Talk:Winning strategy

Passage deleted

I've removed the following passage:

A winning strategy need not describe what is to be done in all possible situations. In particular it doesn't need to tell you how to 'get out of' a situation that you would not have 'got into', if correctly playing the strategy. That is, a strategy is not necessary a complete theory of the game.

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)

Isn't it potentially helpful to have some such comments? After all, only mathematicians, and possibly lawyers, really treat definitions in the implied way (if it's not covered, you know nothing about it ...). Normal people find explicit demarcation of use, in informal discussion. The points could be perhaps made more carefully. But isn't it worth saying something that clarifies that a 'winning strategy for chess' is restricted, and not robust, in ways that differentiate it from expertise? Charles Matthews 18:27, 27 July 2005 (UTC)

So I thought about it and I may have misinterpreted the passage. I was thinking it was saying that a winning strategy didn't have to specify any move in a position that can't be reached while following the strategy. That strikes me as adding an extra complication to the definition.

But maybe the original author was saying only that a winning strategy doesn't have to give you a good move in such a position (it can even give you a move, say, that turns a won position into a lost position). That probably would be a useful point to make--but not, I think, with the original wording, which could confuse others as it confused me. Have at it if you've got a good idea. --Trovatore 19:35, 27 July 2005 (UTC)

Well, I have written some more, and tried to isolate the points somewhat, while still using informal language. By the way, I notice that we don't have a game quantifier article, as such. In the sense of explaining alternations of existential and universal, that is. Charles Matthews 19:59, 27 July 2005 (UTC)

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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)

Um - as a games player, I think it is a partial function. One of the harder general things to teach beginners is that if you get into positions where you don't know what's going on, that's speculative and irresponsible. Of course you may be quite correct that this is not of the essence. But it's an odd prejudice, in a sense, that extending a partial function to a total one by adding random stuff is 'simplifying'. I bear the scars of trying to teach go to people who ask 'what if' questions. Charles Matthews 20:13, 27 July 2005 (UTC)

Well, maybe this page needs to decide whether it's aimed at people interested in real-life games, or at people interested in determinacy. The standard definition in determinacy is that it's a total function. It's just shorter to say than a partial function whose domain includes thus and such. It would be nice to have a page that introduces both concepts (especially as I'm not excited about having incompatible definitions of "winning strategy" floating around, but maybe it's too ambitious. --Trovatore 20:32, 27 July 2005 (UTC)

OK, so under policy we go with the standard definition. Charles Matthews 20:44, 27 July 2005 (UTC)

Not just sure how to incorporate this agreement. Really there's a broad organizational question involving several articles. I'll start a new section and summarize my thoughts so far. --Trovatore 02:37, 28 July 2005 (UTC)

I've edited this thought in now. Charles Matthews 05:26, 28 July 2005 (UTC)

Organizational questions

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

• Axiom of determinacy
• Winning strategy
• Projective determinacy (actually called Axiom of projective determinacy -- main article should be switched with redirect, as primary interest is not axiomatic)
• Axiom of real determinacy
• Tree (descriptive set theory)
• Tree (set theory)

Articles need to be written that better explain

1. What is a 2-player length-ω game of perfect information played on the naturals?
2. What's a strategy for such a game?
3. What do we mean when we say such a game is, say, Σ¹₂?
4. What about more general 2-player length-ω games of perfect information?
   1. Playing objects other than naturals
   2. Playing on a tree
5. What about games of length greater than ω (long games)? These may be played on a Tree (set theory)
6. What characterizes a strategy as winning, in each of the above circumstances?
7. What's a quasistrategy? What's a winning quasistrategy? Relationship to axiom of choice and axiom of dependent choice (the latter is needed to show that you can't have a length-ω game where both players have winning quasistrategies).
8. What's an infinite game of imperfect information (a Blackwell game)? What constitutes a strategy for such a game, what is its value, what does it mean for such a game to be determined?

Then the organizational questions are:

• How many articles do we need?
• What should they be called?
• How should the above information be distributed among them?

--Trovatore 02:54, 28 July 2005 (UTC)

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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)

Rule for Winning?

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)

Merger proposal

Perhaps a merge with Dominance (game theory). --70.111.218.254 21:10, 12 November 2006 (UTC)

I'm against merging. Unlike dominance, "Winning strategy" doesn't appear in the index of any of the standard game theory textbooks I have on hand: Osborne & Rubenstein, Fudenberg & Tirole, Gibbons (1992), Gintis (2000), it also doesn't appear in the following game theory texts on my shelf: Williams (1954), Luce & Raiffa (1957), Dresher (1961), Rapoport (1966), Hargreaves & Varoufakis (1995). I've never heard the term used as described by the article. I'm prepared to beleive that this is a commonly used term in Combinatorial game theory, but I'm pretty sure it's foreign to game theory. Pete.Hurd 21:32, 14 November 2006 (UTC)

Whups, I should have read User talk:Trialsanderrors/SCIENCE#Test case: Winning strategy first. Obvious merge and redirect would be to Axiom_of_determinacy, or Determinacy#Winning strategies. Or import some of those articles' encyclopedic tone into this and begin it with something like "In set theory...". Pete.Hurd 21:39, 14 November 2006 (UTC)

I think a redirect would be in order, I don't know if there's anything that can be merged. ~ trialsanderrors 23:08, 14 November 2006 (UTC)

I redirected. Feel free to revert but someone would have to look up sources. ~ trialsanderrors 08:09, 20 November 2006 (UTC)