Dice probability problem

[Tomi Lindberg]

Hi,

I'm trying to find a way to calculate a distribution of 
outcomes with any combination of dice. I have the basics 
done, but I'm a bit unsure how to continue. My main concern 
is how to make this accept any number of dice, without 
having to write a new list comprehension for each case?

Here's a piece of code that shows the way I'm doing things 
at the moment.

-- code begins --

# A die with n faces
D = lambda n: [x+1 for x in range(n)]

# A pool of 3 dice with 6 faces each
pool = [D(6)] * 3

# A List of all outcomes with the current 3d6 pool.
results = [x+y+z for x in pool[0] for y in pool[1]
            for z in pool[2]]

# A dictionary to hold the distribution
distribution = {}

# If outcome is already a key, adds 1 to its value.
# Otherwise adds outcome to keys and sets its value
# to 1.
def count(x):
     if distribution.has_key(x): distribution[x] += 1
     else: distribution[x] = 1

# Maps the results with above count function.
map(count, results)

-- code ends --

Thanks,
Tomi Lindberg