Programming a Conditional Probability Problem

Hi all. I have been working my way through the Probability course, specifically the section on Conditional Probability, when I fell upon this linked problem.

By solving the linked problem recursively, you find that you have a 13\frac{1}{3} probability of winning the game.

I thought this would be a fun problem to program, so I wrote a program in Python 3 to solve this using Monte Carlo methods. The program and output of the program can be seen below.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
from random import choice
trials = 10000000                   #number of times the game is played (10,000,000)
lose = 0
win = 0
for game in range(1, trials):
    options = [1,2,3,4,5,6]         #can roll any of these numbers
    chips = 1                       #starting point for each game
    while chips > 0 and chips < 4:  #continue this loop for as long as you haven't lost or won
        roll = choice(options)      #picking random number out of options, like rolling a die
        if roll == 1 or roll == 2 or roll == 3:
            chips -= 1
        elif roll == 4 or roll == 5:
            chips += 1
        elif roll == 6:
            chips += 2
    if chips <= 0:
        lose += 1
    elif chips >= 4:
        win += 1

print(win/lose)                     #probability of winning

Output:

0.5001471644515492

Assuming the program is correct, the probability of winning the game is approximately 12\frac{1}{2}, as opposed to the original solution that states you have a 13\frac{1}{3} chance of winning the game.

Can anyone explain what is going on here (it is very possible that my code has something wrong with it, or I am misunderstanding some fundamental concept. If you catch anything please point it out :)?

Note by Sam Everett
2 years, 2 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Excellent simulation. Your code is mostly correct, except for a small typo in line 21. Can you figure it out?

Agnishom Chattopadhyay Staff - 2 years, 1 month ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...