Single-electron pulse-height spectra were measured in 0.6 and 1.2 mm parallel-plate chambers developed for the TOF system of the ALICE/LHC-HI experiment. Mixtures of Ar with ethane, isobutane, and SF 6 were studied. The observed spectrum shows a clear peak for all gases, suggesting efficient single-electron detection in thin parallel-plate structures. The pulse-height spectrum can be described by the weighted sum of an exponential and a Polya distribution, the Polya contribution becoming more important at higher gains. Additionally, it was found that the maximum gain, above 10 6, is limited by the appearance of streamers and depends weakly on the gas composition. The suitability of each mixture for single-electron detection is also quantitatively assessed.