Well Game Probability

1. Apr 13, 2012

ryan8200

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. Apr 14, 2012

dikmikkel

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.

3. Apr 15, 2012

ryan8200

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.

4. Apr 17, 2012

dikmikkel

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.

5. Apr 18, 2012