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A Random Walk through Middle Land

How randomness rules our world and why we cannot see it, Part 2
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Imagine that you are a contestant on the classic television game show Let’s Make a Deal. Behind one of three doors is a brand-new automobile. Behind the other two are goats. You choose door number one. Host Monty Hall, who knows what is behind all three doors, shows you that a goat is behind number two, then inquires: Would you like to keep the door you chose or switch? Our folk numeracy — our natural tendency to think anecdotally and to focus on small-number runs — tells us that it is 50–50, so it doesn’t matter, right?

Wrong. You had a one in three chance to start, but now that Monty has shown you one of the losing doors, you have a twothirds chance of winning by switching. Here is why. There are three possible three-doors configurations: (1) good, bad, bad; (2) bad, good, bad; (3) bad, bad, good. In (1) you lose by switching, but in (2) and (3) you can win by switching. If your folk numeracy is still overriding your rational brain (continue reading…)

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