Related papers: How does a coin toss? A look under an asymptotic m…

The problem of assigning probabilities when little is known is analized in the case where the quanities of interest are physical observables, i.e. can be measured and their values expressed by numbers. It is pointed out that the assignment…

Calculations and mechanistic explanations for the probabilistic movement of objects at the highly relevant cm length scales has been lacking and overlooked due to the complexity of current techniques. Predicting the final-configuration…

Coin-flipping is a fundamental cryptographic task where a spatially separated Alice and Bob wish to generate a fair coin-flip over a communication channel. It is known that ideal coin-flipping is impossible in both classical and quantum…

Penney's Ante exhibits non-transitivity when two target strings race to appear in a shared stream of coin tosses. We study instead independent string races, where each player observes their own independent and identically distributed…

The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, that do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational…

After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner,…

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…

The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability.…

Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also…

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…

What would you do if you were invited to play a game where you were given \$25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61…

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…

"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…

Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…

It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum…

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…

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 demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this…

Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the problem of using independent tosses of a coin with probability of heads p (where p\in S is unknown) to simulate a coin with probability of heads f(p). We prove that if…

We show how to simulate a roll of a fair $n$-sided die by one flip of a biased coin with probability $1/n$ of coming up heads, followed by $3\lfloor\log_2 n \rfloor+1$ flips of a fair coin.