Friday, October 3, 2008

Listen to the Martingale

Just a short post to recommend Jordan Ellenberg's article in Slate about the financial meltdown. Ellenberg uses a simple explanation of martingales to illustrate the tradeoff between risk and reward.
The [martingale] is a kind of "upside-down lottery." If you play the Powerball, you'll probably lose the cost of a ticket, but you might win big. In the martingale, you'll probably win a little, but if all six numbered balls match your ticket, then the bank comes around and takes away everything you've got.
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In the article, Ellenberg refers to a little-known but interesting tidbit, which I also noted in my pamphlet Randomness and Reason - namely, that the ordinary process of coin-flipping slightly biases the coin to land the same way it started (51% vs. 49% or so). The link in Ellenberg's article is to Stanford's press release publicizing the research. Here is the actual study in case anyone wants to see:

Diaconis, P., S. Holmes, and R. Montgomery, "Dynamical Bias in the Coin Toss," http://www-stat.stanford.edu/~susan/papers/headswithJ.pdf

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