function throwDices(dices, sides, plus)
    local dmgs = {}
    local lch = 1 / sides
    for dmg = 1, sides do
        dmgs[dmg+plus] = lch
    end
    for side = 1, dices-1 do
        local nextDmgs = {}
        for dmg, chance in pairs(dmgs) do
            for nDmg = 1, sides do
                local tDmg = dmg+nDmg
                nextDmgs[tDmg] = (nextDmgs[tDmg] or 0) + chance*lch
            end
        end
        dmgs = nextDmgs
    end
    return dmgs
end

--for i, v in pairs(throwDices(2, 4, 0)) do
  --print( i, v)
--end

function extendStep(beforeStep, dmgs, stepN, finishVars)
    local results = {}
    local newHp
    local isFinish = true
    for hp, chance in pairs(beforeStep) do
        for dmg, dChance in pairs(dmgs) do
            newHp = math.max(0, hp - dmg)
            if newHp == 0 then
                finishVars[stepN] = (finishVars[stepN] or 0) + chance*dChance
            else
                isFinish = false
                results[newHp] = (results[newHp] or 0) + chance*dChance
            end
        end
    end
    return results, isFinish
end

function battle(startHp, dmgDistribution, fChanceFormat)
    fChanceFormat = fChanceFormat or function(chance) return chance end
    local finishVars = {}
    local current = {[startHp]=1}
    local i = 0
    local isFinish = false
    while isFinish == false do
        i = i + 1
        current, isFinish = extendStep(current, dmgDistribution, i, finishVars)
    end
    local averageStrikes = 0
    print()
    print("strike#", "chance to die")
    for stepN, chance in pairs(finishVars) do
        averageStrikes = averageStrikes + stepN * chance
        print(stepN, fChanceFormat(chance))
    end
    print()
    print("average strikes", averageStrikes)
end

print("Start battle 18 hp vs 2d6+1 dmg")
battle(18, throwDices(2, 6, 1)) -- hp = 10, damage = 2d6+1
print("/end battle")
print("-----------")
print()
print("Start battle 18 hp vs 2d6+1 dmg (format with %)")
battle(18, throwDices(2, 6, 1), function(chance) return chance*100 .. "%" end) -- hp = 10, damage = 2d6+1
print("/end battle")
print("-----------")

print()
print("Other examples. hp=10, dmg 2-3, and 20% chance x3 damage")
battle(10, {[2]=0.4, [3]=0.4,  [6]=0.1,  [9]=0.1})

print("program running time", os.clock())