Related papers: Predicting Winning Lottery Numbers
Stefan Mandel is said to have won the lottery 14 times. He never disclosed the recipe he called combinatorial condensation, which enabled him to hit the Romanian lottery jackpot in the early phase of his betting career. Combinatorial…
We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each…
Unusually large prize pools in lotteries like Mega Millions and Powerball attract additional bettors, which increases the likelihood that multiple winners will have to share the pool. Thus, the expected value of a lottery ticket decreases…
Machine learning has become a common approach to predicting the outcomes of soccer matches, and the body of literature in this domain has grown substantially in the past decade and a half. This chapter discusses available datasets, the…
The probability of a given candidate winning a future election is worked out in closed form as a function of (i) the current support rates for each candidate, (ii) the relative positioning of the candidates within the political spectrum,…
Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…
Conditional masked language model (CMLM) training has proven successful for non-autoregressive and semi-autoregressive sequence generation tasks, such as machine translation. Given a trained CMLM, however, it is not clear what the best…
We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry…
Numeracy is the ability to understand and work with numbers. It is a necessary skill for composing and understanding documents in clinical, scientific, and other technical domains. In this paper, we explore different strategies for…
For a family of multidimensional gambler models we provide formulas for the winning probabilities (in terms of parameters of the system) and for the distribution of game duration (in terms of eigenvalues of underlying one-dimensional…
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…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…
Machine Learning techniques have been used to teach computer programs how to play games as complicated as Chess and Go. These were achieved using powerful tools such as Neural Networks and Parallel Computing on Supercomputers. In this…
We explain how certain tools from convex analysis and probability theory may be used in order to obtain counting results for the number of words with prescribed frequencies of letters in regular languages.
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for…
In this paper, we study the problem of learning the skill distribution of a population of agents from observations of pairwise games in a tournament. These games are played among randomly drawn agents from the population. The agents in our…
The Dependent Chip Model (DCM) is proposed as an alternative to the Independent Chip Model (ICM) usually employed in poker tournament negotiations. DCM constitutes a recursive exploration of a multiplayer Texas hold'em poker game tree…
We find the winning strategy for a class of truncation games played on words. As a consequence of the present author's recent results on some of these games we obtain new formulas for Bernoulli numbers and polynomials of the second kind and…