1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Well Game Probability

  1. Apr 13, 2012 #1
    View attachment 46168

    This is the "well" game (in Chinese) similar to Sudoku. It has 9 areas with different colours. I will draw one number from each area. In order to have a line, at least 3 number drawn must be same row, column or diagonal. I will illustrate an example as below:
    View attachment 46169

    How to calculate the odds of having 1,2...8 lines?

    Anyone can help me or give me some hints?
     
  2. jcsd
  3. Apr 14, 2012 #2
    I use this as a general rule, but i don't really get the game:
    Every time i say and i multiply: What is the probability of a 6-sided dice showing 1 twice(and 1) in a row: 1/6*1/6 = 1/36
    Every time i say or, i add so: What is the probability of a 6-sided dice showing 1 twice in a row or 3 - three times in a row: 1/6*1/6 + 1/6*1/6*1/6 = 1/36 + 1/216 = 6/216+1/216 = 7/216.
    Hope it helps a little.
     
  4. Apr 15, 2012 #3
    The mechanism of the game is illustrated as below,I hope it will help. My main concern is how to calculate the total line formed for all possible numbers been drawn.

    Capture3.jpg
     
  5. Apr 17, 2012 #4
    You could maybe make a matrix describing the game and make a program that plays the game a hell of times and calculate the probabilities so make the program regognize the type of win diagonal etc.
    See it as a nummerical approach maybe.
     
  6. Apr 18, 2012 #5
    As a start think about this.
    How do you get a line along the top row?
    What is the probability of choosing a number in the first column top row, second column top row, third column top row?

    If you have a line in the top row is it possible to choose numbers elsewhere so that no more lines can be drawn?
    If you have a line in the top row is it possible to choose numbers elsewhere so that 1 more line can be drawn?
    If you have a line in the top row is it possible to choose numbers elsewhere so that 2 more lines can be drawn?
    etc.
     
    Last edited: Apr 18, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Well Game Probability
  1. Probability: Dice Game (Replies: 2)

Loading...