Fair coin tosses aren’t fair
Rocky carefully tracks his coin-based trading. The shiny penny with Honest Abe’s countenance (that sits heads-side-up on Rocky’s desk,) performs better than the new quarters with attractive state images (which sit tails-up on his desk.)
An intriguing academic paper explains this — finding that Rocky’s coin toss is biased towards bullishness!
“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. For natural flips, the chance of coming up as started is about 51%.”
The paper is entitled “Dynamical Bias in the Coin Toss,” from statistics professors Diaconis and Holmes at Stanford University, and the full paper can be viewed here :
Rocky’s 51% bullish bias is consistent with the long-term upward drift of prices, but there are more sinister implications for football fans.
In the most recent professional football season, the winner of the overtime coin toss won more than 70% of the games, and since 2002, the coin toss winner is more than 60% victorious. This means that there is the possibility for manipulation, and ceteris paribus, a gambler should always bet on the team that “calls” the outcome of the toss.
Conclusion: A 1% bias is huge. In coin-tosses and in life, things ain’t fair!
[Disclosure: Rocky just tossed his penny, and found that crude oil will rise today. But his quarter says that crude oil will decline today. Accordingly, he took the day off.]