Expected value is a mathematical concept used to describe the average outcome of an event over a very large number of repetitions. This guide provides an informational explanation of expected value and how it is applied in gambling-related analysis, without encouraging gambling activity.
What expected value means
Expected value describes the long-term average result of a process that has multiple possible outcomes. It combines the probability of each outcome with its associated result to produce a single average figure.
Expected value is used to:
- Describe long-term behaviour of a system
- Compare different probability models
- Analyse outcomes across large samples
- Explain why short-term results vary
It is not a prediction tool for individual events.
How expected value is calculated conceptually
At a conceptual level, expected value is calculated by weighting each possible outcome by its probability and summing the results.
Key characteristics include:
- Based on probabilities defined in the model
- Calculated across all possible outcomes
- Relevant only over a large number of repetitions
- Stable over time if the model does not change
The calculation reflects design, not experience.
Expected value in gambling-related systems
In gambling systems, expected value is closely related to design metrics such as RTP and house edge. These values describe how a game is intended to perform statistically over time.
Common relationships include:
- RTP as a form of expected return
- House edge as the complementary expected margin
- Fixed expected value embedded in game design
- Consistency across sessions and users
These values are defined during development and remain constant.
Why expected value does not predict short-term outcomes
Expected value does not describe what will happen in a single event or session. Random variation causes individual results to differ, sometimes significantly, from the long-term average.
Important points to understand:
- Short-term outcomes can be higher or lower than expected value
- Randomness creates natural variation
- Streaks do not contradict expected value
- Convergence occurs only over large samples
Short sessions are not representative of long-term averages.
Expected value and uncertainty
It is important to understand that expected value does not eliminate uncertainty. Even with a known expected value, outcomes remain uncertain on an individual basis.
Expected value does not:
- Reduce randomness
- Guarantee specific results
- Predict timing of outcomes
- Limit short-term variation
Uncertainty is an inherent property of chance-based systems.
Relationship to other analytical concepts
Expected value is often discussed alongside other analytical metrics that describe different aspects of system behaviour.
Related concepts include:
- Probability
- RTP and house edge
- Volatility or variance
- Risk and outcome distribution
Each metric describes a different dimension of long-term behaviour.
Expected value overview
| Aspect | Description |
|---|---|
| Expected value | Long-term average outcome |
| Based on | Probability and outcomes |
| Predicts single result | No |
| Changes over time | No (if model is fixed) |
| Eliminates uncertainty | No |
| Used for | Statistical analysis |
What you can do next
- Learn how expected value relates to RTP
- Read about probability and long-term averages
- Explore how volatility affects short-term variation
- Return to the guides section for more informational content
Informational disclaimer
PokiesHub Australia does not operate gambling services and does not provide financial or gameplay advice. This information is presented for educational purposes only.
The content is intended to help readers understand how expected value is used to describe probability, risk, and long-term behaviour in gambling-related systems.