Every in-game CS2 case is a structured probability distribution. Valve has published the official rarity tiers and approximate drop chances multiple times since 2017, and the math has remained stable through the CS:GO-to-CS2 transition. What follows is the operating model used by economists and trade-up calculator developers to evaluate case-opening expected value — applicable to any of the ~50 active in-game cases.
The five rarity tiers and their weights
Each in-game case contains items across four to five rarity tiers. Within a single roll, the probabilities are weighted as follows according to Valve's published case mechanics:
| Rarity tier | In-game color | Drop chance | Odds (1 in N) |
|---|---|---|---|
| Mil-Spec (Blue) | Blue | 79.92% | 1.25 |
| Restricted (Purple) | Purple | 15.98% | 6.26 |
| Classified (Pink) | Pink | 3.20% | 31.25 |
| Covert (Red) | Red | 0.64% | 156.25 |
| Special / Knife-Glove (Gold) | Gold | 0.26% | 384.62 |
StatTrak as an independent secondary roll
StatTrak is not part of the rarity roll. It is a secondary, independent Bernoulli trial applied to whichever item was selected. Valve has stated the StatTrak rate as approximately 10% on standard cases. The combined probability of a specific outcome — say, a StatTrak Covert — is therefore the product of the two:
P(StatTrak Covert) = P(Covert) × P(StatTrak) = 0.0064 × 0.10 = 0.00064 = 0.064%For a StatTrak knife — combining the 0.26% Special tier rate with 10% StatTrak — the probability is roughly 0.026%, or 1 in 3,846 openings. Note that some operation cases and souvenir-style cases use modified StatTrak weights, and a small number of cases (the early Glove cases, for example) have no StatTrak option at all.
Float and rarity are independent
After the rarity tier is rolled, the specific finish within the tier is selected with uniform probability across that tier's items, then a float value is drawn within that finish's wear range. Float and rarity are statistically independent — pulling a knife does not bias toward Factory New or Battle-Scarred. This is the basis for combined expected value calculations: each component's distribution can be evaluated separately and multiplied together.
Expected value: the core formula
The expected value of a case opening, ignoring StatTrak rolls and float effects, is the sum across all possible outcomes of probability × market value:
EV(case) = Σ over all skins s [ P(s) × MarketValue(s) ]For each skin, the within-tier probability is `P(tier) ÷ N(tier)`, where N(tier) is the number of distinct skins at that rarity in the case. A typical weapon case contains 12 Mil-Spec, 5 Restricted, 3 Classified, 2 Covert, and a knife pool of 19 finishes (each with multiple float exteriors).
| Tier | Items in tier | Tier probability | Per-skin probability |
|---|---|---|---|
| Mil-Spec | 12 | 79.92% | 6.660% |
| Restricted | 5 | 15.98% | 3.196% |
| Classified | 3 | 3.20% | 1.067% |
| Covert | 2 | 0.64% | 0.320% |
| Knife (any finish) | 19 × ~5 wears | 0.26% | ≈0.0027% per finish-wear |
Why almost every case opens at a loss
When you sum the EV across a typical active case priced at $2.49 on the Steam Marketplace plus a $2.49 key, the total spend is roughly $4.98. A practical rule of thumb is that for most active cases the EV of the contents — calculated using current Steam Community Market prices — sits between $1.50 and $2.30. The case-plus-key cost therefore exceeds the EV of the contents by a factor of 2× to 3×.
Variance, not expectation, is what players experience
Expected value is a long-run average. Individual case-opening sessions are dominated by variance — the standard deviation of outcomes is enormous because the highest-value outcome (a high-tier knife) is several thousand times the value of the most common outcome (a Mil-Spec finish). This is why streamers who open hundreds of cases on camera can show wildly different results between sessions; the distribution is heavily right-skewed by a small number of extreme outcomes.
The probability of opening at least one knife in N cases is `1 − (1 − 0.0026)ᴺ`. To reach a 50% chance of at least one knife requires approximately 267 cases opened. To reach a 90% chance requires roughly 886 cases. Neither outcome is guaranteed — and the EV of the cases consumed in the process almost always exceeds the median knife value by a wide margin.
Operation cases and modified weights
Operation-specific cases sometimes use modified rarity weights, particularly when the case contains an Operation-exclusive Covert finish that is meant to be more obtainable. Reading the official case description and any in-game UI tooltips is the only reliable way to confirm whether a case uses the standard 79.92/15.98/3.20/0.64/0.26 split or a modified distribution.
Practical takeaways
- Standard cases share the same five-tier weighting — only the loot pools differ between cases.
- Knife/glove rolls land at 0.26% — roughly 1 in 384 openings.
- StatTrak is independent of rarity (~10%), so a StatTrak knife is approximately 1 in 3,846.
- EV of contents is typically 25–45% of the case-plus-key cost on the Steam Market — meaning most cases are negative-EV by construction.
- Variance dominates short-run experience; the median outcome is far below the mean.
Case opening is a recreational activity with the mathematical structure of a slot machine: heavy-tailed reward distribution, fixed house edge implied by content EV versus cost, and the psychological compounding effect of near-misses inside the rarity grid. Players who treat it as entertainment with an embedded cost generally end up with a coherent worldview; players who treat it as an investment generally do not.
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