Another insight is that switching doors is a different action than choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities. Yet another insight is that your chance of winning by switching doors is directly related to your chance of choosing the winning door in the first place: if you choose the correct door on your first try, then switching loses; if you choose a wrong door on your first try, then switching wins; your chance of choosing the correct door on your first try is 1/3, and the chance of choosing a wrong door is 2/3. Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in "Parade", approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong . Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy . Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savant's predicted result (Vazsonyi 1999). The problem is a paradox of the "veridical" type, because the correct choice (that one should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true. The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox. Steve Selvin wrote a letter to the "American Statistician" in 1975 describing a problem based on the game show "Let's Make a Deal", , dubbing it the "Monty Hall problem" in a subsequent letter . The problem is mathematically equivalent to the Three Prisoners problem described in Martin Gardner's "Mathematical Games" column in "Scientific American" in 1959 (Gardner 1959a) and the Three Shells Problem described in Gardner's book "Aha Gotcha" . The same problem was restated in a 1990 letter by Craig Whitaker to Marilyn vos Savant's "Ask Marilyn" column in "Parade":  Under the standard assumptions, the probability of winning the car after switching is . The key to this solution is the behavior of the host. Ambiguities in the "Parade" version do not explicitly define the protocol of the host.