YALE UNIVERSITY
DEPARTMENT OF COMPUTER SCIENCE

 CPSC 223b: Data Structures and Programming TechniquesHandout #3
Professor M. J. Fischer  January 21, 2007



 

The Game of Can’t Stop
A Parker Brothers game

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[Material in this handout is drawn from Wikipedia and from course notes at the University of New Haven prepraed by Professor Alice Fischer.]
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The Board The game equipment consists of four dice, a board, a set of colored markers for each player called tiles, and three white markers called towers. The board consists of eleven columns of varying heights, one for each of the numbers 2 through 12. The heights, from column two through 12, are 3, 5, 7, 9, 11, 13, 11, 9, 7, 5, 3, respectively, so the columns on the ends (2 and 12) are the shortest with only 3 spaces, and the middle column (7) is the longest with 13 spaces.

The Objective The winner is the first player to capture three columns.

The Play Each player plays in turn moving clockwise around the table. A player’s turn consists of one or more moves, where a move consists of rolling the dice and placing or advancing towers on the board. Towers are used to mark a player’s progress during the course of one turn and are removed from the board at the end of the turn. A turn can end in one of two ways. If a player attempts a move but no tower can be placed or advanced, then the turn is over and the player is said to have gone bust. The player’s tiles do not move forward and any progress made on that turn is lost. If the last move succeeded in placing or moving a tower, the player can choose to stop and end his turn. In this case, any progress made during the turn is recorded by moving the player’s tiles forward in their respective columns to the positions marked by the three towers. If a tower had reached the topmost space of a column, then the player captures that colum. Once a player captures a column, no further play can take place on that column.

The Move To move, a player rolls all four dice. He then chooses to group the four dice into two pairs, each of which has an associated total. (For example, if he rolled 1 - 3 - 3 - 4 he could group them as {1,3} and {3,4} giving totals 4 and 7, or he could group them as {1,4} and {3,3} giving totals 5 and 6.) He must then use each of the two totals to play in the corresponding column(s), if possible. There are two ways to play in a column.

  1. If no tower is present in the column, the column has not been captured, and the player has an unused tower, then the player places an unused tower on that column. The tower goes on the space above the space marked by the player’s tile, or if the player has no tile on the column, then it goes on the first (bottommost) space of the column.
  2. If a tower is present in the column and is not on the topmost space of the column, then the tower advances one space upward.

If neither of the two totals will play in its corresponding column, then the move fails and the player goes bust.

Some clarifications While the above rules are believed to cover all cases, it is useful to clarify some special cases.

Example

The following illustrates a single turn for player Yellow. The first roll was 3 - 4 - 5 - 5. The player chose the grouping {3,4} and {5,5}, giving totals 7 and 10. The player placed one tower on the third space in column 7 (following his tile in space 2), and he placed a second tower on the first space in column 10. The result is shown in Figure 1.


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Figure 1: The board after rolling 3 - 4 - 5 - 5.


On the second move, the player rolls 2 - 3 - 4 - 6 and groups them to produce totals 7 and 8. He advances his tower in column 7 and places the remaining unused tower on column 8. (See Figure 2.


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Figure 2: The board after rolling 2 - 3 - 4 - 6.


On the third move, the player rolls 2 - 2 - 3 - 6 and choses totals 5 and 8. No move is possible in column 5 since he has already placed all three towers, but he advances his tower in column 8. (See Figure 3.


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Figure 3: The board after rolling 2 - 2 - 3 - 6.


He now decides (wisely?) to stop. His yellow tile on column 7 replaces the tower on that column, and yellow tiles are placed on the spaces marked by the towers on columns 8 and 10. (See Figure 4. It is now the next player’s turn.


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Figure 4: The board after choosing to stop.