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From: qts@houxa.UUCP (J.RAMMING)
Newsgroups: net.puzzle
Subject: TWO PLAYER GAMES
Message-ID: <961@houxa.UUCP>
Date: Mon, 24-Feb-86 10:01:31 EST
Article-I.D.: houxa.961
Posted: Mon Feb 24 10:01:31 1986
Date-Received: Wed, 26-Feb-86 07:42:59 EST
Organization: AT&T Bell Labs, Holmdel NJ
Lines: 28



In many games (see my 'pennies puzzle' posting) it is not immediately
obvious that a particular player has a winning strategy.  However,
there may be certain games in which it is immediately clear that a 
particular player DOES NOT have a winning strategy.

Puzzle:  Examine the following proof about two player games.
	 Which condition(s), if any, must exist in order for it to 
	 be valid?  If these conditions exist, cite a game or
	 class of games to which this proof applies.  

	 Alternately, consider the possibility that there is a
	 flaw in the proof.

Proof:   1)  Assume that the second player has a winning strategy.
	 2)  Then clearly, the first player should make a random move.
	     He can then win if, for the remainder of the game, he
	     follows the second's players winning strategy.  
	 3)  This is a contradiction, therefore assumption (1) is 
	     false.  We conclude that THE SECOND PLAYER DOES
	     NOT HAVE A WINNING STRATEGY.

J. Christopher Ramming

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