Exponential thickness frequencies of peritidal carbonate units in the Lower Ordovician Kindblade and West Spring Creek Formations at Ardmore, Oklahoma, are readily interpreted in a context of probabilities of upsection transition from one lithology to another. These largely reflect Poisson (random) processes of deposition from suspended load, traction load, and microbialitic accumulation. Although grainy to muddy particulate and cyanobacterial elements exhibit nearly equal ranges of unit thickness, carbonate generation and/or entrapment via algally mediated processes was less likely to lapse and therefore led to lower probability of transition to some other sediment type. The mean thickness of microbially bound units is roughly double those from the physical transport and deposition of particulate material. Greater persistence of algal accumulation probably related to intrinsically higher biologically induced rates of carbonate precipitation and/or binding by cyanobacteria. Stratigraphic intervals between successive occurrences of suspended load, traction load, and microbial units are also closely approximated by exponential frequency distributions for which regression slopes define probabilities of upsection recurrence of a particular sediment type. Values for grainy and algal carbonates are similar and are nearly twice that of muddy suspended-load units. Although biological processes resulted in significantly lower transition probabilities for thrombolitic bioherms and cryptalgal laminites, spatial dominance of carbonate mud across the region led to higher rates of stratigraphic recurrence and a volumetric dominance of muddy lithologies in the Ardmore sequence. Poissonian distributions of unit stratigraphic duration and recurrence suggest a significant component of haphazard variation in the type and amount of accumulated carbonate sediment. If deposition was influenced by extrabasinal forcing, such control must have been nearly random in both secular and spatial dimensions of water depth change. Stratigraphic durations and recurrences in this sequence more closely reflect the inherently stochastic nature of carbonate accumulation in epicratonic platformal settings than any influence of rhythmic eustatic forcing.