Statistical mode uses model moments (μ, σ) to compute ranges, for example with a normal approximation. Monte Carlo bands estimate percentiles of the simulated outcome distribution. More samples stabilize those percentiles, but they need not match a normal approximation when outcomes are skewed or discrete.
The Expected Value — Monte Carlo Confidence Bands
In Monte Carlo mode, a C% band is the middle C% of simulated box outcomes. It’s computed from percentiles (not z‑scores) and will wiggle from run to run—especially on top‑heavy Collector products. This describes the spread of individual box outcomes, not a confidence interval for the estimated mean EV.
What are they?
A C% band is the interval between two percentiles of your simulated outcomes. For a 95% band, that’s the 2.5th to the 97.5th percentiles. Bands depend on inputs (prices, odds, fee rules) and on how many samples you draw.
Why runs differ: Simulations draw random samples. When a few chase cards carry most of the value, tails dominate and runs can bounce. Run the calculation multiple times and compare ranges; increasing boxes per run steadies the band.
How to read a Monte Carlo band
- Pick a level: 68% (quick gut‑check), 90–95% (planning), 99% (conservative).
- Compare to price: check Chance you lose money vs. your box price.
- Watch width: wider band = more uncertainty; top‑heavy sets widen the upper tail.
This demo uses a fixed illustrative mixture with a mean of approximately $161. Use it to see how a wider range signals greater uncertainty; calculator pages use their own product-specific slot models.
Try a quick simulation
Limits: 100–20,000 boxes per run and 1–25 runs (500,000 samples maximum) to keep the browser responsive.
Tip: On top‑heavy products (e.g., Collector Boosters), outcomes swing more. Re‑run the simulation to see how the band wiggles.
Monte Carlo band (aggregated across all samples): —
Median (aggregated): —
Chance you lose money: —
Run‑to‑run variability
| Run | Lower | Median | Upper | Width |
|---|
Min/Max across runs — Lower: — / — · Upper: — / —
FAQ
How is this different from “Statistical mode” bands?
Why does Statistical mode feel steadier than repeated simulations?
Statistical mode computes the band directly from μ and σ, so it doesn’t depend on random draws. Simulations sample outcomes, so each run varies. More samples reduce simulation noise; they do not remove error in the model or make a normal approximation exact.
Do repeated runs mean the model is wrong?
No—variance is expected. Re‑running exposes sensitivity to rare hits. On Collector products, a few high‑value cards can dominate results.
How many boxes per run should I use?
Use enough to stabilize the percentiles for your decision. Start with a few thousand boxes per run; increase if the band jumps around more than you’d like.
Can the lower bound be negative?
Under a normal approximation, yes; in practice, realized values bottom near $0. The demo clamps negatives to $0 for readability.
Do collation patterns or slot rules change σ?
Yes. Documented slot and replacement rules are modeled on each product page. When manufacturer collation creates additional dependence between pulls, it can narrow or widen the true distribution; an independent-draw assumption should not be read as a guaranteed conservative direction.
Reminder: EV tools are planning aids, not profit guarantees.