Talk:Minimax

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[edit] discussion

This is a minor point, but the phrase "since it is not computationally possible to look ahead as far as the completion of the game" should really read "it is not feasible" or "the time it would require to look ahead as far as the completion of the game but would be far longer than the lifetime of the universe" or "since it is intractable to look ahead as far as the completion of the game"

It is very much possible to the only limiting factors are time and memory

I'm not sure if you can make a generic statement that alpha-beta cuts the ply by half. It's just an empirical observation. I remember reading two-thirds somewhere.

Polished up the English a bit. Took out the hypothetical statement about the absence of an algorithm that would be able to analyse chess. But I'm afraid that this needs more polishing, especially of some statements that seem wrong to me:

A minmax algorithm would not decide infinity to a node if the game is not decided, right? A ply is a move of one player, so we should say the lookahead or number of plies.

I did not change this because my AI knowledge might be outdated, any expert advice available?

Robert Dober 2003-07-05 MEDST

I cut this bit out and will leave in here:

Article originally from FOLDOC; copied with permission. Feel free to update as needed. --/Mat 05:00, 6 Apr 2004 (UTC)

[edit] Non-specialist reading

As an amateur popping in, I can't even begin to understand the math here. Is this a concept that would only be referred to by specialists, or is it possible to add a more extensive plain English section to this article? (A good place to start might be, what do these equations do? How would they be used?) --Dvyost 04:44, 28 October 2005 (UTC)

I agree. Complex equations are fine, but we also need a plain English explanation right at the beginning. Wikipedia:Explain jargon. So I'm slapping that "too technical" tag (Template:Technical) on this article. --DavidCary 07:15, 20 November 2005 (UTC)

[edit] Minimax approximations of continuous functions

I think there's more than one use of the term 'minimax' in mathematics, and consequently there should possibly be a disambig page. I've never heard of the game theory usage of the term, but there's another important usage in relation to the approximation of continuous functions with polynomials. I'm not completely familiar with this so I won't explain it myself, but 'Chebyshev Polynomials' by J.C. Mason and D.C. Handscomb has a fairly good explanation, in particular the use of Chebyshev polynomials (first kind and others) and approximating functions with Chebyshev series on the minimax norm.

Bird of paradox 05:50, 29 October 2005 (UTC)

I agree. This page should be titled Minimax (decision theory). In other math related applications minimax usually refers to an optimization approach minimizing the max error (both continuous and discrete applications actually), as opposed to the squared or absolute error for example. The total error is written something like sum(error^infinity), if I recall. keith 21:48, 24 February 2006 (UTC)

[edit] cases where minimax does *not* give the optimal strategy

• games where at least one of the players doesn't seem to play rationally (such as when a non-zero-sum game is converted to a zero-sum game by adding "nature": we can often predict exactly what nature would do. Nature hardly ever acts like a "rational" Homo economicus.)
• infinite games

Are there any other cases where minimax is non-optimal? --DavidCary 07:15, 20 November 2005 (UTC)

[edit] Rawls?

Something should be said of John Rawls on the page. Maximin, at least, is tossed around in philosophical parley to refer to his theory of ethics/justice. --JMD (talk • contribs) 05:48, 27 July 2006 (UTC)

[edit] Who invented?

If this is a theory someone had to invent it. Anyone know who? -Ravedave ^{(help name my baby)} 17:45, 25 August 2006 (UTC)

[edit] Origin of "minimax"?

Two possible origins of the term "minimax" are given in the text (as of 2006/10/1). Which one is the right one?

"Minimax (sometimes minmax) is a method in decision theory for minimizing the maximum possible loss"

"(A is called the maximizing player and B is called the minimizing player), hence it is called the minimax algorithm."

Eric Le Bigot

Seems to me like they are both the explanation. --Zvika 09:14, 14 October 2006 (UTC)

[edit] Folk usage in gaming?

The article as it stands accurately reflects my understanding of what "minimax" means. However, there appears to be a folk misuse of the term amongst RPG and MMO players in which it refers simply to minimizing less important character stats (e.g., Charisma) in favor of maximizing more directly-applicable combat stats (Strength, Dexterity) when the option to manually adjust those stats exists. Should there maybe be an acknowledgement of this misuse in the article? It seems pretty common. El Mariachi 09:36, 16 November 2006 (UTC)

I think this use you present is fairly minor compared with the mathematical usage of the term and would hinder the article flow if it appears as a different section. I would be willing to consider a {{for}} template pointing to a separate article, if you think there's enough content in the alternate use to warrant an article. --Zvika 20:00, 20 November 2006 (UTC)

Definitely not worth a separate article. How about a one-sentence parenthetical acknowledgement at the end? I'm just concerned that people who are only familiar with the gaming usage will read this entry and think the term has any proper relation. El Mariachi 00:04, 23 November 2006 (UTC)

Again, I have never encountered this use, but if you are sure it really is a common term, then all right, be bold and put it in. --Zvika 14:21, 23 November 2006 (UTC)