| --- Log opened Wed Mar 09 00:00:01 2022 |
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| 00:41 | < Alek> | wtf |
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| 19:29 | | * macdjord ponders a simple game idea |
| 19:29 | <@macdjord> | Gridless Tic-Tac-Toe: Players alternate placing Xs and Os on the playing field, but there's no 3x3 grid; players can place their marker at any real-valued position so long as they don't overlap an existing marker. |
| 19:29 | <@macdjord> | Win condition is getting 3 symbols in a row - specifically, the player must draw a line starting from the centerpoint of one of their symbols which passes through two other of their symbols without being blocked by an opposing symbol. |
| 19:29 | <@macdjord> | I'm thinking maybe the player must chose, each tune, between placing a symbol and trying to draw a victory line? |
| 19:46 | < abudhabi_> | How broad are the pieces? |
| 19:47 | <@macdjord> | Hrm, no, that won't work; there's a simple dominant strategy for the first player: place first symbol in center; place second symbol adjacent to first, on opposite side from wherever the other player went; place 3rd symbol either in line with first two, or 60º left of line, or 60º right of line - enemy cannot have blocked all 3 of these; one 4th turn, win. |
| 19:48 | <@macdjord> | abudhabi_: They'd have to be substantially smaller than 1/3rd the width of the playing field. |
| 19:48 | < abudhabi_> | Hm. There's a bounded field? |
| 19:48 | < abudhabi_> | It isn't an infinite plane? |
| 19:48 | < abudhabi_> | No wrap-arounds? |
| 19:49 | <@macdjord> | abudhabi_: I was assuming bounded, but I suppose infinite would work. |
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| 20:05 | <&Reiver> | macdjord: Infinite tic tac toe is a glorious idea, but it is also, IIRC, provably first-player-wins |
| 20:06 | <&Reiver> | They need make only a triangle |
| 20:06 | <&Reiver> | Which I see you then noted |
| 20:06 | <&Reiver> | However, *as a programming excersize* it is an excellent idea |
| 20:07 | <&Reiver> | There is another game I loved when I saw it, and were I a woodworker I'd make a copy of it, called YINSH |
| 20:08 | <&Reiver> | You have five discs on a triangle grid where you play on the corners (so, hexagons, but) |
| 20:08 | <&Reiver> | Every time you move a disc, you leave behind a marker of your color |
| 20:08 | <&Reiver> | ... five RINGS, that matters later |
| 20:09 | <&Reiver> | oh it's on wikipedia, okay, have that instead and save me the typing pre-coffee :D https://en.wikipedia.org/wiki/YINSH |
| 20:11 | <@macdjord> | Reiver: I'm aware TTT on an infinite grid is solved. Not sure about gridless. |
| 20:11 | <@macdjord> | I mean, the specific case of making a line-of-3 is; I gave the solution above. But line-of-4, maybe... |
| 20:12 | <~Vornicus> | gridless, as long as -- uh -- as long as the pawns have radius less than... uh... |
| 20:15 | <@ErikMesoy> | As grid size approaches infinite, playing your stones interspersed at intervals of some very large highly composite number approaches gridless play. |
| 20:17 | <~Vornicus> | ng, never mind I can't do it in my head |
| 20:18 | <@macdjord> | ErikMesoy: In infinite-grid TTT, each marker still only occupies 1 cell of the grid, though, so there's still a fundamental difference between it and gridless. |
| 20:19 | <@macdjord> | For instance, in infinite, it takes 8 markers to surround another marker; gridless can do it in 6. |
| 20:19 | <~Vornicus> | oh, I can do it in my head. |
| 20:20 | <~Vornicus> | 1 / (1 + 2sqrt(2)), 0.26+. If a stone is smaller than that in a unit square, the triangle trick works |
| 20:21 | <@macdjord> | Vornicus: By unit square, you mean the size of the playing field? |
| 20:21 | <~Vornicus> | yes |
| 20:21 | <@ErikMesoy> | So, both players are using circular markers? |
| 20:21 | <~Vornicus> | yes. |
| 20:21 | <@ErikMesoy> | Because non-circles don't necessarily take 6 to surround. |
| 20:22 | <@macdjord> | ErikMesoy: Given using Xs would require handling asymmetrical game balance, let's say yes. |
| 20:23 | <~Vornicus> | player 1 plays center, player 2 -- heck you don't even need the whole triangle trick, if a player can prevent interpose |
| 20:29 | <@ErikMesoy> | Re line-of-4: https://en.wikipedia.org/wiki/M,n,k-game#Specific_results |
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| --- Log closed Thu Mar 10 00:00:02 2022 |