Complexity theory in games

  • What are the different measures of game complexity?

    Combinatorial game theory has several methods of measuring game complexity.
    This article discusses five of them: state-space complexity, game tree size, decision complexity, game tree complexity, and computational complexity..

  • What is the complexity of a game?

    The state-space complexity of a game is the number of legal game positions reachable from the initial position of the game.
    When this is too hard to calculate, an upper bound can often be computed by also counting (some) illegal positions, meaning positions that can never arise in the course of a game..

  • What is the complexity of the game chess?

    Chess has an estimated state-space complexity of 1046 , the estimated game tree complexity of 10123 is based on an average branching factor of 35 and an average game length of 80 ply ..

  • What is the game-tree complexity of go?

    Game tree complexity
    The computer scientist Victor Allis notes that typical games between experts last about 150 moves, with an average of about 250 choices per move, suggesting a game-tree complexity of 10360..

  • Combinatorial game theory has several methods of measuring game complexity.
    This article discusses five of them: state-space complexity, game tree size, decision complexity, game tree complexity, and computational complexity.
  • Game tree complexity
    The computer scientist Victor Allis notes that typical games between experts last about 150 moves, with an average of about 250 choices per move, suggesting a game-tree complexity of 10360.
Combinatorial game theory measures game complexity in several ways: These measures involve understanding game positions, possible outcomes, and computation  Measures of game complexityGame tree sizeComplexities of some well
Complexity theory in games
Complexity theory in games
This is a list of complexity classes in computational complexity theory.
For other computational and complexity subjects, see list of computability and complexity topics.

Unsolved problem in computational complexity theory

In computational complexity theory, the unique games conjecture is a conjecture made by Subhash Khot in 2002.
The conjecture postulates that the problem of determining the approximate value of a certain type of game, known as a unique game, has NP-hard computational complexity.
It has broad applications in the theory of hardness of approximation.
If the unique games conjecture is true and P ≠ NP, then for many important problems it is not only impossible to get an exact solution in polynomial time, but also impossible to get a good polynomial-time approximation.
The problems for which such an inapproximability result would hold include constraint satisfaction problems, which crop up in a wide variety of disciplines.

Categories

Computational complexity game theory
Complexity theory and computational geometry
Geometric complexity theory pdf
General complexity theory
Geography complexity theory
Research in geometric complexity theory
Complexity theory healthcare
Complexity theory history
Complexity theory helps explain
Complexity theory health
Complexity theory hbr
Complexity theory health services research
Complexity theory hierarchy
Complexity theory hospitals
Complexity theory heuristic
Complexity theory hash function
Complexity theory human
Complexity theory in health care
Complexity leadership theory higher education
Complexity theory in health systems