Related papers: Limit Cases And Strategy In Chutes and Ladders
Dice control involves "setting" the dice and then throwing them carefully, in the hope of influencing the outcomes and gaining an advantage at craps. How does one test for this ability? To specify the alternative hypothesis, we need a…
The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability…
Many natural processes rely on optimizing the success ratio of a search process. We use an experimental setup consisting of a simple online game in which players have to find a target hidden on a board, to investigate the how the rounds are…
Bidding chess is a chess variant where instead of alternating play, players bid for the opportunity to move. Generalizing a known result on so-called Richman games, we show that for a natural class of games including bidding chess, each…
In this paper we consider a stochastic process that may experience random reset events which bring suddenly the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonous…
Strategic decisions are often made over multiple periods of time, wherein decisions made earlier impact a competitor's success in later stages. In this paper, we study these dynamics in General Lotto games, a class of models describing the…
Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation…
We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude…
Given a sequence of numbers $\{p_n\}$ in $[0,1]$, consider the following experiment. First, we flip a fair coin and then, at step $n$, we turn the coin over to the other side with probability $p_n$, $n\ge 2$. What can we say about the…
This paper considers a game in which a single cop and a single robber take turns moving along the edges of a given graph $G$. If there exists a strategy for the cop which enables it to be positioned at the same vertex as the robber…
We consider a two-player game in which the first player (the Guesser) tries to guess, edge-by-edge, the path that second player (the Chooser) takes through a directed graph. At each step, the Guesser makes a wager as to the correctness of…
Unlike repetitions in Western Chess where all repetitions are draws, repetitions in Chinese Chess could result in a win, draw, or loss depending on the kind of repetition being made by both players. One of the biggest hurdles facing Chinese…
Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…
We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…
The emergence of mobile games has caused a paradigm shift in the video-game industry. Game developers now have at their disposal a plethora of information on their players, and thus can take advantage of reliable models that can accurately…
We provide an algorithm to find the value and an optimal strategy of the solitaire variant of the Ten Thousand dice game in the framework of Markov Control Processes. Once an optimal critical threshold is found, the set of non-stopping…
This paper considers a multi-armed bandit game where the number of arms is much larger than the maximum budget and is effectively infinite. We characterize necessary and sufficient conditions on the total budget for an algorithm to return…
A gambler with an initial fortune $x$ starts by betting a dollar, then doubles the bet after every win and halves the bet after every loss. Let $p\in (0,1)$ be the probability of winning for each round. We show that the gambler survives…
In the evolutionary version of the minority game, agents update their strategies (gene-value $p$) in order to improve their performance. Motivated by recent intriguing results obtained for prize-to-fine ratios which are smaller than unity,…
We consider the tail distribution of the edge cover time of a specific non-Markov process, $\delta$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights…