math.randomseed(os.time())
 
local function result_pos(num, max)
	if num == 0 then
		return (max - num) + 1
	else
		return result_pos(num - 1, max) + (max - num) + 1
	end
end
 
local function memoize(fn)
	local t = {}
	return function(...)
		local k = table.concat({...}, ',')
		if not t[k] then
			t[k] = fn(...)
		end
		return t[k]
	end
end
 
local result_pos = memoize(result_pos)
 
local function crazy_dice(n)
	local size = result_pos(n, n)
	local rand = math.random(size)
	for i = 0, n do
		if rand <= result_pos(i, n) then
			return i
		end
	end
	error()
end
 
local tally = {}
local count = 100000
local sides = 30
for i = 1, count do
	local res = crazy_dice(sides)
	if not tally[res] then tally[res] = 1
	else tally[res] = tally[res] + 1
	end
end
 
for i = 0, sides do
	print(i, (tally[i] or 1) / count)
end

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