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I describe a procedure for calculating thresholds for quantum computation asa function of error model given the availability of ancillae prepared inlogical states with independent, identically distributed errors. The thresholdsare determined via a simple counting argument performed on a single qubit of aninfinitely large CSS code. I give concrete examples of thresholds thusachievable for both Steane and Knill style fault-tolerant implementations andinvestigate their relation to threshold estimates in the literature.Comment: 14 pages, 5 figures, 3 tables; v2 minor edits, v3 completely revised,  submitted to PR

Fault-tolerant thresholds for encoded ancillae with homogeneous errors