# Coin Toss and Coin Spin

1. Feb 14, 2005

### Icebreaker

From http://mathworld.wolfram.com/CoinTossing.html

Can someone explain this to me? I can't see why this is the case. Is this statement the result of some kind of mathematical proof or a statistical study?

2. Feb 14, 2005

### polyb

This one is pretty neat Icebreaker, after a quick search this is what I found. Appaerently the work was done by Persi Diaconis(homepage link) who apparently found that because of the extra weight on one side of the coin it was biased when you spin it. You should be able to find some links through his homepage. Here is a write up from science news that gives a quick outline of this interesting research:

Toss Out the Toss-Up: Bias in heads-or-tails

On Wikipedia there is a section on Coin Flipping that also references this phenomena. There are more details and links to the articles that goes further into why this happens. Enjoy and thanx!

3. Feb 15, 2005

### HallsofIvy

There is, of course, no way to prove that mathematically because in mathematics we have to start with assumptions about the basic probabilities.

The only way to prove such a statement would be to actually DO it: spin a penny a large number of times and see what happens.

I think I have heard that the reason that happens is that when the penny is stamped out, the die is never perfectly perpendicular.

4. Feb 15, 2005

### Icebreaker

Yes, but the problem is that it wasn't written if the fact was obtained by experiment, or, with the assumption of a perfect coin, was somehow derived. There could have been some fallacy with the "perfect coin" assumption.

I've always known that a coin flip was biased, but I had no idea that there is such a huge difference when the coin is spun.

5. Feb 15, 2005

### polyb

OK guys, before you run amock have a look at the paper co-authored by Diaconis. From his home page at Stanford:

DYNAMICAL BIAS IN THE COIN TOSS

It's 31 pages long and very detailed. Apparently not only is there emperical evidence to support the bias but there is also a rigorous mathematical description to back it up. Here is the abstract:
Seems there is a lot more to coin flipping than meets the eye!

6. Feb 17, 2005

### Icebreaker

Which coin do they toss before a superbowl game?

7. Feb 17, 2005

### polyb

What do you mean 'which coin'?