Related papers: Note on a Coin Tossing Problem Posed by Daniel Lit…
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…
We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by first applying a reduction, then decomposing the position…
We generalize the problem of coin flipping to more than two outcomes and parties. We term this problem dice rolling, and study both its weak and strong variants. We prove by construction that in quantum settings (i) weak N-sided dice…
The Chow-Robbins game is a classical still partly unsolved stopping problem introduced by Chow and Robbins in 1965. You repeatedly toss a fair coin. After each toss, you decide if you take the fraction of heads up to now as a payoff,…
This paper intends to solve the Transversal achievement on an n times n grid problem proposed by Dr. Martin Erickson. We approach the problem using mathematical induction and case analysis and prove the hypothesis that for all n greater…
ApSimon considered the problem of deciding by a process of two weighings on which of a known number of mints emit either coins of a known genuine weight or emit coins of a different secondary but unknown weight. The combinatorial problem…
A comparison of escape rates from one and from two holes in an experimental container (e.g. a laser trap) can be used to obtain information about the dynamics inside the container. If this dynamics is simple enough one can hope to obtain…
We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing…
Let $a$, $b$, and $n$ be integers with $0<a<b<n$. In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects $a$ chips or $b$ chips. If Alice collects $a$ chips, then Bob collects $b$…
Inspired by the great success of machine learning in the past decade, people have been thinking about the possibility of improving the theoretical results by exploring data distribution. In this paper, we revisit a fundamental problem…
A neat question involving coin flips surfaced on $\Bbb X$, and generated an intensive `storm' of `social mathematics'. In a sequence of flips of a fair coin, Alice wins a point at each appearance of two consecutive heads, and Bob wins a…
This contribution deals with a two-level discrete decision problem, a so-called Stackelberg strategic game: A Subset Sum setting is addressed with a set $N$ of items with given integer weights. One distinguished player, the leader, may…
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…
Circular nim $CN(m, k)$ is a variant of nim, in which there are $m$ piles of tokens arranged in a circle and each player, in their turn, chooses at most $k$ consecutive piles in the circle and removes an arbitrary number of tokens from each…
Suppose we are given a set of t coins which look identical, but a known number s of them are counterfeit, with a known weight different from the others. Our problem is to locate the counterfeits by weighing subsets of the t coins, with as…
We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…
The recent lottery ticket hypothesis proposes that there is one sub-network that matches the accuracy of the original network when trained in isolation. We show that instead each network contains several winning tickets, even if the initial…
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…
The takeoff point for this paper is the voluminous body of literature addressing recursive betting games with expected logarithmic growth of wealth being the performance criterion. Whereas almost all existing papers involve use of linear…
Coin flipping is a cryptographic primitive in which two spatially separated players, who in principle do not trust each other, wish to establish a common random bit. If we limit ourselves to classical communication, this task requires…