Statistical mode uses model moments (μ, σ) to compute ranges (e.g., via a normal approximation). Monte Carlo bands are sample percentiles of simulated outcomes. With enough samples, they converge—but individual runs still wiggle.
What they are
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 (mean ≈ $161) for clarity; your production tools model slots in detail. (Mean note is here for context only; no banner pill is shown.)
Try a quick simulation
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. With large sample sizes, the simulated percentiles settle near the statistical band.
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. Perfect independence slightly overstates variance; real collation narrows it a bit. Your production calculators account for slot rules; any remaining dependence tends to be modest.
Reminder: EV tools are planning aids, not profit guarantees.