 For example, consider the systematic biases in people’s perception of randomness reported in some of Kahneman and Tversky’s earliest work (Kahneman &amp; Tversky 1972). For sequences of flips of a fair coin, people expect to see, even for small samples, a roughly-equal number heads and tails and alternation rates between heads and tails that are slightly higher than long-run averages (Bar-Hillel &amp; Wagenaar 1991). This effect is thought to explain the gambler’s fallacy, the false belief that a run of heads from an i.i.d. sequence of fair coin tosses will make the next flip more likely to land tails. Hahn and Warren argue that the limited nature of people’s experiences with random sequences is a better explanation than to view them as cognitive deficiencies. Specifically, people only ever experience finite sequence of outputs from a randomizer, such as a sequence of fair coin tosses, and the limits to their memory  (section 5.1)  of past outcomes in a sequence will mean that not all possible sequences of a given length with appear to them with equal probability. Therefore, there is a psychologically plausible interpretation of the question, “is it more likely to see HHHT than HHHH from flips of a fair coin?”, for which the correct answer is, “Yes” (Hahn &amp; Warren 2009). If the gambler’s fallacy boils down to a failure to distinguish between sampling with and without replacement, Hahn and Warren’s point is that our intuitive statistical abilities acquired through experience alone is unable to make the distinction between these two sampling methods. Analytical reasoning is necessary.