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Normal Topic A bit if Chess, Game Theory and Statistics (Read 2731 times)
zoo
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Re: A bit if Chess, Game Theory and Statistics
Reply #3 - 04/25/13 at 12:36:46
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Alex_Svitashev wrote on 04/24/13 at 02:58:06:

If someone asked you to assert this percentage of correct choice of a World Chess Champion, a Grandmaster or for an average player, what would your best guess be?
If you had access to an enormous database of chess games, how would you use this information to answer the question?


There are a lot of assumptions/opinions in the OP.  
Interpreting the last question as "how would you use a large database to study the rate of best moves played by an average, GM or WC player ?" :

First I would define a best move in some game-theoretic setting. Two main possibilities :
a) best moves in a position are those maintaining the initial status of the position (win, draw, lose). In this respect, all moves are equally best if they maintain a winning position, and all moves are equally best in a losing position, since none can improve the evaluation of the position. Note that this status in not always known, as chess isn"t solved yet.
b) you can define additional metrics such as "in winning position: shortest distance to mate" or "in losing position: maximum severity of winning sequences", with such severity related to some probability that the opponent loses its winning status, or any other criteria you see fit.

Having chosen a metric you're happy with, you can take a subset of measurable chess positions (e.g. ending tablebases when the metric is either distance to mate or position status), and check your big game database against it. For each position both in the tablebase and in the gamebase, you can score the frequency of (or distance to) "best moves" played in each category. 

That's what I would do anyway if life wasn't so damn short. 
« Last Edit: 04/26/13 at 12:08:11 by »  
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Kazzy
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Re: A bit if Chess, Game Theory and Statistics
Reply #2 - 04/24/13 at 13:08:29
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Scarblac wrote on 04/24/13 at 07:03:15:
I think it is more likely that in many positions, there are in fact quite a few perfect moves. If current position isn't a forced win for either side, then any move that doesn't lose by force is as good as any other, theoretically.

This is certainly true but I think that it's possible to define some kind of best move in the position. 
Take the ending R+B vs. R for example. It's theoretically drawn but the player with R+B can pose some problems for the player with a lone Rook. The defending player is maybe forced to find some only moves or some moves which are difficult to spot for a human player.
The attacking player may has only "perfect moves" as all moves lead to a draw. But it's a difference in practice if you force your opponent to play only moves or if you sacrifice your own Rook so that you have to play some only moves yourself to reach a draw in the B vs. R ending even if sacrificing your Rook is also a perfect move in theory.

So if you try to find a best move in a position, I think you have to take your opponent's possibilities into account to define some kind of best move in the position.
But from a gametheoretical point of view, there are many thousands chess games which had seen only perfect moves by both player, leading to some kind of perfect draw in the end.
  
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Scarblac
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Re: A bit if Chess, Game Theory and Statistics
Reply #1 - 04/24/13 at 07:03:15
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I think it is more likely that in many positions, there are in fact quite a few perfect moves. If current position isn't a forced win for either side, then any move that doesn't lose by force is as good as any other, theoretically. You can observe this by playing a drawn endgame against a computer using tablebases, in many cases any move draws and it just appears to play randomly.

Perfect games have been played many times, for instance there are a lot of short known theoretical draws that are almost certainly perfect (if the game is in fact a draw), and quite a bit of current mainline opening theory may be perfect in the sense that it doesn't lead to a position that loses by force.
  
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Alex_Svitashev
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A bit if Chess, Game Theory and Statistics
04/24/13 at 02:58:06
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Chess is a finite game with perfect information, so (in theory) there exists a perfect game where White plays best-possible-move and Black answers with best-possible-reply on every turn. Obviously, in any given position there is one move which is a part of this perfect play. (The-Best-Possible-Move)
It is not proven yet, but it is safe to assume that the outcome of such perfect game is a draw.

In an average chess game position there is about 40 legal moves for each player. So a machine playing randomly has a 1/40=2.5% chance of making the right (aka the best possible) choice in any given position.

If someone asked you to assert this percentage of correct choice of a World Chess Champion, a Grandmaster or for an average player, what would your best guess be?
If you had access to an enormous database of chess games, how would you use this information to answer the question?
  
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