Related papers: On Variations of Nim and Chomp

Nim is a well-known combinatorial game with several variants, e.g., Delete Nim and Variant Delete Nim. In Variant Delete Nim, the player deletes one of the two heaps of stones and splits the other heap on his/her turn. In this paper, we…

Yama Nim is a two heaps Nim game introduced in the second author's Master Thesis, where the player takes more than $2$ tokens from one heap, and return $1$ token to the other heap. Triangular Nim is a generalization, where the player takes…

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…

We propose a variant of Nim, named StrNim. Whereas a position in Nim is a tuple of non-negative integers, that in StrNim is a string, a sequence of characters. In every turn, each player shrinks the string, by removing a substring repeating…

The authors present formulas for the previous player's winning positions of two variants of restricted Nim. In both of these two games, there is one pile of stones, and in the first variant, we investigate the case that in k-th turn, you…

In this paper, we consider a modular extension to the game of Nim, which we call $m$-Modular Nim, and explore its optimal strategy. In $m$-Modular Nim, a player can either make a standard Nim move or remove a multiple of $m$ tokens in…

We study a variation of the combinatorial game of 2-pile Nim. Move as in 2-pile Nim but with the following constraint: Suppose the previous player has just removed say $x>0$ tokens from the shorter pile (either pile in case they have the…

In this paper, we introduce and examine a variant of the game of Nim (Sharing Nim), where players can either remove or transfer objects from 1 pile to another. The only restriction is that players may not transfer objects from a pile of…

The game of Nim, which has been well known for many years, has numerous variations. One such variation is Circular Nim, where piles of stones are arranged on a circumference, and players take stones from consecutive adjacent piles in one…

Wythoff's Nim is a variant of 2-pile Nim in which players are allowed to take any positive number of stones from pile 1, or any positive number of stones from pile 2, or the same positive number from both piles. The player who makes the…

In chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy? Can a explicit…

We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing then, topping up on a smaller pile provided that the destination pile does not have more tokens then the source pile after the…

The classic game of Nim has been well-known for many years, inspiring numerous variations. One such variant is Delete Nim, where players take turns eliminating one pile of stones and splitting the remaining pile into two smaller piles. In…

Chocolate-bar games are variants of the CHOMP game. A three-dimensional chocolate bar comprises a set of cubic boxes sized 1 X 1 X 1, with a bitter cubic box at the bottom of the column at position (0,0). For non-negative integers u,w such…

Circular nim $CN(m, k)$ is a variant of nim, in which there are $m$ piles of tokens arranged in a circle and each player, in their turn, chooses at most $k$ consecutive piles in the circle and removes an arbitrary number of tokens from each…

A circular Nim game is a two player impartial combinatorial game consisting of n stacks of tokens placed in a circle. A move consists of choosing k consecutive stacks, and taking at least one token from one or more of the k stacks. The last…

In an amalgamation Nim, players are allowed to use a move from the traditional form of Nim or to amalgamate two piles when they are not empty. No formula that describes the set of P-positions of Amalgamation Nim is known. The author gives a…

{\sc Yama Nim} is a variant of two piles {\sc Nim}. In this ruleset, the player chosses one of the piles and removes at least two tokens from the pile. In the same move, the player adds one token to the other pile. We show the winning…

Circular Nim is a two-player impartial combinatorial game consisting of $n$ stacks of tokens placed in a circle. A move consists of choosing $k$ consecutive stacks and taking at least one token from one or more of the stacks. The last…

We describe PNim and RNim, two variants of Nim in which piles of tokens are replaced with integer partitions or hyperrectangles. In PNim, the players choose one of the integer partitions and remove a positive number of rows or a positive…