Question

1. Yes or No? Recall the heuristics from the 8-puzzle problem: h1 is the number of out of place tiles, and h2 is the Manhattan distance. Is a combined heuristic (h1 + h2)/2 also admissible? Provide a justification.

2. In a fully observable, turn-taking, zero-sum game between two perfectly rational players, it does not help the first player to know what move the second player will make.

Answer 1

Solution for 1:

Yes

Justification:

h2 is an admissible heuristic, since in every move, one tile can only move closer to its goal by one step and the eucledian distance is never greater than the number of steps required to move a tile to its goal position.

h1 is an admissible heuristic, since it is clear that every tile that is out of position must be moved at least once.

So, obviously (h1+h2)/2 is admissible heuristic.

Solution for question 2 is:

This statement portrays the game of chess well overall, it meets each one of those measures and is false. "A zero-sum is (confusingly) characterized as one where the all out result to all players is the equivalent for each occasion of the game. Chess is zero-sum in light of the fact that each game has result of either 0 + 1, 1 + 0 or 1/2 + 1/2" (Russell and Norvig, 162). This means just a single player wins and other looses or their is a draw. In the round of chess technique is one of the principle keys for any great player. Every player ought to think a few moves ahead of time, so on the off chance that I make a move I like to ascertain the potential moves my rival will make based off the piece I move so I can make an opening, or draw out a piece that I might want to wipe out.

Since the two players of chess are completely rational they will make the ideal move against their opponent, however that is additionally going to be based on tactics. Chess is anything but a basic game that can be finished in no time flat, it takes thought. There are three phases to a chess game; the opening, middlegame, and endgame. (http://en.wikipedia.org/wiki/Chess) The major part is in the middlegame, and it is useful if you can know what type of strategy your opponent is using.

Hope this helps. Thank you!