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](https://doi.org/10.1007/s00283-018-9855-x)," 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](http://www.math.smith.edu/~jhenle/pleasingmath/sidsackcomments.html) for recording comments about his article, but as of this writing, there are no comments about Hold That Line.



Has Sid Sackson's "Hold That Line" been analyzed?
Jindřich Michalik of Charles University has just proved that the player going first has a winning strategy for the 4 x 4 game. He also analyzes 2 x n and 3 x 3 games in a paper, "A Winning Strategy for Hold That Line" that will appear in *The Mathematical Intelligencer* later this year or early in 2021.


