Talk:M,n,k-game

message: Check  for a discussion on if the strategy stealing argument is valid. 70.111.251.203 13:43, 9 February 2006 (UTC)
thread_title:  Strategy Stealing Argument 

message: The article states:
* k = 3 is a draw for (3,3,3) (see Tic-tac-toe) and a win otherwise if m > 3 and n > 3. If m ≤ 3 or n ≤ 3, the game is a draw.
I think it should state that it is a win if m > 3 OR n > 3. Also, if m ≤ 3 AND n ≤ 3, the game is a draw. For example, (3,4,3) and (4,3,3) are both wins.
Yeah, this was obviously a mistake.  —Preceding unsigned comment added by 129.177.122.124 (talk) 14:26, 18 October 2007 (UTC)
thread_title:  Problem with k=3 

message: If k<m and k<n, there is a draw. Should this be added to the general results section?  —Preceding unsigned comment added by 141.156.40.94 (talk) 17:09, 6 June 2009 (UTC)
thread_title:  General result? 

message: 0A  	3B	----	7A	7B  	7A	6B	1B	2A
0B  	0A	3B  	5C	5B  	5B	1B	2A	----
0B  	1A	4C  	4A	4A  	6A	0C	2C	7C
4B  	4B	4C  	5C	----	3C	3C	2C	7C
----	6C	6B  	2B	2B  	6A	5A	1C	----
6C  	1A	----	3A	7B  	3A	0C	5A	1C
----	8A	----	1A  	1A	8B	----
9A  	5A	4A  	7B  	6A	7B	9B
0B  	5A	3A  	7A  	7A	4B	0A
0B  	2A	4A  	----	6A	2A	0A
----	5B	2B  	1B  	3A	5B	----
8B  	2B	6B  	1B  	6B	4B	8A
----	9B	----	3B  	3B	9A	----
JumpDiscont (talk) 17:23, 20 January 2017 (UTC)
thread_title:  Pairings to draw (9,6,6) and (7,7,6) 

message: What does "m×n" that mean????? Readers don't know Anna Frodesiak (talk) 11:27, 20 July 2017 (UTC)
thread_title:  m×n 

message: This is defined as 'k-in-a-row by the second player does not end the game with a second player win.' What does that mean? What's the winning condition of this game? Surely it doesn't mean "no matter how bad the first player plays, the second player is never declared a winner". 2001:981:4B0C:1:DAA2:5EFF:FE8E:C8D8 (talk) 19:34, 11 September 2017 (UTC)
replies: text: Actually it does, the second player is playing to avoid a loss. If it were a real game you would probably say the second player was the winner if the the first player did not get n-in-a-row, but weak (m,n,k) games are mainly a mathematical tool to analyze normal (m,n,k) games (themselves mostly of mathematical interest). The notion of Maker-Breaker games is very similar. MathHisSci (talk) 09:51, 17 September 2017 (UTC)
thread_title:  weak (m,n,k) game 

message: Consider the case of k-in-a-row on a 2-dimensional hypercube with all edges having length k (more commonly known as a k-by-k square). Then the Hales and Jewett result quoted from the Berlekamp, Conway, Guy book in the aforementioned section of the article applies, with n=2: that is, the game is a draw if k is odd and k ≥ 3^2-1 = 8 or if k is even and k ≥ 2^(2+1)-2 = 6. We already have in the Wikipedia article the statement that (m,n,k) is a draw for k≥9 for any m,n, which is stronger than the "k is odd" case already, but the second case also gives us that both (6,6,6) and (8,8,8) are draws, neither of which is implied by any of the statements in the "General results" or "Specific results" sections as of the writing of this comment. If anyone is familiar with either the BCG book in the references or the apparent Hales and Jewett paper, can they please confirm that the result is indeed proven for n=2? If not, this condition should be mentioned where the result is stated. If so, it seems that (6,6,6) and (8,8,8) need to be added to the "Specific results" section as draws. Note that in the case n=1, i.e. a (k,1,k) game, the HJ result, that this is a draw for all k≥2, trivially holds. Adam Dent (talk) 19:18, 13 July 2018 (UTC)
thread_title:  Two-dimensional corollaries of result stated in section "Multidimensional variant"