Calculate Expected Loss Over Time
Select a game preset or enter custom parameters to calculate expected losses based on play duration.
Average wager per bet or spin
Casino's mathematical advantage
Number of rounds or spins per hour
Total time spent gambling
Multiplier for single bet standard deviation
Extended Play Time Analysis
Analyze how expected losses accumulate over extended periods. This projection demonstrates why the house always wins over the long term.
Session Comparison Tool
Compare expected losses across different gaming scenarios to understand the impact of game selection and bet sizing on long-term outcomes.
Scenario A
Scenario B
Understanding Expected Loss Calculations
Expected loss is a fundamental concept in gambling mathematics that represents the average amount a player can expect to lose over time. This calculation is essential for affordability assessments required by regulators like the UK Gambling Commission and Malta Gaming Authority.
The Expected Loss Formula
The expected loss calculation follows a straightforward mathematical formula that combines bet size, house edge, and total number of bets:
Total Action = Bet Size × Number of Bets
Expected Loss = Total Action × House Edge
For example, if a player makes 500 slot machine spins per hour at $25 per spin with a 5% house edge over 4 hours:
- Total Bets: 500 × 4 = 2,000 bets
- Total Action: $25 × 2,000 = $50,000
- Expected Loss: $50,000 × 5% = $2,500
The Role of Variance
While expected loss represents the average outcome, actual results vary due to variance (randomness). The standard deviation of a gambling session can be calculated as:
Variance explains why players can experience winning sessions despite a negative expected value. However, as the National Center for Biotechnology Information (NCBI) research demonstrates, the law of large numbers ensures that actual results converge toward the expected loss over time. This mathematical certainty is why regulators emphasize time limits and session breaks.
Game Speed and Expected Loss
A critical but often overlooked factor in expected loss is game speed. The number of bets per hour varies dramatically across gambling products:
| Game Type | Bets/Hour | Typical House Edge | Expected Loss/Hour ($25 bet) |
|---|---|---|---|
| Online Slots | 500-600 | 3-10% | $37.50 - $150.00 |
| Live Casino Slots | 300-400 | 3-8% | $22.50 - $80.00 |
| Blackjack (Live) | 60-80 | 0.5-2% | $0.75 - $4.00 |
| European Roulette | 30-40 | 2.7% | $2.03 - $2.70 |
| Baccarat | 60-80 | 1.06-1.24% | $1.59 - $2.48 |
| Craps (Pass Line) | 80-120 | 1.41% | $2.82 - $4.23 |
This data illustrates why the UK Gambling Commission and other regulators have focused attention on online slots—the combination of high speed and relatively high house edge creates the potential for rapid losses.
Regulatory Implications
Understanding expected loss is crucial for compliance with modern customer interaction requirements. Regulators increasingly require operators to:
- Calculate and display theoretical loss metrics to players
- Implement affordability triggers based on loss velocity
- Conduct affordability assessments when losses exceed thresholds
- Provide reality checks showing actual vs. expected outcomes
The Financial Action Task Force (FATF) also references expected loss metrics in the context of identifying unusual gambling patterns that may indicate money laundering—players who gamble at high volumes but show losses inconsistent with expected loss calculations may warrant enhanced due diligence.
Affordability and Harm Prevention
Expected loss calculations form the foundation of affordability assessment frameworks. According to research from the GambleAware foundation, understanding the relationship between play time, bet size, and expected loss helps identify when gambling expenditure becomes disproportionate to income.
For compliance professionals, this calculator demonstrates why regulators like the UK Gambling Commission have proposed spending thresholds—at certain loss velocities, the expected annual loss can quickly exceed what would be considered affordable for median-income households.