Related papers: A Birthday Attack on Roulette
The Parrondo's paradox is a counterintuitive phenomenon where individually-losing strategies can be combined in producing a winning expectation. In this paper, the issues surrounding the Parrondo's paradox are investigated. The focus is…
In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…
Consider a uniformly random deck consisting of cards labelled by numbers from $1$ through $n$, possibly with repeats. A guesser guesses the top card, after which it is revealed and removed and the game continues. What is the expected number…
The discrete logarithm in a finite group of large order has been widely applied in public key cryptosystem. In this paper, we will present a probabilistic algorithm for discrete logarithm.
We present new versions of the Parrondo's paradox by which a losing game can be turned into winning by including a mechanism that allows redistribution of the capital amongst an ensemble of players. This shows that, for this particular…
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where…
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…
The Monty Hall puzzle has been solved and dissected in many ways, but always using probabilistic arguments, so it is considered a probability puzzle. In this paper the puzzle is set up as an orthodox statistical problem involving an unknown…
Roulette-wheel selection is a frequently used method in genetic and evolutionary algorithms or in modeling of complex networks. Existing routines select one of N individuals using search algorithms of O(N) or O(log(N)) complexity. We…
This paper examines the relationship between casino rules, players' gambling strategies, and their expected returns, and derives the formula about the players' expected return.
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…
In late May of 2014 I received an email from a colleague introducing to me a non-transitive game developed by Walter Penney. This paper explores this probability game from the perspective of a coin tossing game, and further discusses some…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
We give an elementary statistical analysis of two High Performance Computing issues, processor cache mapping and network port mapping. In both cases we find that, as in the birthday paradox, random assignment leads to more frequent…
Birthday problem is a well-known classic problem in probability theory widely applied in cryptography, and bubble sort is a popular sorting algorithm leading to some interesting theoretical problems in computer science. However, the…
Risk is a well-known turn based board game where the primary objective is nothing less than the world domination. Gameplay is based on battles between armies located in adjacent territories on the map of Earth. The combat's outcome is…
Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. We present a suitable version…
In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…
Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged -- namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the…