math.randomseed(os.time())
 
local result_pos_t = {}
local function result_pos(num, max)
	local k = num .. ',' .. max
	if not result_pos_t[k] then
		if num == 0 then
			result_pos_t[k] = (max - num) + 1
		else
			result_pos_t[k] = result_pos(num - 1, max) + (max - num) + 1
		end
	end
	return result_pos_t[k]
end
 
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 = 10
for i = 1, count do
	local res = crazy_dice(sides) - crazy_dice(sides)
	if not tally[res] then tally[res] = 1
	else tally[res] = tally[res] + 1
	end
end
 
for i = -sides, sides do
	print(i, (tally[i] or 1) / count)
end

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