Related papers: Simulating a die roll by flipping two coins
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that,…
An unbiased coin is tossed $n$ times independently and sequentially. In this paper, we will study the length of the longest consecutive switches, and prove that the limit behaviors are similar to that of the length of the longest head-run.
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we formalize the pile shuffle and investigate its capabilities as a sorting device. Our study is novel in that we consider pile shuffle in three…
Winning the coin toss at the end of a tied soccer game gives a team the right to choose whether to kick either first or second on all five rounds of penalty kicks, when each team is allowed one kick per round. There is considerable evidence…
We study a sequential coin-flipping game in which a player starts with~$n$ coins, each landing heads independently with probability~$p$. In each round the player flips all remaining coins and must set aside at least one coin showing heads;…
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.…
A generalized $N$-sided die is a random variable $D$ on a sample space of $N$ equally likely outcomes taking values in the set of positive integers. We say of independent $N$ sided dice $D_i, D_j$ that $D_i$ beats $D_j$, written $D_i \to…
This article introduces an algorithm to draw random discrete uniform variables within a given range of size n from a source of random bits. The algorithm aims to be simple to implement and optimal both with regards to the amount of random…
You play the following game: you start out with $n$ coins that all have probability $p$ to land heads. You toss all of them and you then need to set aside at least one of them, which will not be tossed again. Now you repeat the process with…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
We review the quantum version of a well known problem of cryptography called coin tossing (``flipping a coin via telephone''). It can be regarded as a game where two remote players (who distrust each other) tries to generate a uniformly…
"God does not play dice. He flips coins instead." And though for some reason He has denied us quantum bit commitment. And though for some reason he has even denied us strong coin flipping. He has, in His infinite mercy, granted us quantum…
In this article we show for the first time that quantum coin flipping with security guarantees that are strictly better than any classical protocol is possible to implement with current technology. Our protocol takes into account all…
Coin flipping is a fundamental cryptographic primitive that enables two distrustful and far apart parties to create a uniformly random bit [Blu81]. Quantum information allows for protocols in the information theoretic setting where no…
In this paper, we focus on a special framework for quantum coin flipping protocols,_bit-commitment based protocols_, within which almost all known protocols fit. We show a lower bound of 1/16 for the bias in any such protocol. We also…
All proper scoring rules incentivize an expert to predict \emph{accurately} (report their true estimate), but not all proper scoring rules equally incentivize \emph{precision}. Rather than treating the expert's belief as exogenously given,…
Given a $p$-coin that lands heads with unknown probability $p$, we wish to produce an $f(p)$-coin for a given function $f: (0,1) \rightarrow (0,1)$. This problem is commonly known as the Bernoulli Factory and results on its solvability and…
We prove an easy but very weak version of Chernoff inequality. Namely, that the probability that in $6M$ throws of a fair coin, one gets at most $M$ heads is $\leq 1/2^M$.
In this paper, we systematize the modeling of probabilistic systems for the purpose of analyzing them with model counting techniques. Starting from unbiased coin flips, we show how to model biased coins, correlated coins, and distributions…
We discuss games involving a counterfeit coin. Given one counterfeit coin among a number of otherwise identical coins, two players with full knowledge of the fake coin take turns weighing coins on a two-pan scale, under the condition that…