In Wason’s selection task, participants select whichever of four cards could provide evidence about the truth or falsity of a conditional rule. As our meta-analysis of hundreds of experiments corroborates, participants tend to overlook one of the cards that could falsify the rule. 15 distinct theories aim to explain this phenomenon and others, but many of them presuppose that cards are selected independently of one another. We show that this assumption is false: Shannon’s entropy for selections is reliably redundant in comparison with those of 10,000 simulated experiments using the same four individual probabilities for each real experiment. This result rules out those theories presupposing independent selections. Of the remaining theories, only two predict the frequencies of selections, one (due to Johnson-Laird & Wason, 1970a) provides a better fit to the experimental data than the other (due to Klauer et al., 2007). We discuss the implications of these results.