相关论文: The Game of Band or Bump

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…

We investigate the expected number of calls required to achieve Bingo in a generalized (n,m)-Bingo game, where each n x n card is filled by sampling n numbers from m possible values per column. Using the inclusion-exclusion principle, we…

We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…

The game of war is one of the most popular international children's card games. In the beginning of the game, the pack is split into two parts, then on each move the players reveal their top cards. The player having the highest card…

We consider a model of language development, known as the naming game, in which agents invent, share and then select descriptive words for a single object, in such a way as to promote local consensus. When formulated on a finite and…

We study several variants of the classical card game war. As anyone who played this game knows, the game can take some time to terminate, but it usually does. Here, we analyze a number of asymptotic variants of the game, where the number of…

A deck of $n$ cards is shuffled by repeatedly moving the top card to one of the bottom $k_n$ positions uniformly at random. We give upper and lower bounds on the total variation mixing time for this shuffle as $k_n$ ranges from a constant…

A recent paper by Bhatia, Chin, Mani, and Mossel (2026) defined stochastic processes aimed at modeling the game of War for {\em two players} with $n$ cards. That paper showed that these models, assuming uniform random decks, are equivalent…

Tournaments can be used to model a variety of practical scenarios including sports competitions and elections. A natural notion of strength of alternatives in a tournament is a generalized king: an alternative is said to be a $k$-king if it…

In this note, we investigate combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random). In this model, we provide closed-form expressions for the expected number of turns in a…

Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, $U$ and $D$. A gambler gains 1 point for each occurrence of $U$ (including overlapping occurrences) and loses 1 point for each…

We define a general framework of partition games for formulating two-player pebble games over finite structures. We show that one particular such game, which we call the invertible-map game, yields a family of polynomial-time approximations…

We consider the effect on the length of the game of Cops and Robbers when more cops are added to the game play. In Overprescribed Cops and Robbers, as more cops are added, the capture time (the minimum length of the game assuming optimal…

The Cops and Robber game is played on undirected finite graphs. $k$ cops and one robber are positioned on vertices and take turn in moving along edges. The cops win if, after a move, a cop and the robber are on the same vertex. A graph is…

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of…

Consider a randomly shuffled deck of $2n$ cards with $n$ red cards and $n$ black cards. We study the average number of moves it takes to go from a randomly shuffled deck to a deck that alternates in color by performing the following move:…

Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude are given. The first game is described by the quantum formalism of spin one half system for which two noncommuting observables…

Consider the following method of card shuffling. Start with a deck of $N$ cards numbered 1 through N. Fix a parameter $p$ between 0 and 1. In this model a ``shuffle'' consists of uniformly selecting a pair of adjacent cards and then…

We study the generalization of the game Lights Out in which the standard square grid board is replaced by a graph. We examine the probability that, when a graph is chosen uniformly at random from the set of graphs with $n$ vertices and $e$…

Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…