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Knight's Pawn to--Ahh, Why Bother



 
 
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  #1  
Old July 10th 15, 05:07 PM posted to alt.chess,alt.math,alt.alien.vampire.flonk.flonk.flonk
mimus[_2_]
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Default Knight's Pawn to--Ahh, Why Bother

While the von Neumann minimax theorem establishes the solvability of all
two-person rectangular games, even those in which, say, a 1,000,000 by
2,000,000 matrix is involved, there still remains the task of considering
more general games-- in which there may be more than two players and each
player may have several moves, etc. However, it turns out there is no new
theoretical difficulty, providing a general game is _ finite _, that is,
only involves a finite number of moves with a finite number of
alternatives at each move. A finite game, as we shall illustrate shortly,
can always be "normalized", that is, converted into an equivalent matrix
game. Hence the minimax theorem and the method of solution we have
discussed apply to all finite games, even the most general . . . .

It will be observed that after the generalized game above was normalized,
the solution was effected more easily than in some of the more elementary
games we have illustrated. This was because the strategy matrix of the
more complicated game had saddle points, and hence had solutions in terms
of pure strategies. This relative ease of solution will always occur in
any game having "perfect information", which means that at any move the
player has complete knowledge of the choices made in all prevous moves. A
special theorem of game theory establishes the fact that in all games
with perfect information the normalized form, that is, the _ strategy
matrix _, will have at least one saddle point and hence a solution in
terms of pure strategies . . . .

Edna Kramer, _ The Nature and Growth of Modern Mathematics _


Basically, you can only win in chess etc. if you don't and the other
player does **** up.

Or, more accurately, given the complexity of the strategy matrices
involved (there's a little information-problem _there_, too), she wins
who ****s up the least often or badly.

--

Edna's a classic, once you get past
her initial obsession with place-notation,
admittedly another Great Sumerian Idea
(their abacus being the classic place-notation tool
for millenia until displaced by the digital latch).
  #2  
Old July 12th 15, 10:25 AM posted to alt.chess,alt.math,alt.alien.vampire.flonk.flonk.flonk
Contrarian
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Posts: 3
Default Knight's Pawn to--Ahh, Why Bother

In alt.alien.vampire.flonk.flonk.flonk mimus wrote:
While the von Neumann minimax theorem establishes the solvability of all
two-person rectangular games, even those in which, say, a 1,000,000 by
2,000,000 matrix is involved....



Edna Kramer, _ The Nature and Growth of Modern Mathematics _



life is tough


  #3  
Old July 12th 15, 10:42 AM posted to alt.chess,alt.math,alt.alien.vampire.flonk.flonk.flonk,alt.support.depression
%
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Posts: 5
Default Knight's Pawn to--Ahh, Why Bother

Contrarian wrote:
In alt.alien.vampire.flonk.flonk.flonk mimus
wrote:
While the von Neumann minimax theorem establishes the solvability of
all two-person rectangular games, even those in which, say, a
1,000,000 by 2,000,000 matrix is involved....



Edna Kramer, _ The Nature and Growth of Modern Mathematics _



life is tough


no it's not

hi
  #4  
Old July 12th 15, 12:07 PM posted to alt.chess,alt.math,alt.alien.vampire.flonk.flonk.flonk,alt.support.depression
Contrarian
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Posts: 3
Default Knight's Pawn to--Ahh, Why Bother

In alt.support.depression % wrote:
Contrarian wrote:
In alt.alien.vampire.flonk.flonk.flonk mimus
wrote:
While the von Neumann minimax theorem establishes the solvability of
all two-person rectangular games, even those in which, say, a
1,000,000 by 2,000,000 matrix is involved....



Edna Kramer, _ The Nature and Growth of Modern Mathematics _



life is tough


no it's not



well maybe not right now but just you wait


oh I forgot


you're in .bc.ca


a smart choice


hi

  #5  
Old July 14th 15, 08:15 AM posted to alt.chess,alt.math,alt.alien.vampire.flonk.flonk.flonk
Contrarian
external usenet poster
 
Posts: 3
Default Knight's Pawn to--Ahh, Why Bother

In alt.alien.vampire.flonk.flonk.flonk mimus wrote:
While the von Neumann minimax theorem establishes the solvability of all



someday I'll drag out my copy of Ian Fletcher's

Free Trade Doesn't Work


and look for some theorem (I think it was termed that)
that's discussed there



 




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