One of my first posts on the Geomblog was about coin-tossing. A paper by Diaconis, Holmes and Montgomery had just shown that physical coin-tossing is inherently biased (the result of the toss is the same as the starting position roughly 51%) of the time.

The full paper is now available. It takes the precession of a tossed coin into account when doing its analysis, and among other things has some nice pictures of coin-tossing machines.

The following section made me wonder (emphasis added):

Poincare's arguments suggest that as a roulette ball is spun more and more vigorously the numbers become closer and closer to uniformly distributed. There are numerous studies ( [Barnhart, 1992], [Bass, 1985]) suggesting that real roulette may not be vigorous enough to wash out the initial conditions.

Hmm. So I'm writing my grant proposal for the NSF, and in the travel section I put down 2 trips to Las Vegas ? 1 to Reno ? Maybe a couple to Monte Carlo for completeness ? And what about some legal fees when I get arrested for throwing roulette balls "vigorously"?

These are important questions ....