from random import randint

playing_board = [0] * 100 # board is 100 positions long
position = 0 # player starts at position 0 on the board
while position < 100: # end when position moves off board
    playing_board[position] = 1 # player was here
    position += randint(1, 6) # throw a die and move

# what's the probability that playing_board[n] == 1?
# there is a prize if you land on position n
# but a cost for playing the game
# let's run N times

def probability():
    N = 10000 # maybe this isn't big enough
    successes = [0] * 100
    for _ in range(N):
        playing_board = [0] * 100
        position = 0
        while position < 100:
            successes[position] += 1
            position += randint(1, 6)
    ret = []
    for s in successes:
        ret.append(s / N)
    return ret

# what if we add a rule
# if the player lands on square 99, they teleport back to 0

playing_board = [0] * 100 # board is 100 positions long
position = 0 # player starts at position 0 on the board
while position < 100: # end when position moves off board
    playing_board[position] = 1 # player was here
    position += randint(1, 6) # throw a die and move
    if position == 99: position = 0 # snakey snake

# can you calculate the probability of the prize now?