Related papers: The Monty Hall problem revisited

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…

The Monty Hall problem is a classic probability puzzle known for its counterintuitive solution, revealing fundamental discrepancies between mathematical reasoning and human intuition. To bridge this gap, we introduce a novel explanatory…

The basic Monty Hall problem is explored to introduce into the fundamental concepts of the game theory and to give a complete Bayesian and a (noncooperative) game-theoretic analysis of the situation. Simple combinatorial arguments are used…

The Monty Hall problem is notorious for its deceptive simplicity. Although today it is widely used as a provocative thought experiment to introduce Bayesian thinking to students of probability, in the not so distant past it was rejected by…

A quantum version of the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied by analyzing the classical expectation…

Elementary decision-theoretic analysis of the Monty Hall dilemma shows that the problem has dominance. This makes possible to discard nonswitching strategies, without making any assumptions on the prior distribution of factors out of…

Game versions of the Monty Hall Problem are discussed. The focus is on the principle of eliminating the dominated strategies, both in the zero-sum and noncooperative formulations.

I argue that we must distinguish between: (0) the Three-Doors-Problem Problem [sic], which is to make sense of some real world question of a real person. (1) a large number of solutions to this meta-problem, i.e., many specific…

The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…

We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be…

Computing the marginal likelihood or evidence is one of the core challenges in Bayesian analysis. While there are many established methods for estimating this quantity, they predominantly rely on using a large number of posterior samples…

The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…

This paper argues that a combined treatment of probabilities, time and actions is essential for an appropriate logical account of the notion of probability; and, based on this intuition, describes an expressive probabilistic temporal logic…

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which…

Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…

We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…

We emphasize the dominance in the Monty Hall problem, both in the classical scenario and its multi-door generalization. This is used to show optimality of the class of always-switching strategies for nonuniform allocation of the prize and…

We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the…

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…

Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering…