Talk:Strategy-stealing argument

message: Hi, why both players are females ? i think the neutral gender in english in the male gender .. —the preceding unsigned comment is by 200.78.53.94 (talk • contribs) 05:40, 13 February 2005
:See Gender-specific pronoun -- Dominus 15:20, 18 July 2005 (UTC)
thread_title: Gender

message: I don't see how strategy-stealing applies here.  Player 1 can never pretend to be player 2 -- whenever it's player 2's turn to play there are an even number of vacant squares, but when it's player 1's turn to play there are an odd number of vacant squares.  —Preceding unsigned comment added by 72.93.194.10 (talk) 22:07, 24 May 2008 (UTC)
replies: text: You're right, the argument needs a little elaboration.  Suppose there is a winning second-player strategy.  The first player can place an X at random and thereafter pretend to be the second player.  Having an extra mark on the board cannot hurt him.  If the strategy calls for him to play where the extra X is, he can simply play somewhere else at random.  This cannot make his position worse than it was, so the winning strategy is still a winning strategy. -- Dominus (talk) 10:03, 25 May 2008 (UTC)
replies: text: I have made the argument more rigorous and hopefully more clear by explaining that first player may "ignore" the extra X so as to treat his position exactly as the second player's, and thus use the supposed winning second-player strategy. Denziloe (talk) 21:45, 27 August 2014 (UTC)
thread_title: Tic-Tac-Toe

message: Shouldn't Go be considered in this? 
If it is true, then in Go you can steal the strategy as well. It is a symmetrical game and there is no penalty for having an extra move (you can pass, and you can lose maybe one territory for putting down a stone in your own territory; you may even lose a lot of territory if you put a stone in one of 2 eyes when the territory is surrounded completely by the other side... not sure if all this is necessarily a penalty). —the preceding unsigned comment is by 128.6.175.45 (talk • contribs) 21:07, 19 October 2005 (UTC)
replies: text: I think the problem with that is that if there's a winning second-player strategy and the first player passes, then the second player would also pass, and it could continue like that forever, making the game undecidable.  It would be known that whoever made the second move would automatically win, and therefore it would never be advantageous to play first.  If there's some draw rule in Go based on consecutive passes, or some limit on consecutive passes, this might not be an issue.As for whether making an actual move (not passing) is ever a penalty, I am neither a game-theorist nor a Go player (beyond a cursory knowledge of most of the rules), so I'm afraid I don't know.  Game theory is a mathematical discipline, of course, so even if no one's thought of any disadvantageous moves yet, they can't be assumed not to exist until their existence is proven impossible. —Simetrical (talk) 02:18, 26 December 2005 (UTC)
replies: text:  Actually, if there are two passes in a row, it ends the game and the determination of dead or not dead pieces begins. The board would have to be at least "half full" before people would actually pass. with just two moves, it is hardly conclusive and there is so much space that it wouldn't be a disadvantage to have an "extra move." Interestingly, it can be a disadvantage to move later in the game, perhaps the endgame. Similar to the zugzwang in chess, Go has kamikaze/suicide attacks. If the player has other options of course they can move those before. But we also have to consider perfect strategy. Although the strategy stealing argument doesn't lead one to perfect strategy besides perhaps strategy stealing (though I think you would always be a move behind), we have to assume perfect strategy in the process of the game, and we have no idea what it would be. 70.111.224.85 13:36, 5 January 2006 (UTC)
thread_title: Go

message: I deleted:
:The strategy-stealing argument is non-constructive. It proves that a strategy exists, but provides no help in discovering what that strategy is. In other words it is an existential proof of a win or draw for the first player.
There's a lot of confusion on this point, but the SSA shows the absence of a strategy for second player.  A constructive proof of such a negated proposition means that one can construct an absurdity from any purported winning 2nd player strategy, which looks like proof by contradiction but is not.  If the SSA is used as part of an argument that there is a first-player win, that argument is in all likelihood non-constructive, but constructive arguments may indeed form part of non-constructive proofs.
There's enough confusion about this that it maybe deserves inclusion in the article. — Charles Stewart (talk) 14:01, 18 March 2009 (UTC)
thread_title:  Constructivity 

message: The chess section states, "In chess, it is common knowledge that having the first move is a small but significant advantage for White"
An advantage cannot be both small and significant.  The words have opposite meanings.  Perhaps the writer meant something like "small advantage that can be significantly exploited by a skilled player".  I know next to nothing about chess strategy so I'm not going to try and correct this.  But somebody should! 99.23.132.69 (talk) 22:49, 5 September 2009 (UTC)
replies: text: I disagree that an advantage cannot be both small and significant.  —Dominus (talk) 02:40, 6 September 2009 (UTC)
thread_title:  Chess 

message: It probabl;y needs to say better the conditions too as Determinacy shows how even with a well determined outcome the result isn't assured. Dmcq (talk) 16:04, 26 November 2009 (UTC)
thread_title:  Possibly infinite games