Game Theory: Winning Moves for (20, 21, 28)

In summary, the winning moves for the game (20,21,28) are (20,4,16), (0,20,20), (20,20,0), (20,0,8), (0,21,21).
  • #1
math_nerd
22
0
(1 pt) We shall denote a position in three-pile Nim by (a,b,c), so that there are a chips in the first pile, b in the second, and c in the third.

Given the following position in Nim, list all winning moves. As an example, if the piles are (2,2,2) then we can list all winning moves as (0,2,2),(2,0,2),(2,2,0).

For game (20, 21, 28), the winning moves are:


I thought it should be (20,4,16), (0,20,20), (20,20,0), because when you calculate their nim sum you get (0,0,0), but this answer is incorrect. Can anyone help me understand what I am doing wrong?

Thank you!
 
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  • #2
You are almost correct! The winning moves for the game (20,21,28) are (20,4,16), (0,20,20), (20,20,0), (20,0,8), (0,21,21). You are missing the move (20,0,8) since it also produces a nim sum of 0.
 

Related to Game Theory: Winning Moves for (20, 21, 28)

1. What is game theory?

Game theory is a mathematical framework for analyzing decision-making in situations where the outcome of one person's decision depends on the decisions of others. It is used in various fields, including economics, political science, and psychology, to understand strategic behavior and make predictions about the best course of action.

2. How does game theory apply to winning moves?

In the context of "Game Theory: Winning Moves for (20, 21, 28)", the game refers to a specific scenario with three players and three possible outcomes, each associated with a certain payoff. By using game theory, we can analyze the possible moves and strategies of each player and determine the optimal move that will result in the highest payoff for a player.

3. How do you calculate the optimal winning move in this game?

To calculate the optimal winning move, we use mathematical tools such as Nash equilibrium and dominant strategies. These methods help us determine the best course of action for each player, taking into account the potential actions of the other players.

4. Can game theory be applied to real-life situations?

Yes, game theory can be applied to real-life situations where there are multiple players with conflicting interests. For example, it can be used to analyze pricing strategies in a competitive market, negotiate in a business deal, or make political decisions.

5. Are there any limitations to game theory?

While game theory is a useful tool for decision-making, it does have some limitations. It assumes that all players are rational and have complete information, which may not always be the case in real-life situations. Additionally, it does not account for emotions or unpredictable behavior, which can also impact the outcome of a game.

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