing to do. Just how can I make the probability = 1/3, 1/3, 1/3?" Well, all I have to do, I figured, is make the edge have the same area as one of the faces. But it just doesn't feel right. I mean the shape of the third edge is different than the shape of the two faces. Might the shape of this forgotten edge affect the probability? And if it does, might the surface texture of the floor affect the probability, also? ( i.e., concrete vs. carpet ). And what if we incline the floor to various angles? Is our penny going to roll down the floor on its edge or is it going to slide down on one of its faces? What is one to do? I don't know. I just know I'm on my way to the hardware store to find some three-sided coins. I'll keep you posted.
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