rolling a die (@erugli)

_D = Dict{Tuple{Int,Int},Int}()

# count number of ways to write 't' as sum of 'l' integers in [1,6]
count = function(t,l)
    get!(_D,(t,l)) do
      if l < 1
          0
      elseif l == 1
          1 <= t <= 6 ? 1 : 0
      else
          sum(Array{Int}(map(i -> count(t-i,l-1), 1:6)))
      end
    end
end

expected_stopping_time = sum(map(l->l*(1//6)^l*sum(map(i->i*count(6+i,l-1),1:6)),3:13))
# = 9136402849//2176782336 ≈ 4.19720552574348