Raffle drawer

This is a script that draws raffle winners with modified probabilities, depending on the number of tickets that a user purchaed.

Description

In the "uniform case", where all tickets are equivalent, the standard deviation around the expected number of tickets $x$, is approximately $\sqrt{x}$.

This script introduces a mapping ($x' = A * x^{B}$), which allows one to modifiy the standard deviation for a given expected number of tickets by perform the drawing of winners in surrogate $x'$ space. To adjust the standard deviation you need to modify constants $A$ and $B$. The effect of constant $A$ is straight forward:

$\sigma(x | A,B=1) \approx \sqrt{x/A}$

The effect of $B$ is somewhat more intricate, but the following guidlines can be used:

$\sigma(x | A, B=2) \approx 0.5$

$\sigma(x | A, B=3) \approx 1 / \sqrt{A * x}$

For simulating the general $\sigma(x| A, B)$ check the Jupyter notebook stdev.ipynb.

Usage

The script will read the data provided in data.csv (you will have to keep the structure of data as in the provided example). The ouput of the script will be an array of objects with the following structure:

{
    wallet: string      // Wallet address of the user
    tickets: number     // Number of tickets purchased
    rewards: number     // Number of winning tickets
    delta: number       // The difference between actual winning tickets and the expected number
}

A sensible choice for mapping parameters is $A \sim 5$ and $1 \lesssim B \lesssim 1.5$.