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    Der Minimax-Algorithmus ist ein Algorithmus zur Ermittlung der optimalen Spielstrategie für int max(int spieler, int tiefe) { if (tiefe == 0 or keineZuegeMehr(​spieler)) return bewerten(); int maxWert = -unendlich; da) { fuehreNaechstenZugAus(); int wert = min(-spieler, tiefe-1); macheZugRueckgaengig(); if (wert > maxWert). Spieltheoretische Formulierung[Bearbeiten | Quelltext bearbeiten]. Der Hauptsatz für John von Neumann, Oskar Morgenstern: Theory of Games and Economic Behavior, Verlag Princeton Paperback, Princeton, , ISBN 2-ply game. MAX. 3. 8. 6. 4. 2. 5. 2. MIN. 3. A. 1. A. 3. A. 2. A. A. A. A. A. A. A. A. A. 3. 2. 2. B. Beckert: Einführung in die KI. In this work, we are going to study a differential game related to terrorism: min-​max two persons differential game, the question and discuss the . Die klassische Min-Max-Suche wird angewendet auf diesen Baum The Game of Hex: An Automatic Theorem Proving Approach to Game.

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    Die klassische Min-Max-Suche wird angewendet auf diesen Baum The Game of Hex: An Automatic Theorem Proving Approach to Game. Der Minimax-Algorithmus ist ein Algorithmus zur Ermittlung der optimalen Spielstrategie für int max(int spieler, int tiefe) { if (tiefe == 0 or keineZuegeMehr(​spieler)) return bewerten(); int maxWert = -unendlich; da) { fuehreNaechstenZugAus(); int wert = min(-spieler, tiefe-1); macheZugRueckgaengig(); if (wert > maxWert). Spieltheoretische Formulierung[Bearbeiten | Quelltext bearbeiten]. Der Hauptsatz für John von Neumann, Oskar Morgenstern: Theory of Games and Economic Behavior, Verlag Princeton Paperback, Princeton, , ISBN

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    Also field of vision. Also invincibility frames , invulnerability period , mercy invincibility. Also gameplay mechanics. Also gameplay mode.

    Ghost cars in racing games generally appear as translucent or flashing versions of the player's vehicle.

    Based on previously recorded lap times, they serve only to represent the fastest lap time and do not interact dynamically with other competitors.

    A skilled player will use the ghost to improve their time, matching the ghost's racing line as it travels the course. Some also have ghosts set by staff members and developers, often showing perfect routes and lap times.

    A variation of the feature, dubbed by Firemonkeys Studios as "Time-Shifted Multiplayer", was implemented in the mobile racing game Real Racing 3.

    These ghost cars can collide with the player and other vehicles, and are fully visible to the player. In some rhythm game s, such as the Elite Beat Agents and Osu!

    Also: infinite health , infinite life , invincibility , invulnerability. Also hit points. Also damage ring.

    Also independent video game. Also heads-up display HUD. A stage or level in a video game often an arcade game that stops the player's progress due to a software bug.

    Notable arcade kill screens include: [ relevant? Also multi-user domain , multi-user dungeon. Also cross-platform. Also platformer.

    Very occasionally may refer to the result of repeatedly balancing a game primarily through buffs , thus making every character substantially more powerful than they were at release.

    Also rerolling. Also old-school gaming. Also grenade jumping. This is different from games such as first-person shooter s FPS , wherein the player-character in those games are all standardized forms and the physical skills of the player involved are the determining factor in their success or failure within the game.

    In an RPG, a human player can be the best player in the world at the game, but if they are using a character build that is substandard, they can be significantly outplayed by a lesser player running a more-optimal character build.

    Also check point. Also game save , savegame , or savefile. A skill tree is called a "tree" because it uses a tiered system and typically branches out into multiple paths.

    A tiered skill tree will require a player to achieve certain skills before the next tier of skills become available.

    The player may be required to achieve all skills in one tier before moving on to the next, or may only be required to complete prerequisites for individual branches.

    Skill trees are a common tool used for in-game balancing by game designers. Skill trees also offer a "game within a game" in which players are not only playing a video game, but their decisions on how they allocate points into their skill trees will affect their overall gaming experience.

    The action roleplaying game Diablo II , released in , is often cited as the true innovator of in-depth skill trees. Also meat shield.

    Also tech tree. The initial screen of a computer , video , or arcade game after the credits and logos of the game developer and publisher are displayed.

    Early title screens often included all the game options available single player, multiplayer, configuration of controls, etc.

    This can be attributed to the use of the title screen as a loading screen , in which to cache all the graphical elements of the main menu.

    Older computer and video games had relatively simple menu screens that often featured pre-rendered artwork. In arcade games, the title screen is shown as part of the attract mode loop, usually after a game demonstration is played.

    The title screen and high score list urge potential players to insert coins. In console games, especially if the screen is not merged with the main menu, it urges the player to press start.

    Similarly, in computer games, the message "Hit any key " is often displayed. Controls that lack an actual "Start" button use a different prompt; the Wii , for example, usually prompts to press the "A" button and the "B" trigger simultaneously, as in Super Mario Galaxy 2 or Mario Party 9.

    Fan-made games often parody the style of the title that inspired them. Also CPU vs. From Wikipedia, the free encyclopedia.

    Redirected from Min-maxing. List of definitions of terms and concepts related to video games. This article has multiple issues.

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    This video game -related list is incomplete ; you can help by expanding it. For the film, see Action Point. For the magazine, see Kill Screen.

    Not to be confused with minimax. For the video game developer, see Splash Damage. Although only the blue player in the center takes a direct hit, everyone within the circle takes splash damage.

    The damage may decrease further from the point of impact; this is known as damage falloff. Schwartz, Janet Schwartz.

    Retrieved January 5, Retrieved January 5, Archived from the original on February 2, Retrieved February 2, Archived from the original on May 28, Retrieved May 28, Lee Laughead.

    Retrieved May 2, Addison-Wesley Professional. Hoboken, New Jersey: Wiley. Retrieved May 24, Retrieved 2 June Massively Multiplayer Games for Dummies.

    Basel: Birkhäuser. Retrieved March 3, Assume the payoff matrix for B is the same matrix with the signs reversed i.

    Then, the minimax choice for A is A2 since the worst possible result is then having to pay 1, while the simple minimax choice for B is B2 since the worst possible result is then no payment.

    However, this solution is not stable, since if B believes A will choose A2 then B will choose B1 to gain 1; then if A believes B will choose B1 then A will choose A1 to gain 3; and then B will choose B2; and eventually both players will realize the difficulty of making a choice.

    So a more stable strategy is needed. Some choices are dominated by others and can be eliminated: A will not choose A3 since either A1 or A2 will produce a better result, no matter what B chooses; B will not choose B3 since some mixtures of B1 and B2 will produce a better result, no matter what A chooses.

    These mixed minimax strategies are now stable and cannot be improved. Frequently, in game theory, maximin is distinct from minimax.

    Minimax is used in zero-sum games to denote minimizing the opponent's maximum payoff. In a zero-sum game , this is identical to minimizing one's own maximum loss, and to maximizing one's own minimum gain.

    In non-zero-sum games, this is not generally the same as minimizing the opponent's maximum gain, nor the same as the Nash equilibrium strategy.

    The minimax values are very important in the theory of repeated games. One of the central theorems in this theory, the folk theorem , relies on the minimax values.

    In combinatorial game theory , there is a minimax algorithm for game solutions. A simple version of the minimax algorithm , stated below, deals with games such as tic-tac-toe , where each player can win, lose, or draw.

    If player A can win in one move, their best move is that winning move. If player B knows that one move will lead to the situation where player A can win in one move, while another move will lead to the situation where player A can, at best, draw, then player B's best move is the one leading to a draw.

    Late in the game, it's easy to see what the "best" move is. The Minimax algorithm helps find the best move, by working backwards from the end of the game.

    At each step it assumes that player A is trying to maximize the chances of A winning, while on the next turn player B is trying to minimize the chances of A winning i.

    A minimax algorithm [5] is a recursive algorithm for choosing the next move in an n-player game , usually a two-player game. A value is associated with each position or state of the game.

    This value is computed by means of a position evaluation function and it indicates how good it would be for a player to reach that position.

    The player then makes the move that maximizes the minimum value of the position resulting from the opponent's possible following moves.

    If it is A 's turn to move, A gives a value to each of their legal moves. This leads to combinatorial game theory as developed by John Horton Conway.

    An alternative is using a rule that if the result of a move is an immediate win for A it is assigned positive infinity and if it is an immediate win for B , negative infinity.

    The value to A of any other move is the maximum of the values resulting from each of B 's possible replies. For this reason, A is called the maximizing player and B is called the minimizing player , hence the name minimax algorithm.

    The above algorithm will assign a value of positive or negative infinity to any position since the value of every position will be the value of some final winning or losing position.

    Often this is generally only possible at the very end of complicated games such as chess or go , since it is not computationally feasible to look ahead as far as the completion of the game, except towards the end, and instead, positions are given finite values as estimates of the degree of belief that they will lead to a win for one player or another.

    This can be extended if we can supply a heuristic evaluation function which gives values to non-final game states without considering all possible following complete sequences.

    We can then limit the minimax algorithm to look only at a certain number of moves ahead. This number is called the "look-ahead", measured in " plies ".

    For example, the chess computer Deep Blue the first one to beat a reigning world champion, Garry Kasparov at that time looked ahead at least 12 plies, then applied a heuristic evaluation function.

    The algorithm can be thought of as exploring the nodes of a game tree. The effective branching factor of the tree is the average number of children of each node i.

    The number of nodes to be explored usually increases exponentially with the number of plies it is less than exponential if evaluating forced moves or repeated positions.

    The number of nodes to be explored for the analysis of a game is therefore approximately the branching factor raised to the power of the number of plies.

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