Constraint-based mining has been proven to be extremely useful for supporting actionable pattern discovery. However, useful conjunctions of constraints that support domain driven mining tasks generally need to set several parameter values and how to tune these parameters remains fairly open. We study this problem for substring pattern discovery, when using a conjunction of maximal frequency, minimal frequency and size constraints. We propose a method, based on pattern space sampling, to estimate the number of patterns that satisfy such conjunctions. This permits the user to probe the parameter space in many points, and then to choose some initial promising parameter settings. Our empirical validation confirms that we obtain efficiently good approximations of the number of patterns that will be extracted.