Odd/Even

by Angie Tilaro

Angie is a former public school teacher. Her interest in plant identification grew during her four years as a sixth grade camp teacher. Her

current interests include any outdoor sports and reading.

Instructional Objective Odd/Even is a mathematical game for reinforcing adding skills.


Learners/Context Grades 4-7 (regular version). Odd/Even could be used for a variety of basic math skills for different age groups and at different skill levels. (See "Revisions", 6, 7, and 9.)

Author's Note This game was originally designed as a math game for children. However, testing the game showed possibilities for extremely advanced and strategic plays, i.e., strategies used by adults in Backgammon, Othello, and Chess could be used.


Equipment One hexagonal playing board

Two 12-sided, hexagonal" dice" containing numbers 1-12

50 White and 50 Black hex markers ("hexors")


Rules Time required is 30 to 60 minutes.

Object To reach the opposite side of the board with one playing piece, but only after having blocked at least one horizontal row on the hexagonal board. (See "Revisions", 3, 5, and 8 for other variations.)

1. This game is for two (2) players. One player is "Odd", the other is "Even".

2. The players sit facing each other with the hexagonal board between them. To determine who goes first, each player rolls both dice. The player with the higher sum is first; that player also makes a choice of being Odd or Even and chooses either the White or Black hexors.

Example: One player rolls 4 and 8; the other player rolls 7 and 3.

Since 4+8=12 is greater than 7+3=10, the first player is first.

3. The hexagonal board is placed on the playing surface so that the Odd edge is turned toward the Odd player, and vice versa. All hexors are off the board at the beginning of the game.

4. A player takes his turn by rolling both dice. When the dice stop rolling, the value on the top surface on each die (i.e., the surface parallel to the playing surface) is the point value.

5. The values on both dice are added up. The resulting sum determines the maximum value that player may advance on the board.

6. New hexors are started from each player's Home Row at the edge of the hexagonal board.

* The Odd player starts hexors from the odd row of all 1's; the Even player starts hexors from the even row of 2's.

* A player may bring new hexors onto the board at any time.

* A player must move every turn, i.e., he must either bring a new hexor onto the board or move any hexor already on the board.

7. After a hexor is on the board, it may be moved in any direction to any adjacent hexagon. By adding up the values of hexagons as they are passed through, the player continues advancing until:

* the values of the hexagons passed through equals the exact sum found on both dice, or

* the values of adjacent hexagons are too large to advance any further, or

* adjacent hexagons have already been passed through, or

* the other player's hexors block further advance.

Example: The Odd player rolls the dice and gets a 4 and a 5, for a sum of 9. A new hexor can be moved onto the first row of the board, which has a value of 1. That hexagon is adjacent to hexagons with values of 1, 4, 10, and 1. Since hexagon 10 is too large, the only possible moves are to hexagons 4 or 1, so the player moves to hexagon 4. Now the adjacent hexagons are 2, 3, 5, 10, and 1 (in the first row). Rather than move backwards to the first row, the player decides to move to 3. The total value of hexagons passed through is now 1+4+3=8. Even though the sum on the dice was 9, the player can only move to a maximum value of 8 for that turn. It is now the other player's turn.

8. Movement can only be made onto or through adjacent hexagons not blocked by the other player's hexors. In other words, a player must go around hexagons containing the other player's hexors. However, each player may "jump" over his own hexors to advance in any direction horizontally or diagonally. Note: When jumping over other hexagons, the move must be made in a straight line to another hexagon in that same row. Movement may not be made across a corner where three hexagons meet.

9. Only one hexor can be moved per turn.

10. The player who blocks at least one horizontal hexagonal row and reaches the opposite side of the playing board (i.e., the other player's Home Row) with one of his hexors is the winner.

Restrictions

* In order to win the game, the row blocked by the Odd player must be an odd-numbered row, and vice versa. Either player may block other rows, but those rows would not qualify for winning the game.

* A player may not make the final move into the opponent's Home Row until after a complete row is blocked.

11. If a player rolls doubles (two 2's, etc.), that player takes his turn and can then select one of the other player's hexors and move it in any direction to any adjacent hexagon.

Restriction

* A hexor blocked in by other hexors cannot be moved.

Strategy 1. A player could choose to charge across the board toward the

opponent's end, or could first concentrate on blocking a horizontal row, or could do both simultaneously (as in to Backgammon). Also, a player could either concentrate hexors on one side of the board or advance up the middle en masse.

2. If possible, a player should try to move his hexors onto the low-value hexagons, thus leaving only the high value hexagons for his opponent.

3. As soon as a player sees where his opponent is setting up a block, at least one hexor should be moved into the row to prevent any blocking action (see Rules 10 and 11).

4. Blocking in your own hexors can also be used to advantage (see Rule 11 Restriction.)

* Toward the end of the game, blocking in the opponent's hexors is important to prevent the opponent from moving a hexor into the Home Row.

Revisions 1. Instead of moving the other player's hexors one hexagon, the

hexor could be removed from the board (see Rule 11).

2. The number of hexors available to each player (50) could be reduced/increased.

3. In order to go out and/or advance, a player would have to have the exact amount on the dice.

4. Instead of only advancing one hexor per turn, multiple hexors could be moved (see Rule 9).

5. Instead of having to block an entire horizontal row, a player would be able to go out after moving a designated number of hexors (5, for instance) to the other player's Home Row (see Rule 10). Another possibility: A player would be required to fill up his opponent's Home Row to go out.

6. For learners with poor adding skills, only one die could be used per turn. Alternatively, instead of using 12-sided dice, regular 6-sided dice could be used.

7. If two differently colored dice were used, the hexagonal board could be used for learning to subtract. (Also, different versions of the board could be created to work with fractions or decimals or to add/subtract large numbers.)

8. A totally different game could be played using the flower-like "Home Zones" on the board:

* At the beginning of the game, each player would start with 14 hexors placed on the Home Zones on their own side of the board.

* The object of the game would be for each player to shift 7 hexors from their own Home Zones to fill up one of the other player's Home Zones. (Only one die would be used.)

9. A second version of the board (with smaller numbers) is for Grades K-2:

* Odd numbers 1, 3, and 5, and Even numbers 0, 2, and 4 are on the board.

* The object of the game is to get five hexors across the board to the other player's Home Row.

* Only one regular 6-sided die is used.

* To move a hexor, the exact number must be reached.

* Cooperative play could be encouraged by allowing players to "share" a hexagon.