Well, for starters in might have something to do with the way you are creating your hash %hash. Each time you cycle through the outer loop @start_array grows in size (by a factor of 5) so each throw of the die results in every more iterations in the inner two loops. Here is what the count looks like:

throw of die: 1:
iterations in inner two loops: 25
total iterations: 25

throw of die: 2:
iterations in inner two loops: 125
total iterations: 150

throw of die: 3:
iterations in inner two loops: 625
total iterations: 775

throw of die: 4:
iterations in inner two loops: 3125
total iterations: 3900

throw of die: 5:
iterations in inner two loops: 15625
total iterations: 19525

throw of die: 6:
iterations in inner two loops: 78125
total iterations: 97650

throw of die: 7:
iterations in inner two loops: 390625
total iterations: 488275

throw of die: 8:
iterations in inner two loops: 1953125
total iterations: 2441400
...
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Did you mean for @start_array to be growing in size this way? By dice throw 10, @start_array will have 5 to the 10th power number of elements and the 10th throw will require 5*11 iterations to complete.