Saturday, April 27, 2013

The Statistical World: Part 2

As someone who use to gamble much more than I do now,  I have a visceral understanding of probability that non-gamblers do not have.

For example, if we reach this position in a game of backgammon, here are the odds of winning.

If it's black's turn: game over. Black wins 100% of the time.

If it's White's turn: There are exactly 19 rolls that win and 17 rolls that lose. It's a little better than flipping a fair coin, which would be 50%-50%. This rounds to 52.8% chance to win and a 47.2% chance to lose.

The only thing to question is if "fair dice" exist, or even "fair coins". Lots of data has been compiled and the answer is yes. Most coins in your pocket will come up heads when flipped about 50% of the time, and most dice have a roughly even distribution of the six possible numbers.

And then there is randomness in the real world. if you saw the first episode of Mad Men, you might recall that the Surgeon General's 1960 report on the effects of smoking and the subsequent publishing in Reader's Digest was a major plot point. To drive home the point that Don Draper is not just a pretty face, he comes up with the Lucky Strike slogan "It's toasted" on the spot when pitching to the worried owners.

If fact, the slogan is real and pre-dates the 1960 advertising crisis by several years. Mad Men's first episode gets several things right, including that the tobacco industry would be barred from using testimonials from doctors or even dentists in the years to come.

But what are the exact probabilities of cigarette smoking causing you harm and shortening your life? Here the numbers get hazy. Many different factors can be considered other than smoking, some that make things better and some that make things worse. It is about as far as you can get from an exact science, but serious experts take randomness into account and still claim smoking has multiple ways it can screw up your health, many of them very significant changes for the worse indeed.

Tomorrow, we talk about the randomness.

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