If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed. To start viewing messages, select the forum that you want to visit from the selection below. 


Thread Tools  Display Modes 
#1




Knight's Pawn toAhh, Why Bother
While the von Neumann minimax theorem establishes the solvability of all
twoperson 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 informationproblem _there_, too), she wins who ****s up the least often or badly.  Edna's a classic, once you get past her initial obsession with placenotation, admittedly another Great Sumerian Idea (their abacus being the classic placenotation tool for millenia until displaced by the digital latch). 
#2




Knight's Pawn toAhh, Why Bother
In alt.alien.vampire.flonk.flonk.flonk mimus wrote:
While the von Neumann minimax theorem establishes the solvability of all twoperson 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




Knight's Pawn toAhh, Why Bother
Contrarian wrote:
In alt.alien.vampire.flonk.flonk.flonk mimus wrote: While the von Neumann minimax theorem establishes the solvability of all twoperson 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




Knight's Pawn toAhh, 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 twoperson 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




Knight's Pawn toAhh, 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 
Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Mate in 64 problem (request starting position to this amazing chess problem)  darkme  rec.games.chess.misc (Chess General)  6  May 8th 12 06:44 PM 
An interesting post from ChessForums.org  Offramp  rec.games.chess.misc (Chess General)  7  June 24th 11 01:44 AM 
ruy lopez exchange variation  ironmarshal  rec.games.chess.analysis (Chess Analysis)  63  December 4th 05 05:58 PM 
Looking for comments  Adam Maloney  rec.games.chess.analysis (Chess Analysis)  7  November 4th 05 04:44 PM 
Please check this out  Richard  rec.games.chess.analysis (Chess Analysis)  9  October 25th 05 05:48 PM 