diff options
| -rw-r--r-- | preroll.go | 19 |
1 files changed, 11 insertions, 8 deletions
@@ -1,4 +1,4 @@ -/* Copyright (C) 2011, 2013-2014, 2017 Luke Shumaker <lukeshu@sbcglobal.net> */ +/* Copyright (C) 2011, 2013-2014, 2017, 2019 Luke Shumaker <lukeshu@sbcglobal.net> */ package main import ( @@ -35,14 +35,17 @@ func rollSpec(spec string) (mean float64, variance float64) { dice = 1 } - // mean is E(X) + // - Let 'd' be the die_size + // - Let 'X' be the the uniform random variable that is the result of a 1d${d} roll + // - E(X) = (1+d)/2 mean = float64(1 + die_size)/2.0 - - // sum is Σi² for i=1..die_size - sum := (die_size*(die_size+1)*(2*die_size+1))/6 - // mean2 is E(X²) - mean2 := float64(sum)/float64(die_size) - variance = mean2-(mean*mean) + // - Var(X) = E(X²)-E(X)² + // - E(X²) = (Σi² for i=1..d) / d + // = ¹/₆d(d+1)(2d+1) / d + // = d(d+1)(2d+1) / (6d) + // ∴ Var(X) = (d(d+1)(2d+1) / (6d)) - ((1+d)/2)² + // = ¹/₁₂(d+1)(d-1) + variance = float64((die_size+1)*(die_size-1))/12.0 mean *= float64(dice) variance *= float64(dice) |