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As in the Monty Hall problem, the intuitive answer is 1 / 2 , but the probability is actually 2 / 3 . The Three Prisoners problem, published in Martin Gardner's Mathematical Games column in Scientific American in 1959 [7] [55] is equivalent to the Monty Hall problem. This problem involves three condemned prisoners, a random one of ...
A 2-spot game of Sprouts. The game ends when the first player is unable to draw a connecting line between the only two free points, marked in green. The game is played by two players, [2] starting with a few spots drawn on a sheet of paper. Players take turns, where each turn consists of drawing a line between two spots (or from a spot to ...
A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. [1] [verification needed] [clarification needed] Often, such games have simple rules and match procedures, such as tic-tac-toe and dots and boxes. Generally, mathematical games need not be conceptually intricate to involve deeper ...
Determined game (or Strictly determined game) In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. [2] [3] Dictator A player is a strong dictator if he can guarantee any outcome regardless of the other players.
The unique games conjecture states that for every sufficiently small pair of constants ε, δ > 0, there exists a constant k such that the following promise problem (L yes, L no) is NP-hard: L yes = {G: the value of G is at least 1 − δ} L no = {G: the value of G is at most ε} where G is a unique game whose answers come from a set of size k.
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Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics includes the aesthetics and culture of mathematics, peculiar or amusing stories and coincidences about mathematics, and the personal lives of mathematicians.
Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set, the rules of the puzzle determine all subsequent changes and moves.