Expected gain
Encyclopedia
The expected gain is the weighted-average most likely outcome in gambling
, probability theory
, economics
or finance
.
and probability theory
, there is usually a discrete set of possible outcomes. In this case, expected gain is a measure of the relative balance of win or loss weighted by their chances of occurring.
For example, if a fair die is thrown and numbers 1 and 2 win $1, but 3-6 lose $0.5, then the expected gain per throw is
the game is thus fair.
and finance
, it is more likely that the set of possible outcomes is continuous (a numerical or currency value between 0 and infinity). In this case, simplifying assumptions are made about the distribution of possible outcomes. Either a continuous probability function is constructed, or a discrete probability distribution is assumed.
Gambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
, probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
or finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
.
Discrete scenarios
In gamblingGambling
Gambling is the wagering of money or something of material value on an event with an uncertain outcome with the primary intent of winning additional money and/or material goods...
and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, there is usually a discrete set of possible outcomes. In this case, expected gain is a measure of the relative balance of win or loss weighted by their chances of occurring.
For example, if a fair die is thrown and numbers 1 and 2 win $1, but 3-6 lose $0.5, then the expected gain per throw is
- $1 × 1/3 − $0.5 × 2/3 = $0
the game is thus fair.
Continuous scenarios
In economicsEconomics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, it is more likely that the set of possible outcomes is continuous (a numerical or currency value between 0 and infinity). In this case, simplifying assumptions are made about the distribution of possible outcomes. Either a continuous probability function is constructed, or a discrete probability distribution is assumed.