1. Introduction to Morris Games Originally Compiled by Michelle Sharp With contributions by Walter Voit, Kedar Naidu, & James Latham 7 February 2007

2. Morris Games in History This is a classic, ancient game The game has many different names: Merelles, Merrills, Merreles, Merrels, Merrelus, Marels, Marelles, Marrills, Muhle, Muehle, Muller, Morell, Morelles, Molenspel, Mills, Mylla, Mlynek, Mylta and Morris The name merels comes from the low Latin word merrelus, meaning a 'token, counter or coin' Versions have been found dating all the way back to 1400 BC.

3. Morris Games in History (cont) Found carved into such diverse places as Egyptian pyramids, a shrine at Ceylon, and in a burial site in Bronze Age Ireland In Britain, buildings have boards in positions that are impossible to play, so it is assumed that stonemasons played on them before using the stone in construction. Mentioned in Shakespeare’s A Midsummer Night’s Dream Reached height of popularity in 14 th Century Europe

4. Modern Morris Games One variation still extremely popular with children Three Men’s Morris ≈ Tic Tac Toe Most popular version with adults is Nine Men’s Morris World Championships held until 1997 Most popular in German-speaking countries Multiple online discussion groups exist Game is used often in AI classes and for research Gasser solved Nine Men’s Morris in 1993 Conclusion: when played well, it always comes to a draw

5. Variations Game play is simple but strategy is complex Entire books have been written on play strategy Variations in board layouts and number of game pieces Number in title dictates number of pieces per player Board layouts get more complex as number in title increases We will use Morris Game, Variant-C, a variant of Nine Men’s Morris

6. Example Layouts Seven Men’s Morris Nine Men’s Morris, Var C Eleven & Twelve Men’s Morris Five & Six Men’s Morris Three Men’s Morris Three & Four Men’s Morris Our Project

7. Variant-C Modified Nine Men’s Morris Game board 9 pieces per side; black vs. white Can only place on line intersections, yielding 21 spaces

8. Handout Handout is only to provide background on game and to help students get familiar with it Only includes resources, analyses and implementations of Nine Men’s Morris because it is most popular and closest to our game Shareware and commercial software links excluded Except where noted, only looked at references that are in English

9. Rules Remember: For the purposes of the class, the teacher’s version of the rules is the only one that matters! Game play is like a cross between Tic Tac Toe and Checkers. Goal is to capture your opponent’s pieces by getting three pieces in a row (called a “mill”) The winner is the first player to reduce the opponent to only 2 tokens, or blocks the opponent from any further moves There are three phases of play

10. Rules (cont) Opening Players take turns placing pieces on any vacant board intersection spot until all pieces have been placed Midgame Once all the pieces are placed, then take turns moving one piece along a board line to any adjacent vacant spot Endgame When a player is down to only three game pieces, then they may move a piece to any open spot, not just an adjacent one (“hopping”)

11. Mills At any stage if you get three pieces in a row along the same straight board line, then you may remove one isolated opponent’s piece from play. An isolated piece is a piece that is not part of a mill. Rules (cont)

12. "We describe the combination of two search methods used to solve Nine Men's Morris. An improved analysis algorithm computes endgame databases comprising about 10 billion states. An 18-ply alpha-beta search then used these databases to prove that the value of the initial position is a draw. Nine Men's Morris is the first non-trivial game to be solved that does not seem to benefit from knowledge-based methods." In other words, they got the machine to work out and tabulate 10 billion positions that they knew were a win for one side or the other, then worked forward 18 moves from the beginning of the game until their opening analysis met their endgame analysis. Result, a recipe for perfect play that guarantees either side freedom from defeat. --From Ralph Gasser’s paper Following the pros

13. Let’s Play!Let’s Play!