Random numbers are essential to our lives. They are used to conduct simulations, pick winners, and secure the Internet with cryptography.
A computer is a deterministic machine. How do we make it pick a random number? The most common way to do so is by using Pseudo-Random Number Generators (PRNGs). This method uses a seed (a number of your choice) to create a list of numbers that appear to be random. One property of this method is that anyone with the same seed can generate the same list of random numbers.
The other way to generate random numbers is to use True Random Number Generators (TRNGs). TRNGs rely on a physical phenomenon to create randomness. The weather or radioactivity decay is an example of a good source.
RANDOM.ORG offers “true random numbers to anyone on the Internet”. by generating randomness via atmospheric noise. This site provides, among others, the following services and API: coin flip, lottery pick, dice roller, shuffle. Why not use a True Random Number Generator when playing your next board game?
I encourage you to continue reading their Introduction to Randomness and Random Numbers page.
The On-Line Encyclopedia of Integer Sequences (OEIS) catalogue number sequences. You must have heard of Fibonacci or Prime numbers. This is the kind of number sequences you can find and query with the OEIS.
Some sequences produce lovely illustrations.