How We Estimate Expected Value (EV)

Model: Monte Carlo CLT compared Example: OTJ Play Boosters

1) Choosing a statistical model

Most EV calculators likely use a Central Limit Theorem (CLT) approach. CLT is fast and efficient, but for products with high variance (e.g., collector boxes) the tails can extend unrealistically, sometimes “reaching past 0.” I instead use a Monte Carlo method, which samples full packs repeatedly to produce a distribution with tighter tails.

In practice, for **Play Booster** boxes, I’ve found the median EV from CLT and Monte Carlo to be within a few dollars of each other. If you make purchase decisions on the median, the model choice often doesn’t change the go/no‑go call much.

2) Gathering pack‑composition data

Using OTJ (Outlaws of Thunder Junction) as an example, we pull pack rules and card pools from:

Note: Newer “Collecting” pages increasingly include the Play Booster rarity breakdown directly. When they don’t, the Play Booster article fills the gap.

3) From data to an EV calculator

Once the model is chosen and the pack structure is verified, we can build an EV calculator. Conceptually:

After that, it’s just entering how much product you plan to open and deciding if the juice is worth the squeeze.

4) Why the numbers change between runs

With Monte Carlo, every time you click Calculate, the simulation re‑draws packs — so results vary in a statistically consistent way. A pure CLT model won’t fluctuate (it’s a closed‑form estimate), which is why it appears “constant” between runs.

FAQ: How This EV Calculator Compares to Other Calculators

How does this compare to Mox Alpha?

For recent sets where Wizards of the Coast has provided detailed odds for Play Boosters, our numbers can—and should—be very close. The main differences usually come down to timing (when prices were pulled) and minor modeling choices. In cases where Wizards has been more vague, like with chase cards in Collector Boosters, everyone does their best with the information available.

The further back in time we go, the more likely our models diverge. Some older sets have less detailed pack information, and in some cases, the modeling data is scattered across multiple articles. When I modeled Outlaws of Thunder Junction (OTJ), there was about a 20% gap between their model and mine. That led me to approach the set from multiple angles, cross-checking different assumptions to pinpoint the issue. I still don’t know the exact cause—and may never know—but my hypothesis is that one of the card slots was mis-modeled. Working through this process helped me develop a reliable framework for accurately modeling modern sets.

  • Price source & timing: This calculator runs client-side and pulls prices at render time; Mox Alpha’s prices are fetched server-side. Even small timing differences can move EV.
  • Inclusion rules: Handling of The List (SPG), Bonus Sheet, land slot, and foil vs. wildcard probabilities may differ in subtle ways.
  • Price floors (“sift”): You can optionally exclude sub-floor cards from EV here. If Mox applies a different floor (or applies it differently), totals will diverge.

Unlike Mox Alpha, this tool’s calculations are done client-side. That means other developers can inspect the logic and offer feedback directly.

How does this compare to Anon’s EV calculator (formerly YourFriendsHouse)?

Anon’s calculator is actively maintained and fixes ship quickly. Issues on older sets have been corrected after reports. Small edge cases (like box toppers) can still be missed occasionally, but overall their recent outputs have been very accurate—often tracking official slot math closely and, in many cases, more consistently than Mox Alpha on modern sets.

When our totals diverge from Anon’s, it’s typically for the same reasons EV tools can diverge from Mox Alpha: price timing, slot interpretation, and optional filters. For Collector Boosters where Wizards’ guidance is vague, both tools make best‑effort assumptions and document them.

  • Price source & timing: This site fetches prices client‑side at render; Anon also updates frequently. Even small timing differences or thin markets can swing EV.
  • Coverage & edge cases: Handling of Box Toppers, Bonus Sheets, The List (SPG), basic land slots, and language‑specific prints may differ. Anon has improved coverage on older sets, though small omissions can still occur.
  • Odds interpretation: Details like the 3‑card R/M cluster’s ≤1‑foil constraint, surge vs. non‑surge splits, and colorful/serialized shares can meaningfully change results.
  • Filters / floors: This calculator supports a “sift” (price floor) option; if Anon applies a different floor, or applies it differently, totals will diverge.
Which one is more accurate?

There isn’t a single definitive answer. I aim for high fidelity and full transparency so you can review and stress-test the assumptions.

Practical guidance: if a box is in ample supply, use the EV calculator (at 0.25 sift) that sits closest to market cost of a box plus seller fees. For OTJ at the time of writing, Mox Alpha shows a healthy profit while major sellers have not sold out nor raised prices. This calculator’s EV implies roughly break-even if you crack and sell at 0.25 sift. In this scenario, the estimate closer to break-even is likely the more realistic since there is little to no market friction.

Why that stance? Businesses with sorting infrastructure and distribution pricing can profitably sift boxes even when hobbyists struggle to break-even. When product becomes scarce or hype-driven, box prices can float well above any “expected value” because some buyers pay for the opening experience, not resale economics.

Reminder: EV fluctuates and is not a guarantee of profit. Treat it as a planning tool, not a promise.

Why isn’t there a “Direct Seller” pricing option?

After TCGplayer’s acquisition by eBay, new public Market API keys have not been broadly issued. As a result, this tool uses Scryfall pricing by default. If programmatic access to TCGplayer Market data becomes available again, I intend to add it.

How can I help improve accuracy?

This calculator runs in your browser. If you spot a mismatch, you can inspect the model, file an issue, or suggest changes to the probability assumptions, price inputs, or fee logic. Community scrutiny makes the numbers better.

Have suggestions or ideas for new tools? We’d love to hear them. If you spot any errors or have questions, please contact us — we’re here to help.

Confidence levels (for Statistical mode)

For a given purchase, a C% band would contain your realized value about C% of the time under the model. Higher confidence ⇒ wider band.

Confidence z-score (±z·σ) Coverage inside band Outside band (each tail)
68%~1.00~68%~16% lower / ~16% higher
90%~1.645~90%~5% lower / ~5% higher
95%~1.96~95%~2.5% lower / ~2.5% higher
99%~2.576~99%~0.5% lower / ~0.5% higher

Notes: Per-print pulls assumed independent; real collation correlations narrow true variance slightly.