Related papers: On sequences arising from randomizing subtraction …
In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth nothing and a tie worth 1, and the payoff of winning (the incentive a) as a variable, this game is called as generalized RPS game. The generalized RPS game is a…
We will try to tackle both the theoretical and practical aspects of a very important problem in chess programming as stated in the title of this article - the issue of draw detection by move repetition. The standard approach that has so far…
We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is riffle-shuffled exactly one time. Given a value $p\in(0{,}1)\setminus\{\frac12\}$, the riffle shuffle is assumed to be…
We study a model of a competing population of N adaptive agents, with similar capabilities, repeatedly deciding whether to attend a bar with an arbitrary cutoff L. Decisions are based upon past outcomes. The agents are only told whether the…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
The ``losing positions" of certain combinatorial games constitute linear error detecting and correcting codes. We show that a large class of games that can be cast in the form of *annihilation games*, provides a potentially polynomial…
The relationship between topology and dynamics of complex systems has motivated continuing interest from the scientific community. In the present work, we address this interesting topic from the perspective of simple games, involving two…
In trick-taking card games, a two-step process of state sampling and evaluation is widely used to approximate move values. While the evaluation component is vital, the accuracy of move value estimates is also fundamentally linked to how…
Flip a coin repeatedly, and stop whenever you want. Your payoff is the proportion of heads, and you wish to maximize this payoff in expectation. This so-called Chow-Robbins game is amenable to computer analysis, but while simple-minded…
We describe a graph reduction operation, generalizing three graph reduction operations related to gene assembly in ciliates. The graph formalization of gene assembly considers three reduction rules, called the positive rule, double rule,…
We study rational circular billiards. By viewing the trajectory formed after each reflection point to another inside the circle as the number of circle divisions into regions we derive a general formula for the number of division regions…
We present three versions of the classic two-pile game \textsc{one-or-one-or-one-of-both} generalized to the multi-pile context. In each case, we explore the resulting $\mathcal{P}$-positions. In the first version, there is a simple…
In this paper we describe several player preferences in games with $N \geq 2$ players, in particular the case $N = 3$, and use them to simplify game trees, using the game of Clobber as our example. We show that, using a fixed starting…
We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…
The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
We study algorithmic complexity of solving subtraction games in a~fixed dimension with a finite difference set. We prove that there exists a game in this class such that any algorithm solving the game runs in exponential time. Also we prove…
The redundancy principle provides the framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. But what is $n$ large? To estimate large $n$ with respect…
We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…