Mark Thompson
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 MacBeth

MacBeth, by Christiaan Freeling

(Apparently Freeling has chosen to capitalize the B.)  This is a variant, perhaps an improvement, of Othello/Reversi on a hexagonal board of 72 cells.  There are six hexes along each side of the board, which would make for 91 cells (the formula for the number of cells in a hexagonal array of side n being 3n2 – 3n + 1), but 19 cells are removed from the board to leave “holes” as shown.  (By the way, the formula for the number of cells in a board of this type is 3n(3n – 1), where a side is 2n. )  Otherwise Othello rules apply.  You can play MacBeth at the MindSports Arena site.

Picture

I’m no expert at either Othello or MacBeth, but I have a feeling MacBeth may be the subtler game.  Note that here a disk can only be flipped along two directions instead of four, and a corner can’t be used as a base for attacks into the center.  It seems to me that therefore the basic Othello strategies -- avoid being first out to the edges, try to leave your opponent with few options even if it means capturing fewer pieces, try at all costs for a corner, and so avoid at all costs a cell adjacent to a corner -- will be much more nuanced in MacBeth.   Perhaps someone who reads this and knows either or both games better would share his thoughts on this with me.

It wasn’t hard to make equipment for MacBeth.  I took some of the green posterboard I had left from my Congo project, carefully cut 72 congruent hexagons 7/8 inch on a side, and laid them out and rubber-cemented them onto a 20 inch square of black foamboard.  A tip:  I think it works best to lay out cells A1 and K11 first, measuring carefully to position them symmetrically, then space cells C3, E5, G7, and I9 evenly between them, then build outward to the edges.  At least that’s how I did mine.

Of course for pieces you can just borrow the disks from a couple of Othello sets, which are sometimes available cheap at thrift shops, flea markets, or rummage sales.  You’ll need 72 pieces, which is more than one set affords.  Alternatively you could epoxy together some miniature white and blue poker chips.  As soon as I get a photo of my handmade MacBeth board I’ll post it here.

World Game Review #13 a number of curious Othello games that people have constructed, which suggest analogous meta-game puzzles for MacBeth.  For example, at the Chicago Mensa annual gathering over Halloween (1999), Oriel Maxime and I found that one player can be forced to pass as early as the 12th move.  Experimenting since then, I find what may be the earliest possible pass, after only 8 moves:  1. g8  h7  2. g5 e4  3. d5 e7  4. d3 c2 5. (pass).  (As in Othello, a player can only pass when no move is available.)

Other questions inspired by WGR#13 include, What is the shortest possible MacBeth game?  the shortest possible tie game? the smallest winning disk count?  If you research any of these matters let me know and I’ll happily post your results here.

Questions, corrections, comments:  Send me e-mail at  markthom@flash.net

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