import random

# returns the number of jumps taken in a simulation of `pads` pads
def frog_game(pads):
    # init the counter at 1
    jumps = 1
    # take a random jump between 1 and `pads`
    jump = random.randint(1, pads)
    # now calculate the remaining jumps:
    # while the current number of pads we've jumped in total is not enough
    # to get to the other side
    while jump != pads:
        # increment the number of jumps
        jumps += 1
        # make another jump (between 1, and the number of remaining pads), and
        # add it to the running total
        jump += random.randint(1, pads - jump)
    # we break out of the loop when the number of total pads jumped is equal to
    # the total number of pads to be jumped, thus we are at the bank
    # return the number of jumps taken
    return jumps

if __name__ == "__main__":
    pads = 0
    while pads >= 200:
        pads += 5
        jumps_array = []
        # where i is incremented by 1 10,000,000 times
        for i in range(1000000):
            # add the number of jumps required by a simulation of `pads`, to a list of all jumps
            jumps_array.append(frog_game(pads))
        # print the average by summing the list of all jumps, and dividing by its length
        print("%s: %s" % (pads, sum(jumps_array) / len(jumps_array)))