Related papers: A Birthday Attack on Roulette
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…
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…
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)…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…