CS:GO Skin Unboxing Probabilities

by Tom Burns

YouTuber 3kliksphilip recently posted a video titled "Case Unboxing Millionaire #2", wherein he showed a single run simulation of him 'unboxing' cases for the first-person-shooter computer game Counter Strike: Global Offensive. These cases are digital items which, when opened, unlock a decorative weapon 'skin'. These skins can be used by players in the game to show off to their friends. Such skins have developed quite a market for themselves and can be bought and sold for hundreds or even thousands of dollars through various online marketplaces.

3kliksphilip uploaded another video titled Case Unboxing Millionaire #3, where he did a simulated run of unlocking the "eSportsCase 2013" until he opened a knife. My previous analysis showed the expected value to be a loss of $5,720.96. This analysis calculates the information for the "Winter Offensive Weapon Case", as 3kliksphilip has challenged viewers to submit a guess for this case in his latest video. 

It costs $5.20 to open, and can contain skins worth between a few dollars to around $300. 3kliksphilip challenged his viewers to estimate his profit or loss from opening this case up until he unlocked a knife skin, the rarest skin to obtain. I have calculated this expected value to be a loss of $415.03.

How did I do this?

 

Method

  1. I downloaded historical price data, in the JSON format, available here. I focused on averaged Steam marketplace data from the past 90 days.
  2. I obtained information on which items were available from this case.
  3. I used publicly available information to infer or explicitly state the probabilities of skin drops and skin conditions.
  4. Using this information, I calculated the expected value of each case opening.

For a full, step-by-step walk-through of my methods, please feel welcome to inspect the code here.

 

The expected value of each case opening can be calculated by:

Calculating the average value of every item, by finding the market balue for every item-condition pair, e.g. an AWP | Redline (Field-Tested) is currently valued around $18.19 on the Steam Marketplace. Then, using the skin conditions probability distribution, calculate the average value.

Once the average value of every item is calculated, we can find the average value of any colour or rarity of item for a box by assuming all items of a given rarity level for a case are equally likely. So, we just take the average of the averages of those items.

Then, calculated the avarage value of any opening of the case is as simple as multiplying by the skin drops probability distribution.

In this case, we calculate that the average value of each opening of the "Winter Offensive Weapon Case" is $3.08. Since it costs $5.20 to open, the expected loss per opening is -$2.12. Given the probability of opening of opening a knife is ~0.25%, we can estimate that it will take ~200 case openings to open a knife (or, ~200 case opening to reach a probability of 0.5 that a knife will be opened).

Given this, we can expect an average loss of -$415.03 if we open cases until we open a knife.