CS2 Loot Distribution Calculator

Interactive Loot Distribution Calculator

Enter the number of CS2 cases you plan to open to see the expected distribution of items across all rarity tiers, complete with confidence intervals showing the likely range of outcomes.

Understanding CS2 Loot Distribution

When you open CS2 cases, each opening is an independent random event with fixed probabilities. Understanding how these probabilities translate into expected distributions helps you set realistic expectations and make informed decisions.

The Official CS2 Case Odds

Every CS2 case uses the same rarity tier probabilities, which Valve disclosed in 2023 to comply with international loot box transparency regulations. According to Valve's official CS2 announcements, these are the fixed odds:

These probabilities are consistent across all CS2 weapon cases. What varies between cases is the specific items available within each rarity tier, not the probability of hitting that tier.

Why Distribution Matters

Understanding distribution helps you:

• Set realistic expectations: Know that ~80% of your drops will be Mil-Spec before you start
• Budget appropriately: Understand how many cases you'd need to likely get specific tier items
• Recognize variance: Accept that actual results will differ from expected values
• Avoid the gambler's fallacy: Each case is independent regardless of previous results

What Are Confidence Intervals?

A confidence interval provides a range of likely outcomes rather than a single expected value. This is crucial for case opening because actual results always vary from mathematical expectations.

The 95% Confidence Interval

Our calculator uses a 95% confidence interval, meaning:

• There's a 95% probability your actual results will fall within the displayed range
• There's a 2.5% chance of getting fewer items than the lower bound
• There's a 2.5% chance of getting more items than the upper bound

For example, if opening 100 cases shows an expected range of "0-2" for Covert items, this means:

• You'll most likely get 0, 1, or 2 Covert drops
• Getting 3+ is possible but statistically unlikely (less than 5% chance)
• Getting 0 is the most probable single outcome

Why Ranges Are More Useful Than Single Numbers

The expected value (mean) can be misleading. If the expected number of knives in 100 cases is 0.26, you might think "I'll probably get about 0.26 knives"—but you can't get 0.26 of anything. The reality is you'll get 0, 1, or occasionally more. The confidence interval shows this reality more honestly.

Confidence intervals are based on the binomial distribution, which describes the probability of success in a fixed number of independent trials—exactly what case opening represents mathematically.

Variance & Standard Deviation

Variance measures how spread out your potential results are from the expected value. Understanding variance is critical for managing expectations and budgeting for case opening.

How Variance Works

For binomial distributions (like case opening), variance follows a predictable formula:

Variance = n × p × (1 - p)

Where n is the number of cases and p is the probability of hitting the target tier.

Standard Deviation

Standard deviation is the square root of variance and provides a more intuitive measure. Roughly:

• ~68% of results fall within ±1 standard deviation of the expected value
• ~95% of results fall within ±2 standard deviations (this forms our 95% confidence interval)
• ~99.7% of results fall within ±3 standard deviations

Small Sample Variance

With fewer cases, variance has a larger relative impact. Opening 10 cases means your results will deviate wildly from expectations. Opening 1,000 cases brings results closer to statistical averages. This is the Law of Large Numbers in action—actual frequencies converge to theoretical probabilities as sample size increases.

The Binomial Distribution

CS2 case opening follows a binomial distribution—a probability model for counting successes in a fixed number of independent trials, each with the same probability of success.

Why Binomial Applies to Cases

Case opening meets all binomial criteria:

• Fixed number of trials: You open a specific number of cases
• Independent trials: Each case opening is independent of all others
• Two outcomes: Each case either contains your target rarity or doesn't
• Fixed probability: The odds remain constant for every case

The Mathematics

The probability of getting exactly k items of a specific rarity from n cases is:

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

Where C(n,k) is the binomial coefficient ("n choose k"), representing the number of ways to arrange k successes among n trials.

Practical Implications

The binomial distribution reveals several counterintuitive truths:

• Opening 385 cases (the "average" for a knife) only gives you ~63% chance of getting at least one knife
• Opening 1,000 cases still leaves a ~7.5% chance of getting zero knives
• The most likely outcome is often 0 for rare items, even over many cases

Research on loot box mechanics by behavioral scientists shows that players often underestimate this variance, expecting more predictable outcomes than probability allows.

Practical Examples

Let's examine what you can realistically expect from different case opening quantities:

Opening 10 Cases (~$25 investment)

• Mil-Spec: Expect 7-10 (almost certainly 8)
• Restricted: Expect 0-3 (probably 1-2)
• Classified: Expect 0-1 (probably 0)
• Covert: Expect 0 (6.2% chance of 1)
• Rare Special: Expect 0 (2.6% chance of 1)

Opening 100 Cases (~$250 investment)

• Mil-Spec: Expect 72-88 (centered around 80)
• Restricted: Expect 10-23 (centered around 16)
• Classified: Expect 0-7 (centered around 3)
• Covert: Expect 0-2 (most likely 0 or 1)
• Rare Special: Expect 0-1 (77% chance of 0, 22% chance of 1)

Opening 500 Cases (~$1,250 investment)

• Mil-Spec: Expect 382-417 (very narrow range around 400)
• Restricted: Expect 67-93 (centered around 80)
• Classified: Expect 10-22 (centered around 16)
• Covert: Expect 1-6 (centered around 3)
• Rare Special: Expect 0-3 (most likely 1, ~72% chance of at least 1)

Common Misconceptions About Distribution

Several statistical misconceptions lead players to misinterpret case opening results:

Misconception 1: "I'm Due for Good Luck"

Reality: This is the gambler's fallacy. Each case opening is independent. Previous results don't influence future outcomes. Opening 100 cases without a knife doesn't make the 101st case any more likely to contain one.

Misconception 2: "Probability Guarantees Results"

Reality: Probability describes likelihood, not certainty. Even "1 in 385" odds don't guarantee a knife in 385 cases—that's only a 63% probability. Variance means some players get multiple knives in few cases while others open thousands without one.

Misconception 3: "More Cases = Proportionally More Rare Items"

Reality: While expected values scale linearly, confidence intervals don't shrink proportionally. Opening 10x more cases reduces the relative uncertainty but not the absolute range of outcomes as much as you'd expect.

Misconception 4: "If I Didn't Hit Expected Value, Something's Wrong"

Reality: Expected value is an average across infinite trials. Getting exactly the expected value is actually unlikely for any specific session. Getting 0 knives in 100 cases (expected: 0.26) is completely normal and the most probable outcome.

Frequently Asked Questions

Related CS2 Tools

Explore our other probability and analysis tools:

• Case Odds Calculator - Calculate specific probabilities for target items
• Streak Calculator - Analyze dry streak and hot streak probabilities
• Case ROI Calculator - Calculate expected return on investment
• Rarity Visualizer - Visual probability demonstrations
• Cost-to-Odds Calculator - Calculate spending for target probability
• Bankroll Calculator - Budget management and risk assessment
• Case Odds Explained - Comprehensive probability guide
• All Tools - Browse all available calculators