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Abstract: Most of the permutation patterns literature considers avoidance of various patterns in a set of permutations of given size. However, in many real-life situations, we do not observe the whole permutation at the beginning, but we see its elements one by one. Respectively, we often stop looking at the new elements of the permutation once a certain condition holds for the observed prefix (e.g., think of the popular secretary problem). How many of these prefixes do not have an increasing subsequence of length 3? In general, how many prefixes avoid a given permutation pattern? Some computer simulations give promising coincidences with several OEIS sequences for various stopping rules.