The psychologist Ellen Langer has shown how poorly we grasp randomness in a series of experiments. In one, she asked Yale students to watch someone flip a coin thirty times and predict whether it would come up heads or tails. The students could not see the actual flipping but they were told the results of each toss. The results, however, were rigged: all students got a total of fifteen right and fifteen wrong, but some students got a string of hits early while others started with a string of misses. Langer then asked the students how well they thought they would do if the experiment were
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