User blog:Guy Bukzi Montag/Drop Rates Explained: 5th Anniversary (I)


 * DISCLAIMER: The information in this post is based on the assumption that all items without special percentages assigned in the box info have the same chance to appear when a box is opened. I cannot and will not take responsibility for any decision you make because of this post. The values have been calculated with software written on my own, so there is neither a guarantee that the code is error-free nor that there are no typos in the post.

In my previous post I explained why the percentages shown for boxes (when you tap on the icon) don't always represent the real drop rates.

As the 5th Anniversary event slowly comes to an end now, this post tries to provide some help by showing
 * how you can deduct probabilities (drop rates) from given percentages in many cases and
 * how to calculate the probability of getting desired items from a certain amount of boxes.

Overview
If you're not interested in the explanations, here's the overview of all items with their real probability (drop rate) in the "P" columns. Please note that the probabilities of all items counting as "Pro Kit Boxes" are assumed as equal.

How many coins can I earn?

 * Quests: There are 30 quests with three levels rewarding, and . If you accomplish all quests you get a bonus reward of , so the total number of coins you can get from quests is.
 * Ads: Watching ads for 10 days (3 ads per day, average of per ad) grants additional.
 * On track: As some quests require a huge amount of finished races, it is also possible to collect about per day automatically on tracks when playing races, which would result in.

We'll take this total of as a base for further calculations.

Can I build an Audi R8 e-tron SE with those coins?
No.


 * First: The car needs 150 blueprints to be assembled. For you can buy 13 Expert Bundles with each box granting 1 to 7 blueprints. Even if you get 7 blueprints from every single box, you'll need 22 instead of 13 boxes which cost.
 * Second: The chance of getting 7 blueprints from an Expert Bundle is $$\tfrac{1}{7}$$ = 14.29 %. However, the chance of getting 7 blueprints 22 times in a row is $$\tfrac{1}{7^{22}} = \tfrac{1}{3,909,821,048,582,988,049}$$. This is 1 out of 3.9 quintillions.

If you think of buying coins for real money: Don't. The expected (average) number of blueprints in an Expert Bundle is
 * $$1 \cdot \tfrac{1}{7} + 2 \cdot \tfrac{1}{7} + 3 \cdot \tfrac{1}{7} + 4 \cdot \tfrac{1}{7} + 5 \cdot \tfrac{1}{7} + 6 \cdot \tfrac{1}{7} + 7 \cdot \tfrac{1}{7} = 4.$$

So you'd need 38 boxes which cost —and you can't be sure that this is enough because you can still get less than 4 blueprints per box.

Can I build a Mercedes-Benz SLK 55 AMG SE with those coins?
No.

The car needs 18 blueprints to be assembled. For you can buy 32 Specialist Bundles with each box having a 10 % chance to contain 1 blueprint.

Your chance of getting at least 18 blueprints from 32 boxes is


 * $$1.17\times10^{-8}$$ or $$0.0000000117 %$$.

Here are some other probabilities for your information:

Can I build a BMW M2 SE with those coins?
Yes.

The car needs 70 blueprints to be assembled. For you can buy 64 Novice Bundles that already contain 64 guaranteed blueprints for the car.

As the chance to get a second blueprint from a Novice Bundle is 75 %, it is almost certain that you get more than enough blueprints to assemble the car.

The table shows your chances of getting 6 additional blueprints from various amounts of boxes:

Other probabilities
Each box is calculated with the above-mentioned.

Expert Bundle
What you can expect from 13 boxes:

Specialist Bundle
What you can expect from 32 boxes:

Novice Bundle
As calculating with 64 boxes generates extremely large numbers that cause an overflow in my computer, here's what you can expect from 32 boxes instead:

How can I calculate this myself?
The math behind this is quite complex and has to handle large numbers, so I wrote a few functions that do the work for me. I'll explain the mathematical background in my nex post and share the code with you.

It would have taken too much time to write all this down, and as the 5th Anniversary event ends soon I wanted to share the results first.