Age of Steam: production probabilities
The following python script calculates the probabilities of a given cube on a row being produced by the end of a given round in a game of Age of Steam:
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#! /usr/bin/env python
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# Author: J C Lawrence <[email protected]>
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# Date: 25 June 2009
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# Purpose: Calculate AoS cube production probabilities by row and round
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def fact (x):
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if x < 1:
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return 1
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return reduce (lambda x, y: x * y, xrange (1, x + 1))
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def xCy (x, y):
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return fact (x) / (fact (x - y) * fact (y))
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def point_p (d, n):
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c = float (xCy (d, n))
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p = (((1.0 / 6) ** n) * ((5.0 / 6) ** (d - n)))
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return c * p
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def sum_p (d, n):
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rc = 0.0
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for i in range (n, d + 1):
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rc = rc + point_p (d, i)
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return rc
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def main ():
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for p in range (3, 7):
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print "Players: %d" % p
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for r in range (1, [10, 8, 7, 6][p - 3]):
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print "\tRound %d: Row 1 - %f\tRow 2 - %f\tRow 3 - %f" \
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% (r, sum_p (r * p, 1), sum_p (r * p, 2), sum_p (r * p, 3))
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if __name__ == "__main__":
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main ()
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The results:
Players: 3
Round 1: Row 1 - 0.421296 Row 2 - 0.074074 Row 3 - 0.004630
Round 2: Row 1 - 0.665102 Row 2 - 0.263224 Row 3 - 0.062286
Round 3: Row 1 - 0.806193 Row 2 - 0.457341 Row 3 - 0.178260
Round 4: Row 1 - 0.887843 Row 2 - 0.618667 Row 3 - 0.322574
Round 5: Row 1 - 0.935095 Row 2 - 0.740378 Row 3 - 0.467775
Round 6: Row 1 - 0.962439 Row 2 - 0.827219 Row 3 - 0.597346
Round 7: Row 1 - 0.978263 Row 2 - 0.886969 Row 3 - 0.704381
Round 8: Row 1 - 0.987421 Row 2 - 0.927041 Row 3 - 0.788168
Round 9: Row 1 - 0.992720 Row 2 - 0.953411 Row 3 - 0.851205
Players: 4
Round 1: Row 1 - 0.517747 Row 2 - 0.131944 Row 3 - 0.016204
Round 2: Row 1 - 0.767432 Row 2 - 0.395323 Row 3 - 0.134847
Round 3: Row 1 - 0.887843 Row 2 - 0.618667 Row 3 - 0.322574
Round 4: Row 1 - 0.945912 Row 2 - 0.772831 Row 3 - 0.513209
Round 5: Row 1 - 0.973916 Row 2 - 0.869580 Row 3 - 0.671341
Round 6: Row 1 - 0.987421 Row 2 - 0.927041 Row 3 - 0.788168
Round 7: Row 1 - 0.993934 Row 2 - 0.959962 Row 3 - 0.868240
Players: 5
Round 1: Row 1 - 0.598122 Row 2 - 0.196245 Row 3 - 0.035494
Round 2: Row 1 - 0.838494 Row 2 - 0.515483 Row 3 - 0.224773
Round 3: Row 1 - 0.935095 Row 2 - 0.740378 Row 3 - 0.467775
Round 4: Row 1 - 0.973916 Row 2 - 0.869580 Row 3 - 0.671341
Round 5: Row 1 - 0.989517 Row 2 - 0.937104 Row 3 - 0.811313
Round 6: Row 1 - 0.995787 Row 2 - 0.970511 Row 3 - 0.897210
Players: 6
Round 1: Row 1 - 0.665102 Row 2 - 0.263224 Row 3 - 0.062286
Round 2: Row 1 - 0.887843 Row 2 - 0.618667 Row 3 - 0.322574
Round 3: Row 1 - 0.962439 Row 2 - 0.827219 Row 3 - 0.597346
Round 4: Row 1 - 0.987421 Row 2 - 0.927041 Row 3 - 0.788168
Round 5: Row 1 - 0.995787 Row 2 - 0.970511 Row 3 - 0.897210
No accommodations have been made for maps with different numbers of rounds per player count, or the insta-production rules used on most of my maps. Enjoy.