Introduction

Casinos are everywhere in the world. What guarantees casinos to be a profitable business? What guarantees the casinos to win in the long run? This has nothing to do with luck, but that most games in the casinos are not fair games (link to explanation). You may win in a single game or two, but in the long run, the gambler is always the loser. We will now analyse the dice game from a mathematical point of view to see how 'unfair' it is.

To begin, you should have some idea about a topic in Mathematics: Probability. [Click here to read our notes]. If you have already learnt this topic, go ahead!

Theories of probability and gambling originated from Europe in the 16th century. At that time, gambling was very common among the noble classes. It was in this period that two French mathematicians, Pascal and Fermat, made studies in this area and established the fundamental theories of probability and combinatorics.