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Old December 6th 06, 11:20 PM posted to rec.games.chess.analysis
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Default what kind of games are solvable?

Using the definition of "solved game" meaning that the first player
will always win, lose, or draw given perfect play.

I was trying to think of what characteristics of games make them
theoretically solvable or unsolvable. I think games involving random
chance are not solvable (Monopoly). Rock Paper Scissors is not solvable
because the action is simultaneous. Basketball is not solvable because
it doesn't have a finite set of moves.

Is there a simple characteristic that determines whether a game is
theoretically solvable? For example, "All perfect information games are
solvable. All non-perfect information games are unsolvable."

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Old December 7th 06, 12:21 PM posted to rec.games.chess.analysis
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Default what kind of games are solvable?

Bucky wrote:
Using the definition of "solved game" meaning that the first player
will always win, lose, or draw given perfect play.


There are various definitions of `solved'. The one you're using is
often called `ultra-weakly solved', meaning that we know the result of
perfect play but we don't necessarily know what perfect play looks
like. (An example of such a game is chomp.)


Is there a simple characteristic that determines whether a game is
theoretically solvable? For example, "All perfect information games
are solvable. All non-perfect information games are unsolvable."


All finite games of perfect information are solvable. Many infinite
games of perfect information are also solvable (for example, if the
set of winning positions for one of the players forms what is called a
Borel set, the game is solvable).

There are some non-perfect information games that are solvable. I
can't think of any non-trivial examples but here's a trivial one.

You pick a number between one and ten, without telling me what it is.
I pick a number between one and ten, without telling you what it is.
Whatever the numbers are, I win.

:-)

This all falls within the realm of Game Theory.

http://william-king.www.drexel.edu/t...game/game.html

looks like it might be a good introduction but I've not done more than
skim it.


Dave.

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www.chiark.greenend.org.uk/~davidr/ like a fashion statement but not
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erotic!
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