In Wason’s selection task, participants select whichever offour cards could provide evidence about the truth or falsity ofa conditional rule. As our meta-analysis of hundreds of ex-periments corroborates, participants tend to overlook one ofthe cards that could falsify the rule. 15 distinct theories aimto explain this phenomenon and others, but many of thempresuppose that cards are selected independently of one an-other. We show that this assumption is false: Shannon’s en-tropy for selections is reliably redundant in comparison withthose of 10,000 simulated experiments using the same fourindividual probabilities for each real experiment. This resultrules out those theories presupposing independent selections.Of the remaining theories, only two predict the frequenciesof 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 ofthese results.