local initial_deck = { 56, 8, 40}
math.randomseed(1337)

function reset_deck()
    local deck = {}
    for i,v in ipairs(initial_deck) do deck[i]=v end
    return deck
end

function draw(deck)
    local total=deck[1]+deck[2]+deck[3]
    local n = math.random(total)
    for i=1,3 do
        n=n-deck[i]
        if n <= 0 then
            deck[i] = deck[i] - 1
            return i
        end
    end
    error("draw is broken: n="..n.." deck="..deck[1]..','..deck[2]..','..deck[3])
end

function kelly(bank, deck)
    return bank*math.max((deck[1]-deck[3])/(deck[3]+deck[1]), 0)
end

-- what a stupid idea.
function martingale(bank, loss_streak)
    return 1666*math.pow(2, loss_streak)
end

function miller_test()
    local bankk,bankm = 10000,10000

    local loss_streak = 0
    local n,sumk=0,0
    for j = 1,500 do
        print('--- reshuffle ---')
        local deck = reset_deck()
        for i=1,50 do
            local betk = math.floor(kelly(bankk, deck) + 0.5)
            local betm = martingale(bankm, loss_streak)
            n=n+1
            sumk = sumk + betk
            x=string.format("deck={%2d,%d,%2d}, bankk=%10.0f betk=%8.0f; bankm=%8.0f betm=%5d",
                deck[1], deck[2], deck[3],
                bankk, betk,
                bankm, betm)
            local card = draw(deck)
            print(x..' drawn='..card)
            if card == 1 then 
                bankk = bankk + betk
                bankm = bankm + betm
                loss_streak = 0
            elseif card == 3 then
                bankk = bankk - betk
                bankm = bankm - betm
                loss_streak = loss_streak + 1
            else
                loss_streak = 0
            end
            if(bankm <= 0) then 
                print("Martingale is bankrupt!")
                return bankk, bankm, sumk/n
            end
            if(bankk > 1e9) then
                print("Kelly won a billion dollars after "..n.." draws; that's probably enough")
                return bankk, bankm, sumk/n
            end
        end
    end

end

bankk, bankm, avgk = miller_test()
print("Final: kelly="..bankk.." martingale="..bankm)
print("Average kelly bet was "..avgk)