Talk:Combinatorial game theory

message: Having math on the same line as text doesn't render properly. I suggest that for simple expressions, math mode shouldn't be used and more complex ones should be on a separate line. -- Arvindn 12:31, 29 Feb 2004 (UTC)
thread_title:  2004-2005 

message: Please take a look at the Simple English version of this page. Despite some errors, it is much better than this one.
Rcaetano 15:23, 28 May 2005 (UTC)
replies: text: I highly agree.  Now that I've seen a "simple english" version of what this is, I've finally been able to figure out what the complex math notation is saying.  I used the simple english version as a guide to add a "Simpler Definitions" section under formal definitions, which I hope will help people out.  Needs some explanatory images of the tic-tac-toe boards I reference though... I'll see if I have the time to whip some up. Fieari 10:21, July 24, 2005 (UTC)
The Simple English page is wonderful!  You might consider adding a link to it to this page, as it's a great introduction to this one.  It gives a quick, easy overview, and this page adds more technical definitions and examples. Chocolatechipmuffin (talk) 15:51, 13 January 2008 (UTC)

text: Would you be able to suggest a textbook to reference?  I haven't taken a class in this, I'm simply interested on a personal, almost hobby-like level, and to be honest, I can barely understand the current "Formal Definitions" at all.  I simply took the "Simple English" version of this page and added it in... which was the only way I really understood what was going on. Fieari 18:15, 17 May 2006 (UTC)
thread_title: Simple English

message: Using Tic-Tac-Toe as an example seems like a poor choice.  This is not a typical sort of game that is analyzed in CGT, and it does not fit into the framework of the theory very well.  For example, tic-tac-toe games can end in draws, although nonloopy games in CGT always end in one player winning.  Also, it does not make much sense to add tic-tac-toe positions together, so the operation of addition cannot easily be demonstrated.
A better choice would be a game such as hackenbush, domineering, or nim, which are actually played under the Normal Rule.  Positions in these games could be used to demonstrate some of the basic operations in CGT, such as addition and negation, in terms that the layman could understand. — Preceding unsigned comment added by 12.72.242.202 (talk) 19:55, 3 September 2006 (UTC)
thread_title:  Choice of Example Game 

message: The formal mathematical description in this article is vary confusing, even to someone who knows a lot about CGT, since it is completely unorthodox.  The article on Surreal Numbers has a much better approach, that could be the model for this article, as the construction of Surreal Numbers is almost the same as the construction of the class of games.  In general, this article should probably adopt the same notation and conventions as On Numbers and Games, or Winning Ways.  Someone who has read these books should rewrite most of this article in a more orthodox notation. — Preceding unsigned comment added by 12.72.242.202 (talk) 20:01, 3 September 2006 (UTC)
thread_title:  Mathematical Presentation 

message: In the tic-tac-toe example, the "star" scenario is described as
XUL_OUR_XCC_OCR_XLC_OLL_XCL_OUC = {{ | } | { | }}
I believe this is incorrect and that the correct game states are actually
XUL_OUR_XCC_OCR_XLC_OLL_XCL_OUC = {XLR | OLR}
XUL_OUR_XCC_OCR_XLC_OLL_XCL_OUC_XLR = {{ | } | { | }}
This seems more logical to me. 83.226.180.17 (talk) 13:46, 2 November 2010 (UTC)
thread_title:  Errors 

message: I've been watching this article for some time, hoping that it would be improved.
Of the books cited as sources, I own Winning Ways and ONAG. Not even ONAG features the formalism of this article. Therefore, I conclude that said formalism is pulled out of the air, i.e. original research. As has been pointed out above, it uses extremely unorthodox notation, which makes it very hard to understand. You will not see the notation <C,L,R> in ONAG, nor will you see the "0 element" defined to be unique. In fact, ONAG and WW make reference to "zero games," which are just those in which the second player wins with best play. In WW, the position {-2|2} is considered a zero game, whereas in the article it is not connected with the number zero in any way. This is unfortunate. Furthermore, the set P defined in the article is just the set of all zero games. Another problem with the formal portion of the article is that it provides little or no explanations of any of the steps taken.
Equally disconcerting is what is not mentioned in the article. There is no mention of "thermography," for example -- an important topic. The game * is mentioned briefly, but only in the informal section. The ideas of fuzzy, positive, negative, and zero games are not mentioned. The games {0|*} and {*|0} (up and down) are not included; nor is the idea of atomic weight of a game. Finally, the treatement of nimbers is far too brief.
I would try to be bold and fix this myself, but I am certain I would do a poor job. Although I am familiar with CGT, I do not have an intimate knowledge of it. Also, I don't have enough time to do this well.
--N Shar 05:33, 30 December 2006 (UTC)
thread_title:  "Formal Definitions", etc.: Suggestions 

message: I'm about to start working on rewriting this article. If you disagree with some change I make, please don't just revert -- also comment here. I'd really appreciate the input. Anyone else is welcome to join in, of course. --N Shar 02:11, 8 February 2007 (UTC)
thread_title:  Changes in progress 

message: Artificial intelligence research (from the 1950s onward) developed a number of strategies (such as minimax, alpha-beta pruning, etc.) for winning two person games, referred to in AI textbooks as adversarial search. Should this article include a section on these algorithms? Should the articles that refer to these algorithms be included in the category ? Is this the same field of study? ---- CharlesGillingham (talk) 11:01, 21 November 2007 (UTC)
replies: text: * Do you have an opinion on whether they should be mentioned or described in the article? I wasn't sure what to say about this. I kind of think they should be mentioned (at least very briefly), but nevertheless I have an uncomfortable worry, somewhere in the back of my mind, that it would be "polluting" the mathematics. --N Shar (talk · contribs) 06:12, 18 December 2007 (UTC)
replies: text: *Techniques like alpha-beta search and CGT don't mix very well. In alpha-beta search, one generally only searches partway to the end of a game, using numerical scores that have some heuristic intention but no precise mathematical definition beyond the scoring function they are computed by. In computer game programming, when one can search all the way to the end of the game, the scores that are used are instead simple win-loss-draw values, no longer susceptible to more complicated alpha-beta cutoffs. In CGT, on the other hand, the value of a position is well-defined mathematically, generally requires searching out to the end of the game to compute, and can't generally be handled by alpha-beta because not all values are comparable with each other. So while there's some connection, I think it's too tenuous (and would likely require too much original research) to say much about it. —David Eppstein (talk) 06:53, 18 December 2007 (UTC)
replies: text: *Okay, it sounds like this is a different subject and should be left alone. Thanks, everyone. (The real problem I was having is that the lead article in  (game artificial intelligence) does not connect at all with the articles in the category. It's about non-player characters in role-playing games. I now think the solution is to write a survey article about games and AI, and to retitle the existing article.) ---- CharlesGillingham (talk) 04:06, 20 December 2007 (UTC)
thread_title:  Adversarial search 

message: Not long ago, checkers was solved . I don't know enough about CGT to decide exactly how this should fit in the article, but at least it alters the bit about checkers not being solved.Cretog8 (talk) 13:07, 16 April 2008 (UTC)
thread_title:  Checkers solved 

message: Ok, so what exactly are the contributions of this field to the study of games, other than having come up with a name for itself? Neither extensive-form games/backward induction nor alpha-beta pruning (and similar algorithms) are mentioned here, and they obviously apply to the very same type of games. Tijfo098 (talk) 12:21, 21 March 2011 (UTC)
replies: text: It is about defining algebraic values in generalized number systems that mathematically represent the possible outcomes of a game position. It is especially relevant to games such as nim or go or amazons in which the position tends to get split into several independent pieces and at each move a player can choose to move in only one of those pieces — then the mathematical value of the overall game can be calculated as a sum of the values of the separate pieces. —David Eppstein (talk) 13:55, 21 March 2011 (UTC)
replies: text:  I take it you haven't improved the lead because of COI or something (I saw the EL at the bottom). I see now that the contributions are in the unique analysis methods of the game tree. What is less clear to me is if constraint logic and the game complexity results are considered part of this or not. I'll do my best to summarize the stuff in the lead after I grok it at least "from the helicopter". Tijfo098 (talk) 23:42, 21 March 2011 (UTC)
thread_title:  Contributions? 

message: Should we include a separate section on Fraser Stewart's new theory for Scoring Play Combinatorial Games?   This is new theory that was done in a PhD thesis and his papers are currently under review for Games of No Chance 5, but the thesis has been examined and has passed so is it ok to write a section about that now?  — Preceding unsigned comment added by 92.2.128.176 (talk) 11:59, 30 March 2012 (UTC)
replies: text: This sort of material is prohibited by Wikipedia policy for a number of good reasons. You will notice a conspicuous absence of millions of other dissertations like this one. Of course, WP can make exceptions for dissertations which have become famous over time, but this is not such a case. Rschwieb (talk) 02:16, 10 April 2012 (UTC)
replies: text: Probably because the vast number of PhD theses consist of pointless drivel that's why.  If there are "millions of other" theses like that one then I'd like to know where all these great mathematicians are.  Care to show me all the other PhD theses that introduce their own brand new mathematical theory?  Thought not, they don't exist.  — Preceding unsigned comment added by 92.2.119.2 (talk) 20:12, 21 April 2012 (UTC)
replies: text:  Well it's good that you see that we can't admit a thesis automatically, and if you'd just apply that objective conclusion to this situation, you will understand why it's not a good idea to admit that thesis here. Time will tell if this thesis is drivel. It is not a WP editor's place (and even more certainly not the place of someone close to the author of the thesis!) to decide how important or reliable a certain thesis is. A thesis that is introducing a brand new theory is especially suspect as a resource, because there is so little material on the subject matter. Please help keep Wikipedia encyclopedic! Rschwieb (talk) 13:41, 23 April 2012 (UTC)
thread_title: Scoring Play Combinatorial Game Theory

message: I haven't been looking at this article for about six years; in the intervening time it has improved enormously.  The idiosyncratic notation is all gone, replaced by the much more standard Berlekamp/Conway/Guy notation.  This is outstanding work, and the current structure makes it possible to see ways to improve it still more.  I'm going to thing about it for a while and then make a stab at it, but I just wanted to give credit where it's due.  Wikipedia at its best, my friends.ACW (talk) 01:20, 22 April 2012 (UTC)
thread_title:  Big improvements; congratulations to all editors 

message: Is formal CGT really limited to two players?
There has to be a theory or category that includes combinatorial n-player games as well, at least as a theoretical possibility even if there is no active research in that direction. It is strange if one has to resort to general (non-perfect information) game theory in order to have more than two players.
I think the possibility of more than two players needs to be commented in the article.
Chinese checkers is an example of a perfect-information strategy game for up to 6 players.
Anders Hallström
85.230.254.123 (talk) 13:01, 6 January 2013 (UTC)
thread_title:  n-player CGT ? 

message: It is not clearly stated whether combinatorial games are by definition zero-sum. All the examples are zero-sum games. What is the answer? References?
In "Introducing Game Theory and its Applications By Elliott Mendelson" it is part of the definition (p.9 item 5). I'm not sure if this is the standard definition. Experts?
sattath (talk) 18:58, 4 January 2014 (UTC)
replies: text: Combinatorial games have a winner and a loser. They do not have a utility value. They are not part of the classical game theory in which zero-sum games are defined. Additionally, in the classical game theory, players both move simultaneously, and randomization is important, while in combinatorial game theory one player moves at a time and the optimal strategies are deterministic. So your question is meaningless. —David Eppstein (talk) 19:18, 4 January 2014 (UTC)
thread_title:  Zero-sum? 

message: The body of this article (though not the introduction) currently deals only with the Berlekamp-Conway-Guy style of combinatorial games (focusing on games where the winner is determined by who moves last, for example).  Ideally the article should be reworked so that positional games can be discussed on the same level.  Currently the introduction gives the general (in my view, correct) view of a combinatorial game (a game of complete information) but then, in the body, the presentation is based entirely on the Berkekamp-Conway-Guy style.  
Otherwise, in its current form, I would suggest the article be renamed to something like "Additive theory of Combinatorial Games" or something like that.  
Thoughts? Wpegden (talk) 18:39, 9 January 2015 (UTC)
replies: text: Note that the title of the article is already Combinatorial game THEORY, not combinatorial games more broadly. So I think the emphasis on the theory of this sort of games, rather than positional games as a whole, is appropriate. —David Eppstein (talk) 21:14, 9 January 2015 (UTC)
replies: text:  Right, but the emphasis is currently only on the BCG-style THEORY of combinatorial games (tending to have an additive structure) and ignores the THEORY of positional games... this is what I think should be corrected.  Wpegden (talk) 17:01, 12 January 2015 (UTC)
thread_title:  emphasis 

message: Substituted at 01:54, 5 May 2016 (UTC)
thread_title: Assessment comment

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