Same EV, Different Risk: A Variance Worked Example
Two sealed products can have the same mean expected value and still be completely different opening decisions. This intentionally simple comparison isolates the difference between an average, a typical result, and the chance of losing money.
By The Expected Value editorial team · Published
Two simplified $100-EV products
| Product | Possible opened value | Probability | Mean EV |
|---|---|---|---|
| Steady Product | $100 | 100% | $100 |
| Top-Heavy Product | $50 | 90% | $100 |
| $550 | 10% |
The top-heavy mean is (0.90 × $50) + (0.10 × $550) = $45 + $55 = $100. The arithmetic is correct, but the average does not resemble nine out of ten actual openings.
Mean, median, range, and loss rate
| Metric | Steady Product | Top-Heavy Product |
|---|---|---|
| Mean EV | $100 | $100 |
| Median opened value | $100 | $50 |
| Central 90% modeled interval | $100–$100 | $50–$550 |
| Chance opened value is below $90 | 0% | 90% |
A buyer who looks only at the $100 mean might treat both products as equivalent at a $90 cost. A buyer who cannot absorb a $40 shortfall would see a decisive difference. The top-heavy product offers a large upside, but its typical opening is the $50 outcome.
How this appears in real products
Real booster products have hundreds or thousands of possible combinations rather than two outcomes. The same pattern emerges when rare serialized cards, premium treatments, short-print chase cards, or unusually expensive mythics carry a large share of mean EV. A high top-five contribution share and a wide simulated interval are signs that the headline average depends on a small number of outcomes.
This does not make the model wrong. It means the mean answers “what is the long-run average under these assumptions?” while the median and percentiles answer different questions about an individual opening. A business opening large volume may care about the long-run mean; a person buying one box may care more about the median and loss probability.
Why repeated simulations move
A Monte Carlo run samples a finite number of openings. If only 10% of outcomes produce the $550 result, one run may sample slightly more or fewer hits than another. The estimated mean and percentiles therefore move. Increasing the number of samples reduces sampling noise, but it does not remove the product's underlying variance.
The Low, Mid, and High summary should come from the same new result set whenever the calculation reruns. A middle value that remains frozen while the tails move gives the impression of stability that the simulation did not produce.
Practical use
- Compare mean and median; a large gap suggests a skewed distribution.
- Compare product cost with the loss probability, not only with mean EV.
- Inspect which card groups contribute most of the total.
- Rerun the model and increase samples if percentile estimates are unstable.
- Stress-test the decision with lower chase prices, a realistic sift, and your own selling fees.
Try the interactive confidence band demonstration, then return to the complete calculator checklist.