Dice

local sqrt, log, random, pi, floor = math.sqrt, math.log, math.random, math.pi, math.floor

local function gauss(mi, sigmaSquared)
    local x1, x2, w, y1, y2
    repeat
        x1 = 2.0 * random() - 1.0
        x2 = 2.0 * random() - 1.0
        w = x1 * x1 + x2 * x2
    until w <= 1.0

    w = sqrt( (-2.0 * log( w ) ) / w )
    y1 = x1 * w
    y2 = x2 * w
    return y1*sigmaSquared+mi, y2*sigmaSquared+mi
end

local function dice(N, sides)
    local mi, sigmaSquared = N*(sides-1)/2 + 1, (sides-1)*N/(2*pi)
    local y1,y2 = gauss(mi, sigmaSquared)
    y1,y2 = floor(y1+0.5), floor(y2+0.5)
    y1 = (y1<N) and N or ((y1>sides*N) and sides*N or y1)
    y2 = (y2<N) and N or ((y2>sides*N) and sides*N or y2)
    return y1,y2
end