Stochastic process

In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.

The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications.

Bernoulli process
One of the simplest stochastic processes is the Bernoulli process, which is a sequence of independent and identically distributed (i. i. d.) random variables, where each random variable takes either the value one or zero, say one with probability $$p$$ and zero with probability $$1-p$$. This process can be linked to repeatedly flipping a coin, where the probability of obtaining a head is $$p$$ and its value is one, while the value of a tail is zero. In other words, a Bernoulli process is a sequence of i. i. d. Bernoulli random variables, where each coin flip is an example of a Bernoulli trial.

As random gameplay elements in Asphalt are usually about getting a desired item or not (1 or 0), all of them are stochastic processes, and most of them also Bernoulli processes:
 * Opening a Pro Kit Box (only a Bernoulli process if cards are completely random. If there are guarantees for a specific card, for instance a V8 Engine, this card has another probability distribution and is therefore a separate process.)
 * Daily ads
 * Daily Tasks

Other stochastic processes in Asphalt include
 * Multiplayer matchmaking
 * Multiplayer track selection
 * the distribution of Quality checks and Festival coins on race tracks.