Hex IAQ
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Description: Answers to infrequently asked questions, by Bert Enderton.
Answers to infrequently asked questions about the game of Hex (Most of this material was written in 1995, but some was added in April 2000) Only "ultra-weakly," to use Victor Allis's terminology. John Nash proved in 1949 that the first player has a theoretical win, but his proof is non-constructive; i.e., it does not indicate how to win. The proof goes like this: Either there is a winning strategy for the first player, or there is a winning strategy for the second player (note there are no draws). Suppose there were a winning strategy for the second player. The first player could "steal" this strategy by making an arbitrary first move and then pretending to be the second player from then on. Whenever the strategy would call for playing on hex he already occupied (e.g. because that was his arbitrary first play), the first player would just make another arbitrary move. His extra stone could not hurt him. Thus the first player would win, which is a contradiction, therefore the second player does not have a winning strategy, therefore the first player does.
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| Date | activated: 24-Apr-1985 last updated: 16-Sep-2010 expires: 31-Jul-2014 |