Combinatorial game theoryCombinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a position evolves through alternating moves, each governed by well-defined rules, with the aim of achieving a specific winning condition.
Impartial gameIn combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference between player 1 and player 2 is that player 1 goes first. The game is played until a terminal position is reached. A terminal position is one from which no moves are possible.
Normal play conventionA normal playconvention in a game is the method of determining the winner that is generally regarded as standard. For example: Preventing the other player from being able to moveBeing the first player to achieve a targetHolding the highest value handTaking the most card tricksIn combinatorial game theory, the normal play convention of an impartial game is that the last player able to move is the winner.
Sprague–Grundy theoremCombinatorial game theory theorem In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap game of nim, or to an infinite generalization of nim.
Graph (discrete mathematics)In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line).PSPACE-completeIn computational complexity theory, a decision problem is PSPACE-complete if it can be solved using an amount of memory that is polynomial in the input length (polynomial space) and if every other problem that can be solved in polynomial space can be transformed to it in polynomial time.
Édouard LucasFrançois Édouard Anatole Lucas (French pronunciation:; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence and the Tower of Hanoi. The related Lucas sequences and Lucas numbers are named after him. BiographyLucas was born in Amiens and educated at the École Normale Supérieure.
Dots (paper-and-pencil game)Dots (Czech: Židi, Polish: Kropki, Russian: Точки) is an abstract strategy game, played by two or more people on a sheet of squared paper. The goal is to "capture" enemy dots by surrounding them with a continuous line of one's own dots. Once an area containing enemy dots is surrounded, that area ceases to be playable. The game is somewhat similar to Go and also has some similarities to the simpler and smaller dots and boxes game.
Dual graphIn the mathematical discipline of graph theory, the dual graph of a planar graphG is a graph that has a vertex for each face of G. The dual graph has an edge for each pair of faces in G that are separated from each other by an edge, and a self-loop when the same face appears on both sides of an edge.
Hex (board game)Hex (also called Nash) is a two-player abstract strategy board game in which players attempt to connect opposite sides of a rhombus-shaped board made of hexagonal cells. Hex was invented by mathematician and poet Piet Hein in 1942 and later rediscovered and popularized by John Nash. It is traditionally played on an 11×11 rhombus board, although 13×13 and 19×19 boards are also popular. It can also be played with paper and pencil on hexagonally ruled graph paper.
TwixTTwixT is a two-player strategyboard game, an early entrant in the 1960s 3M bookshelf game series. It became one of the most popular and enduring games in the series. It is a connection game where players alternate turns placing pegs and links on a pegboard in an attempt to link their opposite sides. While TwixT itself is simple, the game also requires strategy, so young children can play it, but it also appeals to adults.
Paper-and-pencil gamePaper-and-pencil games or paper-and-pen games (or some variation on those terms) are games that can be played solely with paper and pencils (or other writing implements), usually without erasing. They may be played to pass the time, as icebreakers, or for brain training. In recent times, they have been supplanted by mobile games. Some popular examples of pencil-and-paper games include tic-tac-toe, sprouts, dots and boxes, hangman, MASH, paper soccer, and spellbinder.*As an Amazon Associate I earn from qualifying purchases.