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Act 7

The document outlines a strategy game analysis involving player X and player O, focusing on the representation of game evolutions using a tree structure. It poses questions regarding the outcomes of the game, including the number of wins for each player and draws, as well as probabilities based on random play strategies. Additionally, it discusses the concept of branching factors in games like Go and chess, highlighting their impact on game complexity.

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danielrncn1
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30 views1 page

Act 7

The document outlines a strategy game analysis involving player X and player O, focusing on the representation of game evolutions using a tree structure. It poses questions regarding the outcomes of the game, including the number of wins for each player and draws, as well as probabilities based on random play strategies. Additionally, it discusses the concept of branching factors in games like Go and chess, highlighting their impact on game complexity.

Uploaded by

danielrncn1
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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DNL, Act7

Represent strategy games evolution with a tree

1. X plays first. Who do you think would win in this game?


2. Represent the different evolu ons of the game using a tree.
3. For each terminal node of the tree, indicate the winner.
Use a color code: Blue for X , Red for O, Black for a draw.
4. How many possible games are there?
5.
a. How many wins for X?
b. How many wins for O?
c. How many draws?
6. Assuming a random play strategy, what is the probability of:
a. An X-win?
b. An O-win?
c. A draw?
In Ac vity 4, we observed that Go is harder than chess due to its larger branching factor.
The branching factor is the average number of moves available to a player at each turn.
7. Why is it called a branching factor? (Hint: branches are part of trees).
The maximum number of moves on a Go board is 19×19=361.
In chess, the typical number of legal moves is around 30.
8. We assume a chess game where each player has a constant 30 moves per turn.
a. How many possible games are there a er two rounds (for both players)?
b. How many possible games are there a er four rounds (for both players)?
9. We assume a Go game where each player has a constant 300 moves per turn.
a. How many possible games are there a er two rounds (for both players)?
b. How many possible games are there a er four rounds (for both players)?
10. Why do you think the branching factor is important to determine the difficulty of the game.

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