Related papers: Single-delete Nim
In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match…
Here, we present a variant of the sliding coins game. Two coins are placed on distinct squares of a semi-infinite linear board with squares numbered $0, 1, 2, dots, $. Two players take turns and move a coin to a lower unoccupied square.…
We analyze a two-player game in which players take turns avoiding the selection of certain points within a convex geometry. The objective is to prevent the convex closure of all chosen points from encompassing a predefined set. The first…
We present and analyze PackIt!, a turn-based game consisting of packing rectangles on an $n \times n$ grid. PackIt! can be easily played on paper, either as a competitive two-player game or in \emph{solitaire} fashion. On the $t$-th turn, a…
We present a new family of Nim games where the rules depend on a given `coloring' of the tokens, each token being either black or white. The rules are as in Nim with the restriction that a white token on top of each heap is not allowed. We…
Two players play a game by alternately splitting a surface of a compact $2$-manifold along a simple closed curve that is not null-homotopic and attaching disks to the resulting boundary; the last player who can move wins. Starting from an…
We introduce the game Slow $A$-Nim which generalizes a number of recently studied games. Slow $A$-Nim is played on $n$ stacks of tokens, and the set $A$ indicates the number of stacks a player can play on. Once a player has decided on the…
The game of memory is played with a deck of n pairs of cards. The cards in each pair are identical. The deck is shuffled and the cards laid face down. A move consists of flipping over first one card then another. The cards are removed from…
In card games, in casino games with multiple decks of cards and in cryptography, one is sometimes faced with the following problem: how can a human (as opposed to a computer) shuffle a large deck of cards? The procedure we study is to break…
A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i \to…
We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…
Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…
The authors introduce the impartial game of the generalized Ry\=u\=o Nim, a variant of the classical game of Wythoff Nim. In the latter game, two players take turns in moving a single queen on a large chessboard, attempting to be the first…
The game of Nim as played on graphs was introduced in Nim on Graphs I and extended in Nim on Graphs II by Masahiko Fukuyama. His papers detail the calculation of Grundy numbers for graphs under specific circumstances. We extend these…
New combinatorial games are introduced, of which the most pertinent is Maharaja Nim. The rules extend those of the well-known impartial game of Wythoff Nim in which two players take turn in moving a single Queen of Chess on a large board,…
We solve the problem of one-dimensional Peg Solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for reducing any…
Aim: Present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of…
In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along…
In the game of Graph Nimors, two players alternately perform graph minor operations (deletion and contraction of edges) on a graph until no edges remain, at which point the player who last moved wins. We present theoretical and experimental…
The MandM Game involves two players who begin with I1 and I2 MandM's. During each round, each player tosses a fair coin: if the coin lands heads, that player eats one MandM, and if it lands tails, the player does not eat. If, at the end of…