We introduce a new dimension to the widely studied on-line approximate string matching problem, by introducing an error threshold parameter ∈ so that the algorithm is allowed to miss occurrences with probability ∈. This is particularly appropriate for this problem, as approximate searching is used to model many cases where exact answers are not mandatory. We show that the relaxed version of the problem allows us breaking the average-case optimal lower bound of the classical problem, achieving average case O(n log σ m/m) time with any ∈ = poly(k/m), where n is the text size, m the pattern length, k the number of differences for edit distance, and σ the alphabet size. Our experimental results show the practicality of this novel and promising research direction. Finally, we extend the proposed approach to the multiple approximate string matching setting, where the approximate occurrence of r patterns are simultaneously sought. Again, we can break the average-case optimal lower bound of the classical problem, achieving average case O(n logσ (rm)/m) time with any ∈ = poly(k/m).