Practice Problems on Game Theory Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Game Theory is a topic in competitive programming that involves a certain type of problem, where there are some players who play a game based on given rules and the task is often to find the winner or the winning moves. Game Theory is often asked in short contests with a mixture of other topics like range querying or greedy or dynamic programming. Objectives Game Theory for Competitive Programming:Here we will focus on two-player games that do not contain random elements.Our goal is to find a strategy we can follow to win the game no matter what the opponent does if such a strategy exists. Game theory or combinatorics game theory in which we have perfect information (that is no randomization like a coin toss) such as game rules, player's turn, minimum and maximum involved in the problem statements, and some conditions and constraints.There will be three possible cases/ state win, loss or tie.A terminal condition is well-defined/ specified clearly.E.g. player who picks the last coin will win the game, or a player who picks the second last time coin will win the game or something like that.It is assumed that the game will end at some point after a fixed number of moves. Unlike chess, where you can have an unlimited number of moves possible especially when you are left with the only king, but if you add an extra constraint that says “game should be ended within ‘n’ numbers of moves”, that will be a terminal condition. This is the kind of assumption a game theory is looking for.It turns out that there is a general strategy for such games, and we can analyze the games using the nim theory.Initially, we will analyze simple games where players remove sticks from heaps, and after this, we will generalize the strategy used in those games to other games.Practice Problems on Game Theory:ProblemFind the winner in nim-gameGame of N stones where each player can remove 1, 3 or 4Choice of AreaFinding optimal move in Tic-Tac-Toe using Minimax Algorithm in Game TheoryOptimal Strategy for a GameFind the player who will win by choosing a number in range [1, K] with sum total NOptimal Strategy for the Divisor game using Dynamic ProgrammingChessboard Pawn-Pawn gameFind the winner of the game with N piles of boxesCoin game of two cornersJosephus ProblemVariation in Nim GameGame of replacing array elementsCombinatorial Game TheoryFind winner in game of N balls, in which a player can remove any balls in range [A, B] in a single moveFind the winner of a game of removing any number of stones from the least indexed non-empty pile from given N pilesA Binary String GameTwo player game in which a player can remove all occurrences of a numberMake a palindromic string from given stringFind the player who will win the Coin gameFind the winner of the GameOptimal Strategy for a GameFind the winner of the Game to Win by erasing any two consecutive similar alphabetsFind the winner of a game of removing at most 3 stones from a pile in each turnPen Distribution ProblemFind the winner of game of repeatedly removing the first character to empty given stringFind the player who wins the game by removing the last of given N cardsWinner in the Rock-Paper-Scissor game using Bit manipulationOptimal Strategy for a Game | Special Gold CoinPredict the winner of the game on the basis of absolute difference of sum by selecting numbersFind probability that a player wins when probabilities of hitting the target are givenFind winner when players remove multiples of A or B from Array in each turnPredict the winner of a card game of removing K cards in each turn such that Bitwise AND of K and size of pile is 0Optimal strategy for a Game with modificationsNumber of ways for playing first move optimally in a NIM gameProbability of A winning the match when individual probabilities of hitting the target givenPredict the winner of the game | Sprague-GrundyGame of Chocolates | Wythoff’s GameMinimum operations to reduce N to a prime number by subtracting with its highest divisorFind the winner of a game of donating i candies in every i-th moveLargest odd divisor Game to check which player wins Comment More infoAdvertise with us A anilkumarsingh0160 Follow Improve Article Tags : Game Theory DSA Practice Tags : Game Theory Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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