Hydrophobic attraction is often a physical origin of nonspecific and irreversible (uncontrollable) processes observed for colloidal and biological systems, such as aggregation, precipitation, and fouling with biomolecules. On the contrary, blunt-end stacking of complementary DNA duplex chain pairs, which is also mainly driven by hydrophobic interaction, is specific and stable enough to lead to self-assemblies of DNA nanostructures. To understand the reason behind these contradicting phenomena, we measured forces operating between two self-assembled monolayers of duplexed DNA molecules with blunt ends (DNA-SAMs) and analyzed their statistics. We found the high specificity and stability of blunt-end stacking that resulted in the high resemblance between the interaction forces measured on approaching and retracting. The other finding is on the stochastic formation process of blunt-end stacking, which appeared as a significant fluctuation of the interaction forces at separations smaller than 2.5 nm. Based on these results, we discuss the underlying mechanism of the specificity and stability of blunt-end stacking.