User blog:Banarama/How Many Builds are in Diep.io?

One of the core features of Diep.io is the ability to customize individual aspects of each tank, beyond the premade classes. One can upgrade health and body damage to ram enemy players, or bullet damage and reload to become a hurricane of death. However, just how many different builds are there? It's a difficult question to answer, with seemingly endless configurations of 33 points into 8 different stats. However, there is one method to calculate it formulaically through mathematics. In this blog post, I'll explain this method in detail, and why it works.

There isn't an easy way to simulate the ways to pick stats with typical grade-level math — after all, there are not only dozens of points to arrange, but every stat has a maximum number of points so not every basic configuration is possible. However, through the use of a technique called generating functions, one can represent the possibilities elegantly through polynomials. Here's how they work:

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