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This paper looks into the gain or loss from rolling a fair die multiple times and choosing the highest or lowest number as the outcome over rolling the die just once. Specifically, this paper gives a general formula for the expected value…

General Mathematics · Mathematics 2023-09-18 Fan Jiang , Elvin Jiang

Consider a card guessing game with complete feedback in which a deck of $n$ cards ordered $1,\dots, n$ is riffle-shuffled once. With the goal to maximize the number of correct guesses, a player guesses cards from the top of the deck one at…

Combinatorics · Mathematics 2022-07-22 Tipaluck Krityakierne , Thotsaporn Aek Thanatipanonda

In a casino where arbitrarily small bets are admissible, any betting strategy M can be modified into a savings strategy that, not only is successful on each casino sequence where M is (thus accumulating unbounded wealth inside the casino)…

Computer Science and Game Theory · Computer Science 2020-06-15 George Barmpalias , Nan Fang

In the Penney-Ante game, Player I chooses a head/tail string of a predetermined length $n\ge3$. Player II, upon seeing Player I's choice, chooses another head/tail string of the same length. A coin is then tossed repeatedly and the player…

Combinatorics · Mathematics 2021-07-16 Reed Phillips , A. J. Hildebrand

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…

Probability · Mathematics 2025-12-12 Aditya Guha Roy , Yuval Peres , Shuo Qin , Junchi Zuo

Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…

Computer Science and Game Theory · Computer Science 2021-05-26 Ambareesh Ravi , Atharva Gokhale , Anchit Nagwekar

A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…

Quantum Physics · Physics 2023-08-03 Bernhard K Meister , Henry C W Price

Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this…

Physics and Society · Physics 2014-10-03 J. M. R. Parrondo , L. Dinis

We study the survival probability for long times in an open spherical billiard, extending previous work on the circular billiard. We provide details of calculations regarding two billiard configurations, specifically a sphere with a…

Chaotic Dynamics · Physics 2017-06-29 Carl P. Dettmann , Mohammed R. Rahman

Using game and probability theories, I study the French popular game 421, a perfect information stochastic stage game. The problem is to find strategies maximizing the probability of some expected utility. I only solve a player's round…

Optimization and Control · Mathematics 2007-05-23 Pierre Albarede

Players are arranged on a regular lattice and coded with a specific strategy for a pre-defined game. Each player sums their payoffs from playing the game with each of their neighbors, and then adopts the strategy of the most successful…

Dynamical Systems · Mathematics 2015-08-03 Stewart D. Johnson

In a distributed game we imagine a team Player engaging a team Opponent in a distributed fashion. Such games and their strategies have been formalised in concurrent games based on event structures. However there are limitations in founding…

Logic in Computer Science · Computer Science 2016-07-14 Marc de Visme , Glynn Winskel

In the roleplaying game Tunnels & Trolls the characteristics of player characters are determined by rolling dice in the following manner: First, one rolls three dice and calculates their sum. If the three dice all give the same result,…

Probability · Mathematics 2019-01-23 Tommi Brander

We emphasize the dominance in the Monty Hall problem, both in the classical scenario and its multi-door generalization. This is used to show optimality of the class of always-switching strategies for nonuniform allocation of the prize and…

History and Overview · Mathematics 2011-07-01 Alexander Gnedin

Tit-for-Tat strategy is a strategy in repeated two-player symmetric games which imitates the previous action of the opponent. We show that the Tit-for-Tat strategy is a zero-determinant strategy, which unilaterally equalizes the expected…

Physics and Society · Physics 2022-04-22 Masahiko Ueda

We estimate the Hollyfeld Gambit for the Powerball lottery and its return on investment compared to present and extrapolated federal funding for astrophysical grants. Using a Monte Carlo estimation of rate of return for the Powerball, we…

Instrumentation and Methods for Astrophysics · Physics 2026-04-01 Benne Holwerda

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…

Computer Science and Game Theory · Computer Science 2024-05-16 Toby Walsh

This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…

Disordered Systems and Neural Networks · Physics 2025-12-16 Alexander K. Hartmann

Blackjack or "21" is a popular card-based game of chance and skill. The objective of the game is to win by obtaining a hand total higher than the dealer's without exceeding 21. The ideal blackjack strategy will maximize financial return in…

Artificial Intelligence · Computer Science 2023-08-16 Avish Buramdoyal , Tim Gebbie

The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…

Quantum Physics · Physics 2007-05-23 Andrey Grib , Georges Parfionov