CS2 Binomial Probability Calculator
Calculate the exact probability of getting a specific number of rare drops when opening CS2 cases. Use binomial distribution mathematics to understand your precise chances of achieving exactly X knives, coverts, or other rarity items in N case openings.
Binomial Probability Calculator
Enter your parameters to calculate exact CS2 case opening probabilities
Select the rarity tier you want to analyze
How many cases will you open?
Exactly how many items of this rarity?
Probability Results
Calculating...
Probability Distribution
| k (Successes) | P(X = k) | P(X ≤ k) | 1 in X |
|---|
Quick Calculation Presets
Click any preset to instantly load common CS2 probability questions:
Understanding the Binomial Distribution
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial has the same probability of success. CS2 case opening is a perfect real-world example of this mathematical concept.
Key Components Explained
- n (Number of Trials): The total number of cases you plan to open. Each case is an independent trial with the same probability of dropping each rarity tier.
- k (Target Successes): The exact number of items of your chosen rarity you want to calculate the probability for.
- p (Success Probability): The drop rate for your target rarity, as disclosed by Valve (e.g., 0.26% for knives/gloves).
- C(n,k): The binomial coefficient, representing how many ways you can arrange k successes among n trials. Calculated as n! / (k! × (n-k)!)
Why This Matters for CS2
Understanding binomial probability helps set realistic expectations for case opening. Many players experience frustration because they underestimate how unlikely rare drops are, or conversely, how common "unlucky" streaks are mathematically. According to research on probability distributions from Britannica, the binomial model accurately predicts outcomes in scenarios with fixed trials and constant success probability.
For example, if you open 100 cases hoping for a knife (0.26% chance per case), the probability of getting exactly zero knives is about 77%. This isn't bad luck—it's the mathematical expectation. Our calculator helps you understand these realities before spending money.
Important Note
Each case opening is completely independent. Past results don't influence future outcomes. Opening 500 cases without a knife doesn't make the 501st case any more likely to contain one. This is a core principle of probability theory and applies directly to CS2's RNG system.
CS2 Official Drop Rates
Valve officially disclosed CS2 case drop rates, which form the basis for all probability calculations. These rates are consistent across all weapon cases and apply to each opening independently. According to Steam Support documentation, these rates are:
| Rarity Tier | Drop Rate | 1 in X Cases |
|---|---|---|
| Mil-Spec (Blue) | 79.92% | 1 in 1.25 |
| Restricted (Purple) | 15.98% | 1 in 6.26 |
| Classified (Pink) | 3.20% | 1 in 31.25 |
| Covert (Red) | 0.64% | 1 in 156 |
| Rare Special Items (Gold) | 0.26% | 1 in 385 |
StatTrak variants have a 10% chance of being applied to any drop, meaning StatTrak knives have an effective probability of approximately 0.026% (1 in 3,846 cases). For more details on StatTrak mechanics, see our StatTrak Complete Guide.
Interpreting Your Results
P(X = k) - Exact Probability
This is the probability of getting exactly k successes—no more, no less. For rare events like knife drops, this number is typically very small even when k = 1, because there are so many other possible outcomes (0 knives, 2 knives, etc.).
P(X ≤ k) - Cumulative Probability
This represents the probability of getting k or fewer successes. It's useful for answering questions like "What's the chance I get at most 1 knife in 100 cases?" This cumulative function is particularly important for understanding dry streak scenarios.
P(X ≥ k) - At Least Probability
The complement of P(X ≤ k-1), this tells you the probability of getting k or more successes. Use this to answer questions like "What are my chances of getting at least 2 knives in 500 cases?"
Expected Value and Standard Deviation
The expected value (μ = n × p) tells you the average number of successes you'd expect over many repetitions. The standard deviation (σ = √(n × p × (1-p))) measures how spread out results typically are around that average. Research from Khan Academy's statistics curriculum explains how these values help predict outcome ranges.
Related Tools
Combine this calculator with our other probability tools for comprehensive case opening analysis:
- Streak Calculator - Calculate dry streak and success streak probabilities
- Case Odds Calculator - General odds calculations for all rarity tiers
- Expected Items Calculator - Predict item breakdown across all rarities
- Case ROI Calculator - Calculate expected value and return on investment
- Monte Carlo Simulator - Run thousands of simulations to visualize outcomes
- Case Odds Explained - Comprehensive guide to CS2 probability mechanics
Frequently Asked Questions
What's the difference between this and the Streak Calculator?
The Streak Calculator focuses on consecutive outcomes (dry streaks, success streaks), while the Binomial Calculator computes exact probabilities for getting exactly k successes in n trials regardless of order. Use the Streak Calculator for "no drops in a row" questions; use this for "exactly X drops total" questions.
Why is the "exactly 1 knife" probability so low even when expected?
Even when the expected value is around 1, the probability is spread across many outcomes (0, 1, 2, 3+ knives). For 385 cases (expected 1 knife), P(X=1) is about 37%. The remaining 63% is distributed among 0 knives (~37%), 2 knives (~18%), and higher. This is normal for low-probability events.
Can I use custom probabilities?
Yes! Select "Custom Probability" from the dropdown to enter any percentage. This is useful for analyzing StatTrak-specific drops, combined probabilities, or hypothetical scenarios not covered by standard rarity tiers.
How accurate are these calculations?
The calculator uses mathematically precise binomial probability formulas. For very large n and small p, we use logarithmic calculations to maintain accuracy. The results match what you'd get from any statistical software like R, Python's SciPy, or Excel's BINOM.DIST function.
Why does the distribution chart show limited bars?
For rare events, most probability mass is concentrated near 0. The chart displays the most relevant outcomes where probability is non-negligible. For knife drops across 100 cases, outcomes above 3-4 are essentially impossible and would clutter the visualization.
What if I want to know probability of getting AT LEAST one knife?
Use k=1 and look at the "P(X ≥ k) At Least" result. Alternatively, P(at least 1) = 1 - P(exactly 0). Set k=0 and subtract the exact probability from 100%. This is also covered by our Streak Calculator.
Last updated: January 2026