What are the published CS2 case drop rates?

Valve publishes the per-tier probabilities directly: Mil-Spec (blue) 79.92%, Restricted (purple) 15.98%, Classified (pink) 3.2%, Covert (red) 0.64%, and Rare Special Item (knife or glove) 0.26%. StatTrak rolls independently on top at roughly 10% across all tiers. These numbers come from Valve's legally-mandated disclosure for regulated markets and have been stable since the original CS:GO Arms Deal case.

What is the expected value of opening a CS2 case?

Expected value (EV) is the probability-weighted average payout per case open. For most active cases, EV sits at roughly 35-55% of the combined cost of a case plus a key. That means for every dollar you spend opening, you receive back about 35-55 cents in average market value of the dropped item. Valve's house edge is what funds the rest. EV is a long-run average — any individual open can be a knife or a 3-cent skin.

If knives drop at 0.26%, am I guaranteed one after 384 cases?

No. 1 ÷ 0.0026 ≈ 384 is the average number of cases per knife, not a guarantee. Each open is independent — the probability of zero knives across 384 cases is about (1 - 0.0026)^384 ≈ 37%. You have a roughly 1-in-3 chance of opening 384 cases and seeing no knife at all. To reach a 95% probability of at least one knife you need about 1,150 cases. To reach 99%, about 1,770.

Why does it feel like cases are rigged when I open a bad streak?

Variance. The standard deviation of payout per case is several times larger than the expected value because the distribution is dominated by a tiny probability of a five-figure knife and an overwhelming probability of a sub-dollar skin. That asymmetry produces long runs of "nothing" punctuated by rare jackpots — exactly the cognitive signature humans interpret as rigged. The drop rates are honest; the variance is brutal.

Is there any case worth opening on EV alone?

Almost never for active cases. The cases with the best EV are the discontinued ones — Operation Bravo, Operation Vanguard, CS:GO Weapon Case 1 — where the case itself trades for hundreds or thousands of dollars, making the cost basis dominate. For those, you're effectively buying a lottery ticket on a discontinued knife collection. For all currently-dropping cases, opening is entertainment spending, not investment.

When does opening cases actually make sense?

Three cases: (1) you want a specific skin in that case and unboxing is one path to it; (2) you treat the open as paid entertainment with the dopamine of the animation as the product; (3) you're willing to accept negative EV to participate in the "I unboxed it" emotional ownership. None of those is investment. If you want exposure to CS2 case-skin appreciation, buy the case itself and hold — or buy the skin you want directly.

CS2 Case Opening Math — Expected Value, Variance & Why You Lose

Opening a CS2 case is a transparent, well-documented probability problem. Valve publishes the drop rates. The market publishes the prices. The math is honest — and the math says you lose, on average, about half of every dollar you spend. This guide walks through the expected-value calculation, the variance bounds that make short runs feel rigged, and the small handful of cases where opening is defensible as anything other than paid entertainment.

The drop rates, in full

Every standard weapon case in CS2 has the same per-tier probability structure. Valve disclosed these rates years ago for regulatory compliance, and they have not changed since the original Arms Deal case:

Mil-Spec (blue) — 79.92%
Restricted (purple) — 15.98%
Classified (pink) — 3.20%
Covert (red) — 0.64%
Rare Special Item (knife or gloves) — 0.26%

Those five numbers sum to 100% — every open lands in exactly one tier. On top of that, an independent 10% roll determines whether the dropped skin is StatTrak (kill counter, ~10% premium for non-rare tiers, larger premium for knives). And the wear (Factory New through Battle-Scarred) is drawn from a per-skin float distribution that varies by case and paint kit — for EV math we use the volume-weighted average price across wear buckets, which marketplaces publish directly.

The Rare Special Item — the knife or, for newer cases, the glove — is one slot but contains the entire knife collection for that case rolled uniformly. So if a case has 13 knife finishes and 4 of them are pattern-sensitive (Doppler, Marble Fade, Fade, Case Hardened), the EV of the RSI tier is the average of all 13 finishes × all wear buckets, with the rare-pattern uplift on a handful of seeds factored in (more on that below).

The expected value formula

Expected value is just a weighted sum:

EV(case) = Σ (P(tier) × avg_value(tier))
         = 0.7992 × milspec_avg
         + 0.1598 × restricted_avg
         + 0.0320 × classified_avg
         + 0.0064 × covert_avg
         + 0.0026 × rare_special_avg

Each tier average is itself a weighted mean across the skins in that tier (uniform within tier), each skin’s wear-bucket mix, and the StatTrak premium folded in. The arithmetic is mechanical; the only inputs that vary are the prices, which you pull from a marketplace API and update daily.

From that EV you subtract the cost of opening — the case price plus the key price (Valve charges $2.49 per key on Steam, less on third-party marketplaces where keys are unboxed-and-resold). What’s left is your per-open net EV. For nearly every actively-dropping case this number is deeply negative.

A worked example

Let’s walk a representative active case. Numbers are illustrative — for live data see the cases index which surfaces real-time supply and price context per case. Suppose the tier-average prices look like this:

Mil-Spec avg: $0.10
Restricted avg: $0.55
Classified avg: $2.20
Covert avg: $11.00
Rare Special avg: $380 (volume-weighted across knife finishes & wears)

EV = 0.7992 × $0.10  = $0.0799
   + 0.1598 × $0.55  = $0.0879
   + 0.0320 × $2.20  = $0.0704
   + 0.0064 × $11.00 = $0.0704
   + 0.0026 × $380   = $0.9880
   ───────────────────────────
            EV total = $1.30

The case-plus-key cost on Steam is about $2.49 (key) + $0.40 (case) = $2.89. So per open you receive $1.30 in expected market-value back. That’s an EV ratio of 45% — for every $2.89 spent, you get $1.30 back on average, losing $1.59 each time the animation plays. Across 100 opens, expected loss is $159. Across 1,000 opens, $1,590.

Notice how dominant the Rare Special term is. The $0.99 from the 0.26% knife slot accounts for 76% of the entire EV. The other four tiers combined contribute about 30 cents. That’s why case-opening feels binary: you either get the knife and recover most of your spend (or 10x it), or you don’t and the open is essentially zero. The middle tiers are noise.

Variance — the part that breaks brains

Expected value tells you what happens on average over an infinite number of opens. It tells you nothing about a single session of 50. For that you need variance, and the variance on case opens is enormous.

Standard deviation of payout per open, using the same numbers above, works out to roughly $20 — about 15x the EV itself. That means a typical 100-open session has a standard deviation on total payout of $200 around an expected $130. Your “normal range” of outcomes spans from negative $70 (no knife, mostly blue drops) to positive $330 (one mid-tier knife). Hit a high-end knife pattern and the outcome blows out the entire model.

What this looks like in practice: long stretches where every open is a 5-cent Mil-Spec, interrupted by an occasional Covert that gets your hopes up, and once every few hundred opens, the gold flash. The intervals between gold flashes are geometrically distributed — there’s no “due” knife after a dry spell. The casino game-show pacing humans interpret as rigging is just what a low-probability, high-payoff distribution genuinely looks like.

The pigeon analogy is unfair to pigeons, but: variable-ratio reinforcement is the most addictive reward schedule in behavioural psychology, and CS2 case-opening is a mathematically pure expression of it.

The knife-after-X-opens question

A common heuristic: “1 ÷ 0.0026 ≈ 384, so I should get a knife every 384 opens.” That’s the expected number of trials per success, not a guarantee. Each open is independent, so the probability of zero knives in N opens is (1 - 0.0026)^N. Solving for the cumulative knife probability:

100 opens → 23% chance of at least one knife
250 opens → 48% chance
384 opens (the “expected” number) → 63% chance
500 opens → 73% chance
1,000 opens → 93% chance
1,150 opens → 95% chance
1,770 opens → 99% chance

So roughly 37% of people who open exactly 384 cases will have zero knives at the end. About 7% will still have zero after 1,000. And the knife you do eventually get is, on average, a low-mid tier knife in a worn condition — not the Karambit Fade in your screensaver. The flashy outcomes drive the marketing; the median outcome funds the house.

Why EV is below cost — Valve’s edge

The gap between EV and cost is Valve’s rake. Steam takes 15% on every secondary-market sale (5% game fee + 10% Steam fee), and every case that’s opened was bought from someone who paid market price, plus the $2.49 key Valve sold directly. Combine the key margin and the marketplace fee structure and the house keeps roughly 50% of the gross spending on case openings. That’s a lottery-grade take-rate, comparable to a state-run scratch-off and well above a casino slot machine’s ~5-15% house edge.

Marketplace fees are part of the math too — if you intend to sell whatever drops, you net the Steam Market price minus fees. The marketplace fees reference covers every venue’s rake, and the fee calculator translates list prices to take-home. After fees, real-world EV is typically another 10-15% below the gross EV calculation above.

Pattern uplift — the part nobody factors in

The simple EV formula treats every knife of a given finish as equal value. That’s an approximation. A small fraction of knife seeds — Doppler Sapphire/Ruby/Black Pearl, Marble Fade FFI, Case Hardened blue gem patterns, Fade 100% — trade at 3x to 20x the average finish price. Folding that into the model:

P(rare_pattern | knife) ≈ 1-3% (varies by finish)
EV_uplift = P(rare_pattern) × avg_premium
         ≈ 0.02 × 5x base = 10% boost to RSI tier

That nudges the case EV up by a percent or two — meaningful for tight-spread arbitrage thinking but doesn’t change the conclusion that opening is value-destructive on average. For deep-dive pattern mechanics see the knife patterns guide — it lists which seeds matter on which finishes.

The few cases where opening is defensible

Almost every actively-dropping case is a negative-EV bet. The exceptions sit at the edges:

Discontinued cases with very high case prices. Cases that stopped dropping years ago — CS:GO Weapon Case 1, Operation Bravo Case, Operation Vanguard — now trade for tens to hundreds of dollars per case. The EV math still comes out negative, but the spread between cost and EV is narrower because the unopened case itself holds value. If you’re going to open one, the case-cost dominates the equation and the key is a rounding error.
Targeted unboxing for a specific skin. If you want a particular Mil-Spec or Restricted that’s in a 50-cent case, opening 5-10 cases is a reasonable way to acquire it without paying the marketplace markup. The EV still favours buying direct, but the gap is small enough that the experience plus possibility of a luckier drop can justify it.
Paid entertainment. If you genuinely enjoy the animation, the suspense, the ritual — open a case once a month and budget for it like any other entertainment line item. That’s an honest framing and there’s nothing wrong with it. What doesn’t work is the “just one more, I’m due” framing — the math has no concept of being due.

If you want exposure, don’t open

The alternative to opening cases for skins is, oddly, buying the cases and holding them sealed. Cases appreciate as supply shrinks — every case opened is one fewer case in circulation, and crafting demand from openers, gamblers, and capsule-style speculators pulls supply down steadily. Many cases that were 3 cents on launch now trade for $5-50, with a few discontinued ones in the hundreds. The cases index tracks every case’s circulating supply over time — rarer-supply cases have outperformed the broader market on a 5-year horizon and are the cleanest case-economy investment available.

If you want the specific skin from a case, buy it on a marketplace. If you want a knife, buy a knife. If you want exposure to case appreciation, buy cases and don’t open them. Opening is the value-destruction step; every other path dominates it.

A reasonable mental model

Treat opening cases the way you’d treat buying lottery tickets: the take-rate is bad, the variance is huge, and the probability of life-changing outcomes is negligible. Anyone who tells you a particular case is “profitable to open” either hasn’t done the EV math or is selling you something downstream of it (subscription, affiliate marketplace, betting platform). The transparent maths above is repeatable from public data. Run it on any case you’re thinking of opening before you buy the key.