function make_dice(max_value)
    next = max_value - 1
    r = 0
    function roll()
        r += 1
        next += 1
        next %= max_value
        return next + 1
    end
    function rolls()
        r
    end
    roll, rolls
end

function advance(pos, dice)
    pos += dice()+dice()+dice()
    ((pos - 1) % 10) + 1
end

function solution21_1()
    pos_a = 8
    pos_b = 5
    dice, times = make_dice(100)
    score_a = 0
    score_b = 0
    while true
        pos_a = advance(pos_a, dice)
        score_a += pos_a
        println("a -> $pos_a ($score_a)")
        if score_a >= 1000
            r = times()
            println("$score_b $r $(score_b * r)")
            break
        end
        pos_b = advance(pos_b, dice)
        score_b += pos_b
        println("b -> $pos_b ($score_b)")
        if score_b >= 1000
            r = times()
            println("$score_a $r $(score_a * r)")
            break
        end
    end
end

using Pkg
Pkg.add("Memoize")
using Memoize

DICE = [(a,b,c) for a in 1:3 for b in 1:3 for c in 1:3]

@memoize function round(pa, pb, sa, sb)
    sum(map(DICE) do dice
            npa = pa + sum(dice)
            npa = ((npa - 1) % 10) + 1
            nsa = sa + npa
            if nsa >= 21
                [1, 0]
            else
                circshift(round(pb, npa, sb, nsa), 1)
            end
        end)
end

function solution21_2()
    round(8, 5, 0, 0)
end

solution21_2()