We can do this with binomial distributions: If each security council member has an independent 10% chance of breaking, then the chance that at least 4 of 7 will break is Thus, a stage 0 rollup has a fixed 0.2728% chance of failing. A stage 1 rollup can fail if either the proof system fails and the security council gets >= 3 failures so it can't override (probability multiplied by the proof system failure rate), or if the security council gets 6+ failures and can force an incorrect answer by itself (fixed probability) The chance that a stage 2 rollup will break is just equal to the probability that the proof system fails