## Table of contents

# Introduction

Wordle, as you know, is the new Internet rage. It is a simple word puzzle game, where you have to guess a 5 letter word in 6 tries

## What I wanted to do

I wanted to do something with the stats of the game, particularly the Guess Distribution. I wanted to build a tool which calculates some properties of this distribution.

This was something I enjoyed building. It's Fun!

## How the code works

The number of guesses can be between 1 and 6 (both inclusive), so we use an array to store the frequencies of those guess numbers corresponding to the actual guess number. For example, f[1] = number of 1 guess wins, f[2] = number of 2 guess wins, and so on.

The formula for calculating mean:

where f is the frequency and x is the number of guesses

We use this bit of code to compute it

```
for(int i = 1; i <= 6; i++)
{
printf("How many %d guess wins?\n", i);
scanf("%d", &f[i]);
s1 += i*f[i];
n += f[i];
}
float m1 = s1/n;
```

We also calculate the second, third and fourth order central moments like this

```
// calculate 2nd, 3rd and 4th order central moments
for(int j = 1; j <= 6; j++)
{
s2 += pow((j - m1), 2)*f[j];
s3 += pow((j - m1), 3)*f[j];
s4 += pow((j - m1), 4)*f[j];
}
float m2 = s2/n;
float m3 = s3/n;
float m4 = s4/n;
```

Variance is the second order central moment, we use the third and fourth order central moments to calculate skewness and kurtosis

```
float g1 = m3/pow(m2, 1.5); // skewness
float g2 = m4/pow(m2, 2) - 3; // kurtosis
```

Finally we check the nature of the data from the skewness and kurtosis values

# Conclusion

I went with the arithmetic mean, variance, skewness and kurtosis, but it is definitely possible to include many more parameters here.

You can find the full code here

Thank you