About the Witcher Calculator
In The Witcher books and games, boys who train as witchers undergo the Trial of the Grasses: a series of alchemical mutations meant to grant superhuman speed, strength, and resistance to poison. The process is dangerous by design — many candidates do not survive it. This calculator does not try to reproduce exact in-universe casualty figures, since the source material never pins the survival rate to a precise percentage. Instead, it treats the trial as what it structurally is — a group of independent, identical-odds trials — and applies the standard binomial probability distribution used for exactly that kind of problem in statistics.
You enter three numbers: how many candidates go through the trial (n), the probability that any one candidate survives it (p, as a percent), and how many survivors would count as a "success" for your purposes (k). The calculator returns the expected number of survivors, the standard deviation (how much that count typically varies), the probability of reaching at least k survivors, and the single most likely survivor count.
The formula
For n independent candidates each surviving with probability p, the probability of exactly i survivors is given by the binomial probability mass function: P(X = i) = C(n, i) · pi · (1 − p)n−i, where C(n, i) is the number of ways to choose i survivors from n candidates. From this distribution:
- Expected survivors = n × p
- Standard deviation = √(n × p × (1 − p))
- P(at least k survive) = the sum of P(X = i) for i from k to n
- Most likely outcome (mode) = the integer part of (n + 1) × p
Why this formula, and what it assumes
The binomial model is the standard tool whenever you have a fixed number of independent yes/no trials that all share the same success probability — exactly the setup implied by a cohort of boys each undergoing the same trial. The two assumptions worth stating plainly: candidates are assumed independent (one candidate's outcome doesn't affect another's), and every candidate is assumed to share the same survival probability p. Neither assumption is stated as established Witcher canon — they are the standard simplifying assumptions that make the binomial distribution the right tool, and the 30% default survival rate is a commonly cited approximation for the initial mutation stage, not an official statistic. Change the survival rate input to explore any assumption you prefer.
Reading the results
A wide gap between the expected survivors and your target k, combined with a low probability of reaching k, means the odds are stacked against that outcome under your chosen survival rate. Try raising the candidate count or the survival rate to see how quickly the probability of success climbs — a hallmark of binomial problems is that probabilities can swing sharply with small changes in p when n is large.