Statistics

2607 Submissions

[2] viXra:2607.0055 [pdf] submitted on 2026-07-14 19:28:17

Rating Systems for Gameplayers, and Learning

Authors: Warren D. Smith
Comments: 20 Pages. Based on my 1984 bachelor thesis at MIT and the basis for the rating system used by the "internet chess club." Now uploaded to VIXRA for archival purposes.

This report studies rating systems: systems that produce quantitative measures, called "ratings," of the ability of players in a league, based on game results. By "quantitative,", it is meant that win odds for a game between two players in the league may be estimated from their ratings. We consider both "static" and "dynamic" systems. The latter update the ratings after each game. Attention is given to noise in rating systems and to thedistribution of ratings in the player population. Some real-world data is also included. This subject may be of interest to gamblers, gaming leagues, psychologists, consumer groups, and industry.
Category: Statistics

[1] viXra:2607.0047 [pdf] submitted on 2026-07-11 03:01:14

Discrete Random Variables

Authors: Teo Banica
Comments: 400 Pages.

This is an introduction to probability and discrete random variables. We first discuss games, counting and basic probability, with the mathematics of the binomials and factorials recalled, and with everything explained with numerous illustrations. Then we get into the theory of discrete random variables, with the basic theory explained, with illustrations, notably with results about the binomial and Poisson laws. Then we discuss more advanced distributions, such as the Bessel, hypergeometric and beta binomial ones, with methods from both algebra and analysis. We end with an introduction to continuous phenomena, advanced combinatorics, random matrices and freeness.
Category: Statistics