With its flexibility and simplicity in derivation, the Veytsman statistics is proved to provide a powerful tool for representing association contributions to Helmholtz free energy of lattice fluids. However, based on a heuristic argument the probability function in the statistics is in need of a critical review as to its accuracy and parameter characteristics. For these purposes different probability functions were compared with molecular simulation data of associating hard-sphere chains in this work. Association energy of lattice fluids was found to be equal to the square-well depth of off-lattice fluids. The form and parameter value for probability functions were reviewed and a new probability function was proposed for the best agreements with molecular simulation data. The proposed probability function with optimized parameter yielded the average absolute deviations of monomer fractions and compressibility factors less than 0.04 and 7%, respectively. (c) 2008 Elsevier B.V. All rights reserved.