Related papers: Random Coin Tossing with unknown bias
We present an analysis of a coin-tossing problem posed by Daniel Litt which has generated some popular interest. We demonstrate a recursive identity which leads to relatively simple formulas for the excess number of wins for one player over…
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…
Each classical public-coin protocol for coin flipping is naturally associated with a quantum protocol for weak coin flipping. The quantum protocol is obtained by replacing classical randomness with quantum entanglement and by adding a cheat…
What is the average number of tosses needed before a particular sequence of heads and tails turns up? We solve the problem didactically, starting with doubles, finding that a tail, followed by a head, turns up on the average after only four…
We consider an infinite balls-into-bins process with deletions where in each discrete step $t$ a coin is tossed as to whether, with probability $\beta(t) \in (0,1)$, a new ball is allocated using the Greedy[2] strategy (which places the…
We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying…
In this article, we study a notion of the extraction rate of Turing functionals that translate between notions of randomness with respect to different underlying probability measures. We analyze several classes of extraction procedures: a…
Coin-flipping is a fundamental task in two-party cryptography where two remote mistrustful parties wish to generate a shared uniformly random bit. While quantum protocols promising near-perfect security exist for weak coin-flipping -- when…
Coin tossing is a cryptographic task in which two parties who do not trust each other aim to generate a common random bit. Using classical communication this is impossible, but non trivial coin tossing is possible using quantum…
We study a problem related to coin flipping, coding theory, and noise sensitivity. Consider a source of truly random bits $x \in \bits^n$, and $k$ parties, who have noisy versions of the source bits $y^i \in \bits^n$, where for all $i$ and…
Getting an unbiased result is a remarkably long standing problem of collective observation/measurement. It is pointed out that quantum coin tossing can generate unbiased result defeating dishonesty.
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
A long sequence of tosses of a classical coin produces an apparently random bit string, but classical randomness is an illusion: the algorithmic information content of a classically-generated bit string lies almost entirely in the…
The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describe the exact solution, which is correct…
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.
Aaronson and Drucker (2011) asked whether there exists a quantum finite automaton that can distinguish fair coin tosses from biased ones by spending significantly more time in accepting states, on average, given an infinite sequence of…
The torque-free motion of rigid body in gravitational field is analyzed. The coin lands on a soft surface (such as the palm of the hand) that allows no bouncing. The model assumes the coin as a rigid body with constant angular momentum…
Suppose that X_1,X_2,...,X_n are independent and identically Bernoulli(theta) distributed. Also suppose that our aim is to find an exact confidence interval for theta that is the intersection of a 1-\alpha/2 upper confidence interval and a…
We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online video-game (http://arora.ccs.neu.edu) where players are…