Aggression

1. Aggression Mary Jane O’Neill Stephanie Fan

2. Aggression Rules • Two players • 20 regions • 100 troops • Winner – player with most regions Figure 1: Drawing of regions

3. Aggression Rules Continued… Figure 2: Occupying of regions Figure 3: Invading of regions

4. Aggression Win Condition • No legal moves left • No opponent regions left to cross out due to: • No two opposing regions are adjacent • All troops remaining cannot be crossed out legally Figure 4: Example of a finished game of Aggression

5. Aggression Modified Figure 4: 4 x 4 matrix version of Aggression

6. Ideas • Priority spacing • Troop placement • Vulnerability Figure 5: Edges, corners, and center pieces

7. Approaches • Program • Real-life data • End-states Figure 6: End-state board 1 Figure 7: End-state board 2 with mirrored moves

8. Combinatorics • Any number of regions • Total number of possible boards (close approximation) • r = # of regions • n = # of troops each player has to place • k = total # of regions a player is diving their troops amongst • c = combination • C = composition

9. Combinatorics Chart

10. Future Works • Branching factor • Figure out troop placement and cross out strategy for a 4 x 4 and N x N • Drawing of boards • How to draw (winning strategy)

11. Conjectures • Conjecture 1: The winning strategy for the complete version of the Aggression would be a tie if both players played to the best of their ability. • Conjecture 2: Player 2 has an advantage when it comes down to troop placement because he gets to allocate his troops after the first player, giving him knowledge of where his opponent’s troops are located and how many troops reside in a particular region.

12. Generates list of boards • Starts at top of the list • Board list • Plays game • Weight list • Player 1 wins • Player 2 wins • Tie • Punish