In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one. A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial.
When an experiment is conducted, one (and only one) outcome results—although this outcome may be included in any number of events, all of which would be said to have occurred on that trial. After conducting many trials of the same experiment and pooling the results, an experimenter can begin to assess the relative frequencies of the various outcomes and events that can occur in the experiment and apply the methods of statistical analysis.
Experiments and trials
Random experiments are often conducted repeatedly, so that the collective results may be subjected to statistical analysis. A fixed number of repetitions of the same experiment can be thought of as a composed experiment, in which case the individual repetitions are called trials.
In the Asphalt games, players are intuitively conducting experiments almost every day. In Asphalt 8 for example, obtaining cards from Pro Kit Boxes, watching daily ads, claiming rewards from Daily Tasks, but also the matchmaking in Multiplayer mode are determined by internal random processes.
- Watching a daily ad and getting a reward from Daily Tasks are random experiments, because they have more than one possible outcome.
- Obtaining a card from a 1 V8-Engine Box is deterministic, because there is only one possible outcome: a V8 Engine card.
- Opening a Finish Line Box is a composed experiment as it consists of 3 repetitions (trials) of revealing a card.
- Opening a Daily Kit Box † is a more complex example of a composed experiment. As the box has several hidden rules, the trials are not all the same.
- Exactly 8 cards grant car parts. As there are more than one possible part card, these are 8 repetitions of the same random experiment (trial).
- Exactly 1 card grants an engine. This is also a random trial, but it has different possible outcomes (a different sample space) from the other cards.
- Exactly 1 card is a Tech card. It is always either Mid-Tech or Advanced Tech. As there are exactly two mutually exclusive possible outcomes, this is a Bernoulli trial.
- A Bernoulli process is a composed experiment consisting of independent and identically distributed Bernoulli trials.
- Generally, obtaining a specific desired card from revealing one card of a Pro Kit Box without extra rules is also a Bernoulli trial: The player either gets it or not. Under this premise, every Pro Kit Box without extra rules is also a series of Bernoulli trials—for every revealed card, the player has the chance to get the desired card or not. This is important for the inference of more complex probabilies as Bernoulli trials are easier to calculate with.