I've removed the following passage:
It's certainly possible to define winning strategies in this way, but it doesn't give any substantial extra generality, because it doesn't matter what a strategy tells you to do in a position you can't reach if following the strategy. The strategy could even specify an aggressively stupid move in such circumstances, and it would still be winning. Since I think the passage has the potential for making it harder to figure out the definition, I've removed it. -- Trovatore 17:37, 27 July 2005 (UTC)
I looked at your most recent effort and it still has what I think is an unnecessary complication--basically you're saying a strategy is a partial function from positions to moves. I don't think that's standard. Usually a strategy (winning or otherwise) is a total function from positions to possible moves. It's when evaluating whether a strategy is winning or not that we don't care what move is specified for unreachable positions.
Now certainly you could define a strategy to be a partial function from positions to moves whose domain includes all positions reachable while following the strategy, but as I say I think that's too complicated. -- Trovatore 20:06, 27 July 2005 (UTC)
So there is a group of related articles, some written and some not, dealing broadly with issues of determinacy, games, strategies, quasistrategies, winning strategies and quasistrategies, games of imperfect information, and strategies etc for the last. Existing articles are
Articles need to be written that better explain
Then the organizational questions are:
-- Trovatore 02:54, 28 July 2005 (UTC)
Update: there's now a determinacy article that aims to be a central reference point for all of the above. So the winning strategy article no longer needs to be relevant to determinacy theorists. I've put a dab notice at the top. -- Trovatore 06:05, 2 September 2005 (UTC)
In the article it says that there can be a rule for winning and that that would be winning strategy. But this is too general. There may be rules/principles in certain situations but there may also be a hierarchy or rules above that. For instance the winning strategy (master rule) may be to constantly change subsequently lower ranked rules for instance in the game of Poker. You can't stick to one way of playing (conservative, aggressive) because others will figure out your strategy and exploit it, so you have to adapt to the situation and change accordingly, back and forth, perhaps randomly to stop people from figuring out what you're doing. Even then, they may figure out that you are using a random strategy and play conservative, which leads to aggressive play, the loop continues; the only thing that matters is that you are only one step ahead. Any more and it might not work, you could go so far ahead in strategy that you'd be behind the opponents strategy. The same can be said of Chess. If a person is in one situation, he should do this, but later in the game, he would want to do that. The strategies are different for different situations and you don't know what situation you will end up in until you are in that position or if you can predict the future and know what's going to happen. Thus, you have to stay ahead of the opponent. Also check my comments in the strategy stealing argument article. 70.111.224.85 13:55, 5 January 2006 (UTC)
Perhaps a merge with Dominance (game theory). -- 70.111.218.254 21:10, 12 November 2006 (UTC)
I've removed the following passage:
It's certainly possible to define winning strategies in this way, but it doesn't give any substantial extra generality, because it doesn't matter what a strategy tells you to do in a position you can't reach if following the strategy. The strategy could even specify an aggressively stupid move in such circumstances, and it would still be winning. Since I think the passage has the potential for making it harder to figure out the definition, I've removed it. -- Trovatore 17:37, 27 July 2005 (UTC)
I looked at your most recent effort and it still has what I think is an unnecessary complication--basically you're saying a strategy is a partial function from positions to moves. I don't think that's standard. Usually a strategy (winning or otherwise) is a total function from positions to possible moves. It's when evaluating whether a strategy is winning or not that we don't care what move is specified for unreachable positions.
Now certainly you could define a strategy to be a partial function from positions to moves whose domain includes all positions reachable while following the strategy, but as I say I think that's too complicated. -- Trovatore 20:06, 27 July 2005 (UTC)
So there is a group of related articles, some written and some not, dealing broadly with issues of determinacy, games, strategies, quasistrategies, winning strategies and quasistrategies, games of imperfect information, and strategies etc for the last. Existing articles are
Articles need to be written that better explain
Then the organizational questions are:
-- Trovatore 02:54, 28 July 2005 (UTC)
Update: there's now a determinacy article that aims to be a central reference point for all of the above. So the winning strategy article no longer needs to be relevant to determinacy theorists. I've put a dab notice at the top. -- Trovatore 06:05, 2 September 2005 (UTC)
In the article it says that there can be a rule for winning and that that would be winning strategy. But this is too general. There may be rules/principles in certain situations but there may also be a hierarchy or rules above that. For instance the winning strategy (master rule) may be to constantly change subsequently lower ranked rules for instance in the game of Poker. You can't stick to one way of playing (conservative, aggressive) because others will figure out your strategy and exploit it, so you have to adapt to the situation and change accordingly, back and forth, perhaps randomly to stop people from figuring out what you're doing. Even then, they may figure out that you are using a random strategy and play conservative, which leads to aggressive play, the loop continues; the only thing that matters is that you are only one step ahead. Any more and it might not work, you could go so far ahead in strategy that you'd be behind the opponents strategy. The same can be said of Chess. If a person is in one situation, he should do this, but later in the game, he would want to do that. The strategies are different for different situations and you don't know what situation you will end up in until you are in that position or if you can predict the future and know what's going to happen. Thus, you have to stay ahead of the opponent. Also check my comments in the strategy stealing argument article. 70.111.224.85 13:55, 5 January 2006 (UTC)
Perhaps a merge with Dominance (game theory). -- 70.111.218.254 21:10, 12 November 2006 (UTC)