Peter has nine four-sided (pyramidal) dice, each with faces numbered 1, 2, 3, 4. Colin has six six-sided (cubic) dice, each with faces numbered 1, 2, 3, 4, 5, 6.

Peter and Colin roll their dice and compare totals: the highest total wins. The result is a draw if the totals are equal.

What is the probability that Pyramidal Pete beats Cubic Colin? Give your answer rounded to seven decimal places in the form 0.abcdefg

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In [1]:
```from collections import defaultdict
peter = defaultdict(float)
colin = defaultdict(float)
peter[0] = 1.0
colin[0] = 1.0
for _ in range(9):
for n in range(36, -1, -1):
peter[n] = sum(peter[n-k] for k in [1,2,3,4])/4
for _ in range(6):
for n in range(36, -1, -1):
colin[n] = sum(colin[n-k] for k in [1,2,3,4,5,6])/6
print ("%.7f" % sum(peter[i]*colin[j] for i in range(37) for j in range(i)))

```
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