The snake and a ladder

Computer Science Level 4

In a game of a snake and a ladder, the snake is to move up the ladder of 35 steps. If the number of steps the snake takes up the ladder is determined by a fair six-sided die such that if the number shown on the die is n n , the snake takes n n steps up the ladder.

What is the expected number of die-throws for the snake to reach its destination?


The answer is 10.47.

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Beakal Tiliksew by Beakal Tiliksew , 24, Ethiopia

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1 solution

Brock Brown
Aug 17, 2015

Python 3.4: 

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from random import randint
from time import time
def throws():
    count = 0
    position = 0
    while position < 35:
        position += randint(1, 6)
        count += 1
    return count
total_throws = 0
trials = 0
end = float(input("How long? (seconds) > ")) + time()
while time() < end:
    total_throws += throws()
    trials += 1
print ("Answer:", total_throws/trials)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

this seems a little inaccurate. n should be exactly 10 since through linearity of expectation each dice roll gives you an expected increase of 3.5 steps, so 35/3.5 = 10... This converges to that, but will take some time

Jon Trollston - 2 years, 7 months ago

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