Chutes and Ladders Programming Problem

Make a python simulator for the game shown above, and run simulations to figure out the average number of throws a player need to throw in order to win. Show the distribution of the dice rolls graphically. Consider how many simulations that is necessary in order to come up with an approximate result for the average dice rolls in order to win.

Things to consider:
1: You can only win if you land on the 90th tile
2: There is only one dice
3: Start position is 0 (Tile 0)

#ComputerScience

Note by Lars André Hansen
1 year, 7 months ago

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Comments

Assuming that one can only win by landing on exactly 90, it takes about 42 rolls on average to win the game. Averaging results over 10510^5 games yields this result consistently. Even averaging over 102 10^2 games gives a "reasonably" reliable idea of the number of rolls required.

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import random

countsum = 0
numtrials = 10**5

###########################################################

for j in range(0,numtrials):

    x = 0
    rollcount = 0

    while x < 90:

        x_store = x

        roll = random.randint(1,6)

        x = x + roll

        # Ladders

        if x == 1:
            x = 40
        if x == 8:
            x = 10
        if x == 36:
            x = 52
        if x == 43:
            x = 62
        if x == 49:
            x = 79
        if x == 65:
            x = 82
        if x == 68:
            x = 85

        # Chutes

        if x == 24:
            x = 5
        if x == 33:
            x = 3
        if x == 42:
            x = 30
        if x == 56:
            x = 37
        if x == 64:
            x = 27
        if x == 74:
            x = 12
        if x == 87:
            x = 70

        rollcount = rollcount + 1

        if x > 90:
            x = x_store

    countsum = countsum + rollcount


###########################################################

avrolls = float(countsum)/float(numtrials)

print avrolls

Steven Chase - 1 year, 7 months ago
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