Introduction to Morris Games

Originally Compiled by

Michelle Sharp

With contributions by Walter Voit, Kedar Naidu, & James Latham

7 February 2007

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.

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 14th Century Europe

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

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

Example Layouts

Seven Men’s Morris

Nine Men’s Morris, Var C

Eleven & Twelve Men’s Morris

Five & Six Men’s MorrisThree Men’s Morris

Three & Four Men’s Morris

Our Project

Our Project

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

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

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

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”)

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)

"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

Let’s Play!