A probability model starts from an experiment and a mathematical structure attached to that experiment, namely the space (field) of events. The event is the main unit probability theory works on. In gambling, there are many categories of events, all of which can be textually predefined. In the previous examples of gambling experiments we saw some of the events that experiments generate. They are a minute part of all possible events, which in fact is the set of all parts of the sample space.
For a specific game, the various types of events can be:
- Events related to your own play or to opponents’ play;
- Events related to one person’s play or to several persons’ play;
- Immediate events or long-shot events.
Each category can be further divided into several other subcategories, depending on the game referred to. These events can be literally defined, but it must be done very carefully when framing a probability problem. From a mathematical point of view, the events are nothing more than subsets and the space of events is a Boolean algebra. Among these events, we find elementary and compound events, exclusive and nonexclusive events, and independent and non-independent events.
In the experiment of rolling a die:
