Calculating the Odds of Winning in the Well Game: A Comprehensive Guide

In summary, the conversation discusses a game called "well" which is similar to Sudoku and involves drawing numbers from 9 different colored areas to form lines. The conversation also includes a discussion on how to calculate the odds of having 1-8 lines in the game and possible strategies for winning.
  • #1
ryan8200
7
0
https://www.physicsforums.com/attachments/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:
https://www.physicsforums.com/attachments/46169

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

Anyone can help me or give me some hints?
 
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  • #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.
 
  • #3
dikmikkel said:
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.

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
 
  • #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.
 
  • #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:

1. What is the definition of "Well Game Probability"?

Well Game Probability refers to the mathematical likelihood of a specific outcome occurring in a game, often involving a well or similar structure. It is typically calculated by analyzing the rules and variables of the game and using probability theory to determine the chances of different outcomes.

2. How is Well Game Probability different from regular probability?

Well Game Probability specifically applies to games that involve a well or similar structure, whereas regular probability can be applied to any type of scenario or event. Additionally, well game probability often involves more complex calculations and considerations, such as the number of players and their individual strategies, whereas regular probability may involve simpler calculations.

3. How is Well Game Probability used in real-life applications?

Well Game Probability can be used in various real-life applications, such as analyzing the chances of winning a board game or predicting the outcome of a sports match. It can also be used in decision-making processes, such as determining the best strategy to use in a game or making informed choices in gambling scenarios.

4. Are there any limitations to Well Game Probability?

Like any form of probability, Well Game Probability has limitations and may not always accurately predict the outcome of a game. It is based on mathematical calculations and does not take into account external factors, such as luck or human error. Additionally, the more complex the game, the more difficult it may be to accurately calculate the Well Game Probability.

5. How can someone improve their understanding of Well Game Probability?

To improve understanding of Well Game Probability, it is helpful to have a strong foundation in probability theory and mathematical concepts. Additionally, practicing with different games and scenarios can improve one's ability to calculate and predict Well Game Probability. Consulting with experts or reading relevant literature can also provide valuable insights and knowledge.

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