2. Euler's Family of Dice Derived Game Graphical Illustration Kim Ho Cheung 05/29/2006

3. Parameters of this Game Game Type: Simplified Number of Player: 4 Number of Component utilized: Dice of Distance, Dice of Direction Goal of the Game: Reach the Destination Life for each Player: 3 Behaviour when reach the wall: Trespass The Restrictors affect ALL players

4. Chess Board at the Beginning

5. Starting at a Restricted Square

6. At the beginning Each player choose either Dice of Distance or Dice of Direction at their first step. This is the only step which they need to choose. For instance, Green: Dice of Distance, 6 Choose Direction ↓

7. Chess Board after Green Player make their move

8. Blue Dice of Direction, → Choose Distance 3 The Game continue

9. After Blue Player make the move Blue Dice of Direction → Choose Distance 3

10. Two other players make their move

11. The new Chess Board

12. Free mode for playing

13. Playing in Free mode Green can choose from Distance of 1-6 Blue can choose from Direction Upward, Downward, Leftward and Rightward↑↑ Purple can choose from Distance of 1-6 Yellow can choose from Direction ↑,↓,←,→

14. Playing in Free mode Green choose Distance of 4 Blue choose Direction Downward ( ↓ ) Purple choose Distance 1↑ Yellow choose Upward ( ↑ )

15. The new chess board(Free mode) It would appear that the destination is within reach of Green. However, in most of cases it isn't that easy. It is easy because this is in free mode. Let's see what happen in Determined mode.

16. Determined mode for playing

17. The Beginning Chess Board The Beginning step for each player are identical to Free mode.

18. The Game in Determined Mode Green: Dice of Distance, 6 Blue: Dice of Direction, Upward

19. The Game in Determined Mode Purple: Dice of Direction, Leftward Yellow: Dice of Direction, Upward

20. The New Chess Board in Determined Mode

21. Comparison between two modes 1. Determined: Everything by chance. 2. Free: Player decide one aspect of movement, the other aspect is randomized. Chance interact with chance in a way determine by the player.

22. Special configuration of Chess Board Type 1 Imagine playing with only Distance Restrictor. Can you tell how to get from the starting square to the destination?

23. Special configuration of Chess Board Type 2 Imagine playing with only Direction Restrictor. Can you tell how to get from Starting square to Destination?

24. Imagine playing with only Choice Determiner. Can you tell how to get from Starting square to Destination? Special configuration of Chess Board Type 3

25. The Characteristics of this Game When only Distance Restrictors are employed, there are 6^78 or 4.963608618*10^60 configurations of the game board When only Direction Restrictors are employed, there are 4^78 or 9.134385233*10^46 configurations of the game board When only Choice Determiners are employed, there are 2^78 or 302231454903657293676544 configurations of the game board When all Restrictor and Choice Determiners are employed, there are 12^78 or 1.500158654*10^84 configurations of the game board. Can you tell how to get from Starting square to Destination in any of the cases above?

26. The Innovative Features of this Game Separation of two aspects of movement. Distance Restrictor restrict only one aspect of movement. Direction Restrictor restrict only one aspect of movement. Chance Determiner is a META determiner of movement. Choice Determiner is a META determiner of movement which player can place to affect the randomize aspect of the movement of player landed on it. Different players can play with different chess boards at the same chess board. Player can change the chess board according to their own strategy.