In Sid Sackson's classic book *A Gamut of Games*, he introduces a game that he calls "Hold That Line." Briefly, it is an impartial pencil-and-paper game played on a finite grid of dots. The first player connects two dots with a horizontal, vertical, or diagonal line; thereafter, each player extends the given piecewise-linear curve at one end, making sure to keep it self-avoiding.

Analyzing this game looks like a nice project in combinatorial game theory, suitable for undergraduates, but has it already been studied? A quick search only turned up a brief discussion in Alan Lipp's book *The Play's the Thing*.

**EDIT added March 2019:** This question (among others) was raised by Jim Henle in his Spring 2019 *Mathematical Intelligencer* article, "Mathematical Treasures from Sid Sackson," but without any analysis (other than the observation that the normal form version has a Tweedledum-Tweedledee winning strategy for the first player). Henle has a webpage for recording comments about his article, but as of this writing, there are no comments about Hold That Line.

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