Stairs problem: dynamic programming solution

stairs.py

from decimal import *

def count_ways(n, max_step_size=2):
    table = [Decimal(1), Decimal(1), Decimal(2)]
    assert len(table) >= max_step_size

    for i in xrange(3,n+1):
        table.append(sum(table[i-max_step_size:i]))

    return table[n]

def probability(n):
    return count_ways(n, 2) / count_ways(n, 3)

print probability(2000)