5-6-7 Men's Morris

6 men's morris is a game which was popular during the middle ages but is virtually unknown now.
It has the same rules than 9 men's morris, also known as triples, but uses a smaller board.
The official rules, from the World Merrills Association, can be found here

Nevertheless, I've solved it.
It is a draw when both players play perfectly.
5 men's morris, which uses the same board but only 5 men is a draw too.
If both players use 7 men, it is a draw too.
I've demonstrated this by creating a program which plays all this perfectly.

Interestingly, the deepest (reachable) position in 6 men's morris was a mate in 149, which can be played as well.

A screenshot



The computer always plays red.

To improve the program, minor changes have been made to the database.
To download, press here (6 Mb)





I have also solved 7 men's morris, which has the same rules but is played on this board.



I found it a very strange variant because, as you can see, there are 2 lines with 5 intersections.
This often results in a big dominance if one owns this spot.

And indeed, it is a win for the first player in 25 moves with perfect play.
Even more, if the first player doesn't put his first pawn on the central square, it is a win for the second player !
So it might be a good suggestion to not use the central square until all panws have been placed on the board.
But still, I haven't found anything by which I could conclude these are the not the right rules after all.

7 men's morris isn't available due to the size of the database, about 100Mb.
That's because, there's a higher % of winning lines, there's 1 spot more on the board and the symmetry between the outer and inner square is broken.


Move on to 4 field ko-no

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