Biased Coin Flips & Math of Magic at MIT

Persi Diaconis, a professor of mathematics and statistics at Stanford, demonstrated that flips of fair (unbiased) coins can be biased. Using a contraption built to make and measure coin flips in a consistent manner, Prof. Diaconis and his co-authors found that a flipped coin will land as it started 51% of the time. This is contrary to textbook conventions where an ideal coin flip should have a 50% probability of coming up either head or tail. The title of the research paper is, Dynamical Bias in the Coin Toss, and can be downloaded by clicking the link.

There should be at least two caveats to this finding:

(1) In most real world conditions, the coin toss will neither be consistent nor take place under ideal conditions. This inconsistency actually aids in making coin flips less biased than the research would suggest.

(2) This research is consistent with the notion that coin flips are really deterministic chaotic processes rather than nondeterministic random processes. In other words, because a coin flip is highly sensitive to the conditions under which it takes place, that sensitivity makes the result less predictable (rather than the unpredictability being due to an inherent property of 'true' randomness).

When I was in elementary school, I figured out a trick whereby I could almost always guess the coin flip. My third grade teacher would have a very precise and consistent procedure for flipping and catching a coin. Just as Prof. Diaconis' research suggests, once I knew which side was 'up' at the start of a coin flip, I could simply count the revolutions in the air, see how it was caught and flipped over, and correctly 'guess' the result. My teacher was so consistent and precise that I got close to guessing correctly a 100% of the time.

Speaking of tricks, the motivation behind posting this blog entry was that I noticed Prof. Diaconis is giving a lecture on Mathematics and Magic Tricks at MIT (under the sponsorship of the Clay Mathematics Institute) tomorrow, April 25, 2006, at 7 pm. This is a public lecture, so I would urge people in the Boston/Cambridge, MA area to attend. (This is one of those times when I wish I was still living in the Boston area.)

By the way, Prof. Diaconis is a bit of a hero of mine because of the way he obtained his PhD in Mathematical Statistics at Harvard. At the age of 14, he dropped out of school and became a traveling magician, not to return to formal education again until he enrolled in evening math classes at City College New York at age 24 (and the main reason why he did that was to try to beat a casino that was using shaved dice by attempting to understand the math behind dice throws). Despite his unorthodox background, and rather raw mathematical abilities, Prof. Diaconis was able to get into Harvard based on a recommendation by legendary games guru, Martin Gardner, and the good graces of legendary statistician, Fred Mosteller.

May his story give hope to the rest of us!