Related papers: A Random-Player Game and Derangement Numbers

Here, we present a variant of Nim with two piles. In the first pile, we have stones with a weight of 1, and in the second pile, we have stones with a weight of -2. Two Players take turns to take stones from one of the piles, and the total…

We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…

Edouard Zeckendorf proved that every positive integer $n$ can be uniquely written \cite{Ze} as the sum of non-adjacent Fibonacci numbers, known as the Zeckendorf decomposition. Based on Zeckendorf's decomposition, we have the Zeckendorf…

Parrondo's coin-tossing games comprise two games, $A$ and $B$. The result of game $A$ is determined by the toss of a fair coin. The result of game $B$ is determined by the toss of a $p_0$-coin if capital is a multiple of $r$, and by the…

We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…

In the best choice problem with random arrivals, an unknown number $n$ of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with…

Randomized mechanisms can have good normative properties compared to their deterministic counterparts. However, randomized mechanisms are problematic in several ways such as in their verifiability. We propose here to derandomize such…

Online Ramsey game is played between Builder and Painter on an infinite board $K_{\mathbb N}$. In every round Builder selects an edge, then Painter colors it red or blue. Both know target graphs $H_1$ and $H_2$. Builder aims to create…

We consider the urn setting with two different objects, ``good'' and ``bad'', and analyze the number of draws without replacement until a good object is picked. Although the expected number of draws for this setting is a standard textbook…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

We compare to different extensions of the ancient game of nim: Moore's nim$(n, \leq k)$ and exact nim$(n, = k)$. Given integers $n$ and $k$ such that $0 < k \leq n$, we consider $n$ piles of stones. Two players alternate turns. By one move…

We study impartial take away games on 2 unordered piles of finite nonnegative numbers of tokens $(x,y)$. Two players alternate in removing at least one and at most all tokens from the respective piles, according to certain rules, and the…

A set of $2^n$ candidates is presented to a commission. At every round, each member of this commission votes by pairwise comparison, and one-half of the candidates is deleted from the tournament, the remaining ones proceeding to the next…

Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of…

M\"uller games form a well-established class of games for model checking and verification. These games are played on directed graphs $\mathcal G$ where Player 0 and Player 1 play by generating an infinite path through the graph. The winner…

We consider the following combinatorial game: two players, Fast and Slow, claim $k$-element subsets of $[n]=\{1,2,...,n\}$ alternately, one at each turn, such that both players are allowed to pick sets that intersect all previously claimed…

We consider a Maker-Breaker type game on the plane, in which each player takes $t$ points on their $t^\textrm{th}$ turn. Maker wins if he obtains $n$ points on a line (in any direction) without any of Breaker's points between them. We show…

Domineering is a two-player game played on a checkerboard in which one player places dominoes vertically, while the other places them horizontally. In this paper, we find out the minimum number of moves for a game of Domineering to end on…

We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously…

The 2-player impartial game of Wythoff Nim is played on two piles of tokens. A move consists in removing any number of tokens from precisely one of the piles or the same number of tokens from both piles. The winner is the player who removes…