Firestone: Online Idle RPG – How to Calculate the Probability that the Game is Wrong

How to Calculate

There is a tool from mathematical statistics called the chi-squared test (see Wiki).

What you do is compare your observed statistics with the assumed probability distribution from the game and calculate the probability that they match.

Example: Assume the game tells you that an event occurs with 5% probability. However, after 100 observations the event didn’t occur a single time. What is the probability for that?

We have two categories in the chi-squared test:

  • Category 1: The event occurs. The null hypothesis says this should happen 5 times out of 100.
  • Category 2: The event doesn’t occur. The null hypothesis says this should happen 95 times out of 100.

The chi-squared value is calculated as: (#ocurrences – #expected)^2 / #expected summed over all categories. In our example:

chi-squared = (0 - 5)^2 / 5 + (100 - 95)^2 / 95 = 25/5 + 25/95 = 5.26

Now how probable is this? You look up the probability in the table of p-values for the chi-squared distribution (see Wiki). In our case we have 1 degree of freedom, so we look it up in the first row of that table. A chi-squared value of 5.26 lies between 3.84 and 6.63, so the probability of that happening is somewhere between 1% and 5%.

Volodymyr Azimoff
About Volodymyr Azimoff 944 Articles
I turned my love for games from a hobby into a job back in 2005, since then working on various gaming / entertainment websites. But in 2016 I finally created my first website about video games – Gameplay Tips. And exactly 4 years later, Game Cheat Codes was created – my second website dedicated to legal game cheats. My experience with games started back in 1994 with the Metal Mutant game on ZX Spectrum computer. And since then, I’ve been playing on anything from consoles, to mobile devices.

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