Tree Data Structures & Minimax Algorithm for Games

In summary, the conversation revolves around a game involving removing sticks and how to determine the winner. The game follows a minimax algorithm and if played perfectly, it will always end in a draw. However, the speaker is trying to find a single formula that will determine the winner for any number of sticks. They mention that the player who removes the last stick wins, except in the case of only one stick left, where it is a draw. The conversation also touches on analyzing games and working backwards from the end situation. It is suggested that player 2 will always work towards multiples of 5, unless n is a multiple of 5 plus 2 or 3.
  • #1
wololo
27
0

Homework Statement


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Homework Equations


Tree data structures.
I think it might also have something to do with minimax algorithm, but it was only mentioned once and never discussed extensively in class so I doubt it is required.

The Attempt at a Solution


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If both players play as well as they can, the game will end in a draw. Player 1 will always have the option of choosing to draw rather than lose.
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However I can't find a function that given n sticks will tell me who will win. For 5, 10 and other multiples of 5, player 2 necessarily wins but what about the other cases? How can I find a single formula that will necessarily tell me who will win, given that they play well?
 
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  • #2
Misunderstanding: you can't end in a draw.
 
  • #3
BvU said:
Misunderstanding: you can't end in a draw.
"The player who removes the last match wins, except if there is only one match left, in which case the game is a draw." All the paths that end in 1 in the game tree are draws.
 
  • #4
Oops, sloppy reading... o:)
I remember something about analyzing games like this: start from the end situation and work backwards...
Your "multiples of 5" points that way. So player 2 will always work towards multiples of 5. So will 1. That way you have pinned down "playing well". Apparently you really want the other to start when playing this game, unless n is a multiple of 5 plus 2 or 3.
 

FAQ: Tree Data Structures & Minimax Algorithm for Games

1. What is a tree data structure?

A tree data structure is a way of organizing data in a hierarchical manner, similar to a tree with a root node and branches. Each node in the tree can have multiple child nodes, and the branches represent the relationships between the nodes. Trees are commonly used in computer science to represent data in a logical and easily searchable way.

2. How is a tree data structure used in game development?

In game development, tree data structures are used to represent the game state and possible moves in a game. This allows for efficient decision making and gameplay mechanics. For example, in a chess game, a tree data structure can represent all possible moves for a given position, and the minimax algorithm can be used to find the best move for a player.

3. What is the minimax algorithm?

The minimax algorithm is a decision-making algorithm commonly used in game theory and artificial intelligence. It is used to find the best move for a player in a game by considering all possible outcomes of the game and choosing the move that maximizes the player's chances of winning or minimizes their chances of losing.

4. What are the key components of the minimax algorithm?

The key components of the minimax algorithm are the game tree, which represents all possible game states and moves, and the evaluation function, which assigns a score to each game state. The algorithm then recursively evaluates each possible move and chooses the one with the highest score for the current player.

5. What are the benefits of using a tree data structure and the minimax algorithm in game development?

Using a tree data structure and the minimax algorithm allows for efficient decision making in games, as it considers all possible moves and outcomes. This can lead to more challenging and strategic gameplay for players. Additionally, the structure of the game tree can be modified to represent different game scenarios, making the algorithm adaptable to various games.

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