Y (game)

Lore & Background

Y was first described by John Milnor in the early 1950s, then independently invented in 1953 by Craige Schensted and Charles Titus. The game is typically played on a triangular board with hexagonal spaces; the official board has three points with five-connectivity instead of six-connectivity, but it is just as playable on a regular triangle. Schensted and Titus' book Mudcrack Y & Poly-Y contains many hand-drawn boards that appear irregular but are topologically identical to a regular Y board.

Players take turns placing stones of their color, never moving or removing them. The game ends when a player connects all three sides with a single connected set of stones; corners count as belonging to both adjacent sides. The pie rule can be used to mitigate first-move advantage. It has been formally shown that Y cannot end in a draw.

Schensted and Titus argued that Y is superior to Hex because Hex can be seen as a subset of Y, though the games have different enough tactics to be considered separate. The book also describes Poly-Y, the next game in the series, followed by Star and *Star.

Reader's Guide

Y holds significance as an early connection game that influenced later abstract strategy games. Its inventors, Schensted and Titus, argued that Y subsumes Hex, though the games remain tactically distinct. The game's chief criticism is that on a standard hexagonal board, a player controlling the center can easily reach any edge, making defense difficult. To address this, Schensted and Titus developed successive board versions, culminating in the official board with three pentagons inserted among hexagons. This design was inspired by a hemisphere model where the distance from the north pole to the equator is 1/4 the circumference, improving the distance ratio from 1/3 to 3/4 and making side defense more plausible. The official board is essentially a geodesic dome hemisphere squashed flat into a triangle. Y's legacy includes its formal proof of no draws and its role as a precursor to more complex games like Poly-Y, Star, and *Star, all part of Schensted's evolving game family.

Did You Know?

• Y was first described by John Milnor in the early 1950s and independently invented in 1953 by Craige Schensted and Charles Titus.
• The official Y board has three points with five-connectivity instead of six-connectivity, inspired by a geodesic dome hemisphere squashed flat into a triangle.
• It has been formally shown that Y cannot end in a draw; once the board is complete there must be one and only one winner.
• Schensted and Titus argued that Hex can be seen as a subset of Y, though the games have different enough tactics to be considered separate.