Talk:Strategy-stealing argument

From Wikipedia, the free encyclopedia

Contents 1 Gender 2 Tic-Tac-Toe 3 Go 4 Fatal flaw? 5 Shannon Switching Game

[edit] Gender

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)

It used to be, but not really any more. —Simetrical (talk) 02:18, 26 December 2005 (UTC)

[edit] Tic-Tac-Toe

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)

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)

[edit] Go

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)

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)

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)

[edit] Fatal flaw?

I diagree that the strategy stealing argument means first player can always force a win. Let's say that second player knows the best strategy, first player doesn't. Thus first player moves "randomly" to steal the second players strategy. Second player begins his "best strategy," BUT first player "steals" it. Although the first player has stolen the best strategy, second player has an advantage: initiative. So if this continues out, the second player will win. One might go on to say that second player could steal the first player's strategy stealing strategy, and both players continue to place random pieces down until the game is over by chance! If a game is such that the second player always wins, then that means that it is the first move that is bad. Which means that whereever your first move is, it is a disadvantage because the second player can react to that with the appropriate "best strategy," leaving the first player unable to steal the strategy because he/she is always behind by at least one move. —the preceding unsigned comment is by 128.6.175.45 (talk • contribs) 14:47, 21 October 2005 (UTC)

"Let's say that second player knows the best strategy, first player doesn't" is an invalid premise. Possibly you should take a look at winning strategy—a strategy is only a winning strategy if it wins no matter what the other player does. It must work even if your opponent knows the strategy as well as you do. If both of us know and use a second-player winning strategy, then the one who plays second must win. If it can be proven that in a given game any strategy valid for the second player is equally valid for the first player, which is what the strategy-stealing argument is, then there can be no second-player winning strategy—if there were, we'd both have a winning strategy, which is nonsensical. —Simetrical (talk) 02:18, 26 December 2005 (UTC)

What I said meant that the second player had a winning strategy, while the first tried using the strategy stealing argument as their winning strategy. Now we have to wonder if the second player would later steal the strategy stealing strategy so that they both end up with the same thing. Resulting as I mentioned earlier a perhaps random game, where the players randomly move on the board until the game is done. This game would most likely be won by the first player just because of first move advantage. This is ridiculous of course and leads us to the current strategies in place for all games today. (I'm assuming there is no such game in which if you randomly move, you will win every time.)

Another question that games have to critiqued is fairness. If a game isn't fair, there is no point in even applying the strategy stealing argument, as it could be impossible for a person to win anyway. Since none of the games mentioned are fair (they are proven to be a forced win for first player), they cannot apply. Connect6 is a contender for fairness, but in my experience playing it, a defensive strategy is almost infallible. If both players use this strategy, there is likely to be a draw. More gameplay has to be done to prove/disprove this. 70.111.224.85 14:08, 5 January 2006 (UTC)

[edit] Shannon Switching Game

I'm sure the strategy-stealing argument doesn't apply to the Shannon Switching Game, because although there can be no draws and an extra move is never a disadvantage, the game isn't symmetric. "Short" is trying to join A to B and "Cut" is trying to make this an impossible task by disconnecting A from B, therefore they have different winning strategies. Also, the Shannon Switching Game can be played on any graph, and it is trivial to show that some graphs give an automatic win to Cut and some give an automatic win to Short. Is there, in fact, a particular graph or set of graphs for the Shannon Switching Game for which the strategy-stealing argument DOES apply, or am I just misunderstanding the rules of the game? 91.84.76.81 (talk) 19:33, 6 May 2008 (UTC)