_TKO_
05-10-2006, 10:29 AM
The goal of this game is to stack all balls and get the highest score possible without losing.
You begin with 15 balls.
Each ball is one of 5 different colours: red, blue, yellow, green, or grey.
The colours of the balls are randomly generated at the beginning of the game.
You are able to see the colour of all the balls once the game begins.
You have a container the thickness of one ball, such that all balls will stack one on top of the other.
You are awarded 1 point for every ball that you stack.
When you stack 3 balls in a row of the same colour, the balls are removed from your stack and you are awarded 9 additional points. For example, if you stack 3 grey balls, you will be awarded a total of 12 points: 1 for each ball, plus 9 for stacking 3 in a row.
The base colour of your stack is red, such that if the first ball on your stack is red, it will be removed immediately.
Therefore, the maximum score is 60 points (15/3 = 5, 5*12 = 60), although this will not always be possible.
If you finish the game with more than 7 balls in your stack, you lose.
You begin the game with two special balls as well. You may use a special ball at any time, but you do not have to use any special balls to win the game. When you use a special ball, one of the following 4 events will occur. The event is selected randomly.
1. The colours of all remaining balls are changed to match the colour of the top marble in your stack.
2. The colours of all remaining balls are randomly changed to new colours.
3. All marbles on your stack are removed (no additional points are awarded).
4. Your special ball counter is reset to 2.
Determine, mathematically, the best strategy for getting the highest possible score on any given board.
You begin with 15 balls.
Each ball is one of 5 different colours: red, blue, yellow, green, or grey.
The colours of the balls are randomly generated at the beginning of the game.
You are able to see the colour of all the balls once the game begins.
You have a container the thickness of one ball, such that all balls will stack one on top of the other.
You are awarded 1 point for every ball that you stack.
When you stack 3 balls in a row of the same colour, the balls are removed from your stack and you are awarded 9 additional points. For example, if you stack 3 grey balls, you will be awarded a total of 12 points: 1 for each ball, plus 9 for stacking 3 in a row.
The base colour of your stack is red, such that if the first ball on your stack is red, it will be removed immediately.
Therefore, the maximum score is 60 points (15/3 = 5, 5*12 = 60), although this will not always be possible.
If you finish the game with more than 7 balls in your stack, you lose.
You begin the game with two special balls as well. You may use a special ball at any time, but you do not have to use any special balls to win the game. When you use a special ball, one of the following 4 events will occur. The event is selected randomly.
1. The colours of all remaining balls are changed to match the colour of the top marble in your stack.
2. The colours of all remaining balls are randomly changed to new colours.
3. All marbles on your stack are removed (no additional points are awarded).
4. Your special ball counter is reset to 2.
Determine, mathematically, the best strategy for getting the highest possible score on any given board.