Random Numbers and Simple Games

Abstract

Random numbers have many applications in science and computer programming, especially when there are significant uncertainties in a phenomenon of interest. The purpose of this chapter is to look at some practical problems involving random numbers and learn how to program with such numbers. We shall make several games and also look into how random numbers can be used in physics. You need to be familiar with basic programming concepts such as loops, lists, arrays, vectorization, curve plotting, and command-line arguments in order to study the present chapter. This means that Chaps. 1–5 of the present book should be digested. A few examples and exercises will require familiarity with the class concept from Chap. 7.

The key idea in computer simulations with random numbers is first to formulate an algorithmic description of the phenomenon we want to study. This description frequently maps directly onto a quite simple and short Python program, where we use random numbers to mimic the uncertain features of the phenomenon. The program needs to perform a large number of repeated calculations, and the final answers are ‘‘only’’ approximate, but the accuracy can usually be made good enough for practical purposes. Most programs related to the present chapter produce their results within a few seconds. In cases where the execution times become large, we can vectorize the code. Vectorized computations with random numbers is definitely the most demanding topic in this chapter, but is not mandatory for seeing the power of mathematical modeling via random numbers.