# Introduction

## Combinatorics

Combinatorics is an area of mathematics that deals with counting, probability, logic, etc. and relates very heavily to computer science. In particular, this article will show you how to use combinatorics to accurately predict possible winnings from the freebitcoin faucet. And you can even apply this knowledge to other areas you find useful.

## An Example

Imagine, in basketball, you are a 50% free throw shooter, and you want to know your odds of making at least one basket from taking two shots at the hoop. You may be tempted to say that your odds of making at least one shot are 100%. But logically, we know if something has 50/50 odds of occurring, it isn’t guaranteed to happen once every two tries. Knowing this, how can we get an accurate estimate of our odds? One really simple way to work through this problem is to draw a picture:

This shows, that in fact, the odds of making *at least one* shot are 75%.

## How to Generalize

So what is a general solution to this problem? Our formula is as shown below:

Your odds of failure on many attempts is equal to your odds of failure on one attempt to the power of your number of attempts. Therefore, your likely-hood of at least one success is one minus that number. You can also make a quick estimation if you know your odds of success to be, say 1/S:

This information can be used to calculate your odds of winning higher jackpots on the freeroll for freebitco.in as well as your chances of winning a place in the lottery. It is easy to use these formulas because the exact odds are given to you directly on the website.

## Lottery Take Away

One way I have used this is in deciding how I should play the lottery on freebitco.in. I could go with one of two strategies:

- Spend earned coins every week and get many small chances of success
- Save coins every week for a long time and get one chance of higher success

So after doing the calculations with an example, what comes out to be the better option? You can see here what would happen if you can collect enough coins per week to be equivalent to a 1% chance of winning:

So there you have it! You can move these numbers around to suit your earnings, but no matter what you choose to do, you will be able to predict your earnings accurately.

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