How Casino Bonus Expected Value (EV) Is Calculated

Calculating the expected value of a casino bonus is fundamentally different from calculating the value of normal casino play. This page explains how a bonus's expected value is actually calculated in practice, why simulation is required, and why simple RTP-based formulas break down when wagering requirements, volatility, and balance paths are involved.

Understanding RTP (Return to Player)

Every casino game has a stated RTP (Return to Player). RTP represents the average percentage of total stakes that a game pays back to players over a very large number of bets.

For example, a game with a 96% RTP will, on average, return $96 for every $100 wagered. The remaining 4% represents the casino’s edge. Importantly, RTP describes long-run behaviour over millions of bets, not the outcome of any individual bet or session.

Expected Value of Cash Play

When playing with cash only, calculating expected value is straightforward.

If a game has a 96% RTP, then each dollar wagered has an expected loss of 4 cents. Over time, expected value is simply the amount wagered multiplied by the house edge. If you wager $100 in total, you are mathematically expected to receive $96 back.

Because casino games always have RTPs below 100%, cash play is always a negative expected value. There is no optimisation or strategy that can change this fundamental relationship.

Why Bonus Expected Value Is Different

Calculating the expected value of a casino promotion with wagering requirements is fundamentally more complex.

Consider a $100 bonus funds with a 20× wagering requirement. In theory, this implies $2,000 of required play before the bonus funds convert into withdrawable cash. In practice, however, you will not always complete the full wagering requirement.

Sometimes you may complete the entire $2,000 of wagering. Other times, you may lose your balance after only a few hundred dollars of play. The actual amount wagered changes on each attempt and is not a fixed number.

This uncertainty is what makes calculating the expected value of a promotion valuation more complex. You are no longer calculating expected value based on known data, you are calculating it across many possible outcomes.

How Volatility and Stake Size Affect Expected Value

Game volatility describes how a game distributes its returns.

A low-volatility game tends to produce frequent small wins, while a high-volatility game produces infrequent but much larger wins. While both games may have the same RTP, their paths to that RTP are very different.

Volatility materially impacts the value of a promotion. High-volatility games increase the likelihood of early busting of your balance but also increase the chance of large wins. Low-volatility games reduce variance but may prolong wagering and increase exposure to the house edge.

Stake size interacts with volatility in the same way. Larger stakes increase variance but, on average, result in less turnover as a result of busting more often, while smaller stakes reduce variance but increase the total turnover. These interactions mean that the expected value cannot be separated from how a promotion is played.

Why Simulation Is Required to Calculate Bonus EV

Because the total amount wagered is uncertain, there is no single formula that can accurately describe the value of a bonus with wagering requirements.

Instead, the correct approach is to simulate the promotion many times and observe the average outcome. This is where a Monte Carlo simulation becomes necessary. The same method used by casinos and slot game studios.

To estimate the expected value of a promotion, the simulator runs millions of complete playthroughs of the bonus from start to finish. Each playthrough mirrors the limitations of the promotional terms, uses real game probabilities, accounts for balance changes, bust scenarios, and successful completions.

Our calculator simulates 5 million full promotions from start to finish. Each simulation contains many individual game outcomes, resulting in an extremely large number of probabilistic calculations. This scale allows randomness to average out and produces stable expected value estimates with a very small margin of error.

From these simulations, we estimate:

• The average amount wagered before the promotion ends
• The probability of completing wagering
• The expected final balance
• The overall expected value of the promotion

Calculating Expected Value Before You Play

Rather than relying on guesswork, successful advantage players calculate the expected value of every promotion before deciding whether to participate. If the maths is positive, the promotion may be worth considering. If it is negative, it should be avoided.

Use our free Expected Value Calculator to analyse casino bonuses, determine their expected value, and see if the odds are truly in your favour before you play.