This paper aims to enhance the application of slide attack which is one of the most well-known cryptanalysis methods using self-similarity of a block cipher. The typical countermeasure against slide cryptanalysis is to use round-dependent constants. We present a new probabilistic technique and show how to overcome round-dependent constants in a slide attack against a block cipher based on the general Even-Mansour scheme with a single key. Our technique can potentially break more rounds than any previously known cryptanalysis for a specific class of block ciphers. We show employing round constants is not always sufficient to provide security against slide variant cryptanalysis, but also the relation between the round constants should be taken into account. To demonstrate the impact of our model we provide analysis of two round-reduced block ciphers LED-64 and Zorro, presented in CHES 2011 and CHES 2013, respectively. As a first application we recover the key for 16 rounds of Zorro. This result improves the best cryptanalysis presented by the designers which could be applied upto 12 rounds of its 24 rounds. In the case of LED-64 the cryptanalysis leads to the best results on 2-step reduced LED-64 in the known-plaintext model.