Call a position X an A-position if it does not have an option that is an...
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Call a position X an A-position if it does not have an option that is an O-positions, and call X an O-position if at least one of its options is an A position. (a) Terminal positions, i.e., positions which have no options at all, are A-positions. (b) Consider the following strategy: If X is an O-position, it has an option that is an A-position, so move to it; if X is an A-position, then move at random. Show that this strategy guarantees a win to next player when the game starts at an O-position. That is, every O-position is an N-position. (c) Show that, if X is an A position, then no matter what move the next player makes, the other player has a winning strategy. That is, every A-position is a P-position. We will never use this A- and O- terminology again. We just introduced it along the way to show that this recursive definition of P- and N-positions is equivalent to the strategy definition. Call a position X an A-position if it does not have an option that is an O-positions, and call X an O-position if at least one of its options is an A position. (a) Terminal positions, i.e., positions which have no options at all, are A-positions. (b) Consider the following strategy: If X is an O-position, it has an option that is an A-position, so move to it; if X is an A-position, then move at random. Show that this strategy guarantees a win to next player when the game starts at an O-position. That is, every O-position is an N-position. (c) Show that, if X is an A position, then no matter what move the next player makes, the other player has a winning strategy. That is, every A-position is a P-position. We will never use this A- and O- terminology again. We just introduced it along the way to show that this recursive definition of P- and N-positions is equivalent to the strategy definition.
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a If X is an Aposition then it is impossible for any player in position Y to be in a winning positio... View the full answer
Related Book For
Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
Posted Date:
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