Published in Revista de Matemática: Teoria y Aolicaciones, Volume 6, Issue 2, January 1, 1999, pages 125-132. Copyright © 1999 University of Costa Rica, School of Mathematics.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
A short introduction to goal problems in abstract gambling theory is given, along with statements of some of the main theorems and a number of examples, open problems and references. Emphasis is on the finite-state, countably-additive setting with such classical objectives as reaching a goal, hitting a goal infinitely often, staying in the goal, and maximizing the average time spent at a goal.