Mark Thompson
 Math Education
 Math Recreations
 Abstract Games
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 The Game of Y

The Game of Y, or Mudcrack Y  by Craige Schensted (“Ea”) and Charles Titus (around 1960)

In Y, as in Go, Hex, or Star, two players place stones of their designated color (black or white), one each turn.  Stones are not moved or captured in Y.   The object is to form a Y, that is, a chain of stones of your color that connects all three of the board’s sides.  The concept is simple, but the game has great strategic depth.

For $52 or so, you can get Y equipment from Kadon Enterprises.  They also have a few copies of an excellent book, Mudcrack Y and Poly Y, which gives playing boards, rules and strategic tips for this game and its still-deeper generalization, Poly-Y.  I’ve only seen pictures of their Y set, but they look very handsome indeed.  I feel the game has enough merit that it should also be available in a cheap form, so that more people could find out how good it is before investing that kind of money.  The GIF here would serve as a suitable game board, and players could use go stones (or pennies and nickels) for markers.

Picture

The excellent Richard’s PBeM server also supports a version of Y, but because it uses only ASCII drawings that version is limited to a hex-grid board.  The Kadon board is designed so that three intersections border five points each instead of six, as in the diagram here; this is said to improve the game.  The diagram below is marked with a notation that I suggest as a standard for playing by e-mail.

Picture

The board shown has 93 intersections, and a game is said to take only about twenty minutes.  That probably is good for marketing since Americans seem to get antsy if a game lasts too long, but I wonder whether a larger board would provide a deeper game for serious players.  The lines connecting the “nodes” (intersections where five edges meet) go over five intersections, counting the nodes themselves, and so I would call the Kadon board an order-5 board.  It looks to me like the formula for the number of intersections in an order-n board of this type is 5n2 - 7n + 3, so there would be 141 intersections on an order-6 board and 199 on an order-7.  Perhaps later I will try creating gifs of boards of these orders and post them on this page.

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

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