Timeline for Has Sid Sackson's "Hold That Line" been analyzed?
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2020 at 13:33 | vote | accept | Timothy Chow | ||
| Jun 19, 2020 at 1:44 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added a link to the paper
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| May 15, 2020 at 10:44 | answer | added | Jim Henle | timeline score: 6 | |
| Mar 28, 2019 at 18:02 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added a reference
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| Sep 13, 2012 at 6:04 | answer | added | Thane Plambeck | timeline score: 3 | |
| Jan 10, 2012 at 2:39 | comment | added | Zack Wolske | Ricky Demer's argument works for any grid with a playable line of symmetry, so it also includes all rectangles in Lipp's version. But the same strategy does not work on asymmetric boards, like an L. Or starting with any rectangle, remove an interior point and say that lines cannot cross the missing point. Splitting the game into two disjoint, equal subgames would require passing through the missing point, so you will want to compute the nimbers of smaller subgames instead to find the winning strategy. | |
| Jan 10, 2012 at 0:57 | comment | added | Timothy Chow | Note that even though Demer's observation shows that the normal form is a first-player win on a square grid, it doesn't tell us what its nimber (Sprague-Grundy) value is. | |
| Jan 10, 2012 at 0:53 | comment | added | Timothy Chow | @Gerhard: There are a couple of reasons why I didn't give a full description of the game. The first is that there are many obvious variations possible. In addition to the obvious misere/normal dichotomy, we can allow or disallow diagonal lines at non-45-degree angles (Lipp allows them but Sackson seems to disallow them), and we can allow or disallow a move that connects the free ends to make a closed loop (Sackson leaves this point ambiguous). The second reason is that I'm less interested in how to win a specific version of the game than in what prior work has been done. | |
| Jan 9, 2012 at 18:08 | answer | added | Zack Wolske | timeline score: 2 | |
| Jan 9, 2012 at 5:21 | comment | added | user5810 | @Matt: If that's because you thought there was a specific end that the players extended, $\hspace{0.8 in}$ I was thinking the same thing before Barry's comment. $\;$ | |
| Jan 9, 2012 at 4:18 | comment | added | Kevin O'Bryant | A better description of the rules (or at least somebody's understanding of them) is at books.google.com/… | |
| Jan 9, 2012 at 3:24 | comment | added | Matt Brin | Demer's comment explains why my assumption was wrong and the rules give the win the next to last player. | |
| Jan 9, 2012 at 3:20 | comment | added | user5810 | The first player draws a main diagonal, and then plays to make the piecewise-linear $\hspace{1 in}$ curve symmetric about the center of the grid. $\;$ | |
| Jan 9, 2012 at 2:38 | comment | added | Barry Cipra | Here are the rules, copied from A Gamut of Games (pg. 146): "To play, just draw 16 dots in 4 rows of 4. The first player connects as many dots as he wishes in a straight line [which an illustration indicates may run diagonally]. From either end of the first line the second player draws another straight line. From either free end the first player now makes a line. Continue until no further lines can be drawn. The player who was forced to make the last line is the loser! The completed line must be continuous, with no branches, no crossings, and no dot visited twice." | |
| Jan 9, 2012 at 1:47 | answer | added | Matt Brin | timeline score: 4 | |
| Jan 8, 2012 at 22:38 | comment | added | Gerhard Paseman | For the sake of completeness, you might expand your definition of the game to include how many players, what a win or scoring condition is, and so on. Additionally, there are those of us who might try analyzing Sid's version and giving back to you new information if you do this. Gerhard "I Suspect I'm Not Alone" Paseman, 2012.01.08 | |
| Jan 8, 2012 at 20:54 | history | asked | Timothy Chow | CC BY-SA 3.0 |