Alien RPG Dice Table

P(b, s) + (1 - P(b, s)) * P(b, s+1)

#!/usr/bin/env lua

-- Chances of success and failure on a single die
local SUCCESS = 1/6
local BASE_NO_RESULT = 5/6
local STRESS_NO_RESULT = 4/6
local PANIC = 1/6
local NO_PANIC = 5/6


local function panic_action(stress)
    if stress <= 3 then
       return 0
    end
    if stress >= 9 then
       return 1
    end
    return (stress - 3) / 6
end

local function base_success(base)
    return 1 - (BASE_NO_RESULT ^ base)
end

local function stress_no_panic(stress)
    return NO_PANIC^(stress)
end

local function stress_panic(stress)
    return 1 - NO_PANIC^(stress)
end

local function factorial(n)
    if n <= 1 then
        return 1
    end
    return n * factorial(n - 1)
end

local function exact_stress_result(ndice, nsuccess, npanic)
    if (nsuccess + npanic) > ndice then
        return 0
    end
    local nremain = ndice - nsuccess - npanic
    return 
        (factorial(ndice) / 
         (factorial(npanic) * factorial(nsuccess) * factorial(nremain)))
        * SUCCESS^nsuccess
        * PANIC^npanic
        * STRESS_NO_RESULT^nremain
end

local function stress_success_no_panic(ndice)
    -- TODO: simpler way to get same result?
    local result = 0

    for nsuccess = 1, ndice do
        result = result + exact_stress_result(ndice, nsuccess, 0)
    end

    return result
end

local function stress_success_with_panic(ndice)
    -- TODO: simpler way to get same result?
    local result = 0

    for nsuccess = 1, ndice do
        for npanic = 1, (ndice - nsuccess) do
            result = result + exact_stress_result(ndice, nsuccess, npanic)
        end
    end

    return result
end

local function no_success(ndice)
    return BASE_NO_RESULT ^ ndice
end

local function success_1(base, stress)
    local pact = panic_action(stress)

    if pact == 0 then
        -- No chance of Panic Actions, so strictly based on number of dice
        return base_success(base + stress)
    end

    --[[
    The entire roll succeeds in the following conditions:
    - Base Dice Succeed, Stress Dice have no Panics
    - Base Dice Succeed, Stress Dice have Panic but no Panic Action
    - Base Dice Fail, Stress Dice Succeed with no Panics
    - Base Dice Fail, Stress Dice Succeed with a Panic but no Panic Action
    ]]
    local bsuccess = base_success(base)
    local bfail = 1 - bsuccess
    local nopact = 1 - pact

    return
        bsuccess * stress_no_panic(stress)
        + bsuccess * stress_panic(stress) * nopact
        + bfail * stress_success_no_panic(stress)
        + bfail * stress_success_with_panic(stress) * nopact
end

local function success_2(base, stress)
    local pact = panic_action(stress)

    if pact == 0 then
        -- No chance of Panic Actions, so strictly based on number of dice
        return 1 - no_success(base + stress)
    end

    --[[
    The entire roll *fails* in the following conditions
    - no succes on Base Dice or Stress Dice, with or without panic
    - Base Dice Fail, Stress Dice Succeed but have Panic and Panic Action
    - Base Dice Succeed, Stress Dice have Panic and Panic Action
    ]]
    local bsuccess = base_success(base)
    local bfail = 1 - bsuccess

    local fail = no_success(base + stress)
                 + bfail * stress_success_with_panic(stress) * pact
                 + bsuccess * stress_panic(stress) * pact

    return 1 - fail
end

local function print_table(maxbase, maxstress)
    local mb, ms = (maxbase or 10), (maxstress or 3)
    local rowbuf

    -- print header
    rowbuf = { "Base", "No Stress" }
    if ms > 0 then
        table.insert(rowbuf, " 1d")
    end
    for n = 2, ms do
        table.insert(rowbuf, string.format("%5dd", n))
    end
    print(table.concat(rowbuf, ' | '))

    rowbuf = { ":---:" }
    for n = 0, ms do
        table.insert(rowbuf, "-------:")
    end
    print(table.concat(rowbuf, '|'))

    -- print each row

    for b = 1, mb do
        rowbuf = { string.format(" %2dd ", b) }
        for s = 0, ms do
            local p1, p2 = success_1(b, s),  success_2(b, s)
            local cellstr
            if (p1 - p2) < 0.0001 then
                cellstr = string.format(" %5.2f%% ", p1 * 100)
            else
                cellstr = string.format("%5.2f-%5.2f%%", p1 * 100, p2 * 100)
            end
            table.insert(rowbuf, cellstr)
        end
        print(table.concat(rowbuf, '|'))
    end

    rowbuf = { "**panic**  ", "  " }
    for s = 1, ms do
        local p = stress_panic(s)
        table.insert(rowbuf, string.format(" %5.2f%% ", p * 100))
    end
    print(table.concat(rowbuf, '|'))

    rowbuf = { "*p-action* ", "  " }
    for s = 1, ms do
        local p = stress_panic(s) * panic_action(s)
        table.insert(rowbuf, string.format(" %5.2f%% ", p * 100))
    end
    print(table.concat(rowbuf, '|'))

end

print_table(10, 9)