Response to Hot Hands, Streaks and Coin-flips: How The New York Times Got it Wrong (SIAM News March 2016):
I think I made it clear in my essay for the Times (which began with a reference to Tom Stoppard’s play “Rosencrantz and Guildenstern Are Dead”) that the issue in Miller and Sanjurjo is not what the coin does but what the coin flipper perceives – and that the authors are suggesting how people might acquire a belief in the gambler’s fallacy through what they think they experience. Here is how I put it:
“There is not, as Guildenstern might imagine, a tear in the fabric of space-time. It remains as true as ever that each flip is independent, with even odds that the coin will land one way or the other. But by concentrating on only some of the data—the flips that follow heads—a gambler falls prey to a selection bias.”
Read in context, the paragraph that follows, describing how the Gilovich hot-hand paper might have been flawed by the same kind of misperception, also seems clear in its meaning and intent.
I certainly didn’t say that there was a violation of the laws of probability. The whole point of the piece was to reflect on how easily the human brain, rebelling against the randomness inherent in life, can fool itself into perceiving patterns that do not exist. That is a theme of my book “Fire in the Mind: Science, Faith, and the Search for Order.” The essay in the Times was keyed to the new 20th anniversary edition.
I knew when I was writing the piece that some specialists, parsing it line by line, might quibble with some of my wording. That is something we science journalists struggle with all the time – how to translate the precision of mathematics into words and metaphors that readers will understand. There are inevitably compromises.