tag:blogger.com,1999:blog-3889388775673754833.post6383494426510954091..comments2024-02-24T03:34:18.060-05:00Comments on Stealing Commas: Multi-Dimensional Tic-Tac-Toechris the cynichttp://www.blogger.com/profile/06872875475212333027noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-3889388775673754833.post-66082392597656817852015-03-04T21:30:59.312-05:002015-03-04T21:30:59.312-05:00https://apps.facebook.com/tfour_four_four/?ref=eyJ...https://apps.facebook.com/tfour_four_four/?ref=eyJzaWQiOiIwLjE0Njg1NzEzMzgzMzY5MTQ4IiwicXMiOiJKVFZDSlRJeVZEUWxNaklsTlVRIiwiZ3YiOiI5NGFkMGE1NTE2ZDdhOGQ3YThhZWZiMmY4M2FhZjJlOGU0MjRiMjU2In0tolgahttps://www.blogger.com/profile/16568496815458168714noreply@blogger.comtag:blogger.com,1999:blog-3889388775673754833.post-16949399065126785992013-02-04T10:50:31.419-05:002013-02-04T10:50:31.419-05:00In higher dimensions that might work because it ca...In higher dimensions that might work because it can be confusing to even tell what a plane is at first glance, in 3d it's just too obvious. The idea is no-mistakes=not-losing, but complex to the point it's easy to make a mistake. Seeing that two things are lined up to make for 3 in a row next move is easy to miss, seeing that eight things are lined up to make for a plane next move is harder to miss.<br /><br />I wonder if it might be possible to stick to the original idea, and keep the center piece and thus diagonals if instead of making one line one was required to make two, or (N-1) where N is the number of dimensions.<br /><br />The problem in 4 as it appears above, and 3d with a center is that the first player can force the second to move around the board as they choose, never getting in a free move because of the need to block that first line. If the first line can be given away, that changes everything. Not sure if it solves everything, but it changes everything.<br /><br />One thing that I like about not adding new types of squares (every square above is either a 2d edge or a 2d corner) is that it makes for strange shapes of boards instead of a 3x3x3x.... hypercube.chris the cynichttps://www.blogger.com/profile/06872875475212333027noreply@blogger.comtag:blogger.com,1999:blog-3889388775673754833.post-60292119919398967832013-02-04T10:27:23.083-05:002013-02-04T10:27:23.083-05:00I do believe that you're probably right. In c...I do believe that you're probably right. In certain situations the uncertainty might be able to be accounted for thus allowing a game to be solved, but in other situations, Stratego probably among them, the uncertainty would probably override the possibility of a solution.<br /><br />Finity still means that one can determine all possible games, but when uncertainly reaches a certain point a solution would be probabilistic (right move is the one that has the least possible chance of you losing/highest possibly chance of you winning/whatever your priority is) rather than deterministic.<br /><br />Of course, the same can be said of games with random chance involved. It's possible to determine what leads to the highest possible chance of you winning, it's not possible to solve in the way it is with something like tic-tac-toe or chess.<br /><br />So, I think you're right.chris the cynichttps://www.blogger.com/profile/06872875475212333027noreply@blogger.comtag:blogger.com,1999:blog-3889388775673754833.post-83827922163570164642013-02-04T01:45:28.005-05:002013-02-04T01:45:28.005-05:00In theory, any game that has a finite number of pl...<i>In theory, any game that has a finite number of players, a finite number of moves, and a lack of random chance, can be "solved".</i><br /><br />Actually, I believe you're missing one condition - the game must also have no hidden information (i.e. all players are aware of the complete game state). The game Stratego, for instance, is a game with hidden information (you do not know the values of the other player's pieces until they are revealed by an attack).Redwood Rhiadranoreply@blogger.comtag:blogger.com,1999:blog-3889388775673754833.post-1768474342588324872013-02-03T08:32:35.592-05:002013-02-03T08:32:35.592-05:00If the problem is that there are too many dimensio...If the problem is that there are too many dimensions and therefore too many different ways to put together a line, how about requiring a complete plane in order to win?Firedrakenoreply@blogger.com