Understanding the Probability of Coin Toss and Spin | MathWorld

[Icebreaker]

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

More amazingly still, spinning a penny instead of tossing it results in heads only about 30% of the time (Paulos 1995).

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?

 

[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!

 

[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.

 

[Icebreaker]

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

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.

 

[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:

We analyze the natural process of flipping a coin which is caught in the hand. We prove that vigorously-flipped coins are biased to come up the same way they started. The amount of bias depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on high-speed photography are reported. For natural flips, the chance of coming up as started is about .51.

Seems there is a lot more to coin flipping than meets the eye!

 

[Icebreaker]

Which coin do they toss before a superbowl game?

 

[polyb]

Which coin do they toss before a superbowl game?

What do you mean 'which coin'?

How about this:

A Super Duper Special Superbowl Coin!

Just kidding, I really don't know but I would bet that it is one specially made for that event. Would it be biased? According to the paer if it is flipped vigorously enough it is!