How does the new CS2 Tradeup Algorithm work?

In Valve’s recent update on the 23rd of october for Counter-strike 2, they quietly changed the Trade Up formula regarding the odds and float calculation of the output skins. This update didn’t just change to math: it destroyed the usefullness of filler skins and fundamentally changed the way how output floats are calculated.

The Changes To The Float Calculation Algorithm

The Old CS2 Trade Up Algorithm:

before the patch, the float of you output skin was calculated as a simple weighted average of the input floats:

\[
\text{Average Input Float} = \frac{\sum_{i=1}^{n} F_i}{n}
\]
Now you can input this into the following formula:
\[
\text{Output Float} = (\text{max. Float}_o – \text{min. Float}_o) \times \text{Average Input Float} + \text{min. Float}_o
\]

\[F_i = \text{float value of input skin } i\]

\[n = \text{total number of input skins}\]

The max. FLoat and min. Float reffer to the float range of the output skin so that can be 0 to 1.00 or for example 0 to 0.80. also known as “the float cap”.

Example (Old Algorithm)

10x input skins with a float of 0.30 –> Average float = (10x 0.30) / 10 = 0.30
Output skin float = 0.30 (And then you would adjust for the Float cap like shown in the formula above).
This shows that input float caps don’t have a impact on the float for the output skins.

This meant that if you use a filler skin like for example the populair filler skin: P2000 Amber Fade with a narrow float cap of (0.00 to 0.40) it wouldnt hurt the final average float.

The New CS2 Trade Up Algorithm

The new Trade up Algorothm that Valve introduced is far more compex. It now accounts for the float cap of the input skins aswell when calculating the average input float of the tradeup.

Each input float is first noramalized according to its float cap before averaging the floats like before the update so the new formula is:

\[
\text{Adjusted Float}_i = \frac{F_i – F_{\text{min},i}}{F_{\text{max},i} – F_{\text{min},i}}
\]

Then, Valve calculates the average of all the adjusted floats and uses the output float range like before.

\[
\text{Output Float} = F_{\text{min,out}} +
\left(
\frac{1}{n}
\sum_{i=1}^{n}
\text{Adjusted Float}_i
\right)
\times
\left(
F_{\text{max,out}} – F_{\text{min,out}}
\right)
\]

That results in the complete formula for the new algorithm:

\[
f_{\text{out}} = F_{\text{min,out}} +
\left(
\frac{1}{n}
\sum_{i=1}^{n}
\frac{F_i – F_{\text{min},i}}{F_{\text{max},i} – F_{\text{min},i}}
\right)
\times
\left(
F_{\text{max,out}} – F_{\text{min,out}}
\right)
\]

Where:

This new formula makes it so that inputskins with a restricted float like (0-0.5) are weighted differently than skins with a full float range (0-1). This makes it so that a lot of the tradeups that previously used floats caps in their advantage now are not profitbale anymore because of the adjusted input float.
Because most tradeups will have a higher average adjusted input float than before.

Example (New Algorithm)

First Normalize the float:

This shows that input float caps don’t have a impact on the float for the output skins.

\[
\text{Adjusted Float}_i = \frac{F_i – F_{\text{min},i}}{F_{\text{max},i} – F_{\text{min},i}} = \frac{0.30 – 0}{0.40 – 0} = 0.75
\]

Now we can calculate the new adjusted average float like (0.75*10)/10 = 0.75 average input float
This shows that the input skin floatcap now has a big effect on the float used in the tradeup calulation.
In this example the normal average float was 0.30 and the new adjusted average float = 0.75 that is a 2.5 times increase!#

This means that if we get an output skin with a float cap from 0 to 1 we will get a skin with a float of 0.75 compared to the 0.30 from before the update.

Probability Changes

before the update the probability for each output was based on how many outputs existed in each collection and how many skins you used from a collection.
Now, the chance for each outcome is determined solely by the number of inputs from a collection. Before, people used fillerskins in their tradeup. This where skins with as little outputs as possible to limit the chance of getting that collection. Now, this doesnt matter anymore beacuse its solely based on the number of input skins in the contract.

The new formula

\[
P(\text{output from collection } X) = \frac{\text{number of skins from a collection}}{\text{number of inputs}}
\]

So now you can just use the cheapest input skins from for example the Restricted rarity without having to worry about effecting the odds. This is disadvantageous for trade up contracts because now you cant manipulate the chances of getting a collection you want by using the correct filler skins.

FAQ

Conclusion

Valve’s recent update has fundamentally changed the way of calculating Trade Up outputs in CS2. The new float formula usese input float caps and this makes making low-float outcomes rarer and eliminates the need for tradeup fillers because of the way how the probability of getting a skin is calculated. Finding new profitable tradeups will take some time but I will make sure the upload the updated versions as fast as possible.