Expected Rolls to Hit (Geometric)
Mean rolls to first success plus 50/90/99% confidence thresholds. Based on independent Bernoulli trials.
How this is calculated
E[X] = 1/p · Var[X] = (1-p)/p² · SD[X] = √((1-p)/p²). The k-th percentile of the geometric CDF is ceil(log(1-k)/log(1-p)).
For multi-copy targets, multiply the expected value by the negative-binomial factor (n/p).
