DeepAI

# Aspects of Muchnik's paradox in restricted betting

Muchnik's paradox says that enumerable betting strategies are not always reducible to enumerable strategies whose bets are restricted to either even rounds or odd rounds. In other words, there are outcome sequences x where an effectively enumerable strategy succeeds, but no such parity-restricted effectively enumerable strategy does. We characterize the effective Hausdorff dimension of such x, showing that it can be as low as 1/2 but not less. We also show that such reals that are random with respect to parity-restricted effectively enumerable strategies with packing dimension as low as log√(3). Finally we exhibit Muchnik's paradox in the case of computable integer-valued strategies.

• 9 publications
• 40 publications
07/07/2020

### Strategy Complexity of Parity Objectives in Countable MDPs

We study countably infinite MDPs with parity objectives. Unlike in finit...
04/21/2022

### Online Two-Dimensional Vector Packing with Advice

We consider the online two-dimensional vector packing problem, showing a...
11/29/2021

### Rounds, Color, Parity, Squares

This is a sequel to our paper "Permute, Graph, Map, Derange", involving ...
07/10/2018

### Monotonous betting strategies in warped casinos

Suppose that the outcomes of a roulette table are not entirely random, i...
04/17/2018

### Parity Games with Weights

Quantitative extensions of parity games have recently attracted signific...
11/28/2018

### Hamiltonian cycles and paths in hypercubes with disjoint faulty edges

An n-dimensional hypercube Q_n, is an undirected graph with 2^n nodes, e...
11/06/2019

### Permutations With Restricted Movement

We study restricted permutations of sets which have a geometrical struct...