## FANDOM

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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.

As the 5th Anniversary event slowly comes to an end now, this post tries to provide some help by showing the probability of getting desired items from a certain amount of boxes. It is part I of a series on the maths behind drop rates.

## Update: Hidden rules

After opening 20 Expert Bundles in a row, I can say that there are definitely additional rules not mentionend in the box descriptions and infos. I didn't ever have one single box without either credits (18) or tokens (2). This changes the probability of "currency" to 100 % and makes it impossible to get 3 engines from one box. I have adapted the following table accordingly. The tokens/credits ratio given in the box info (2.5 % / 22.5 % of 4 items) is consistent with the real ratio of 2/18 in my boxes (10 % / 90 % of 2 items).

When I bought a Specialist Bundle, however, I had neither credits nor tokens in it, so the hidden rule only applies to Expert Bundles.

## 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.

Box Price Percentages Items
guaranteed
P Items
random
P

Expert Bundle
4 items:
2 guaranteed
2 random
350 25 % Blueprint Boxes
2.5 % Tokens
22.5 % Credits
50 % Pro Kit Boxes
1-7 BPs Audi R8 e-tron SE 100 % 1 Forced-Induction V8 Engine 7.69 %
1 Token pack ( 50)
or
10 %

1 Custom Racing Engine 7.69 %
1 Credit pack ( 6,000) 90 % 1 Legendary Electric Engine 7.69 %
1 Special Offer – i6 Engine Box 7.69 %
2 Class A Part 7.69 %
1 Rotary Engine 7.69 %
1 F6 Engine 7.69 %
1 V16 Engine 7.69 %
1 F12 Engine 7.69 %
1 V10 Engine 7.69 %
1 V12 Engine 7.69 %
1 W16 Engine 7.69 %

Specialist Bundle
3 items:
3 random
150 10 % Blueprint Boxes
3.33 % Tokens
23.33 % Credits
63.33 % Pro Kit Boxes
1 BP Merc.-B. SLK 55 AMG SE 10 %
1 Token pack ( 20) 3.33 %
1 Credit pack ( 2,500) 23.33 %
1 Forced Four-Stroke Engine 7.04 %
1 V-Twin Engine 7.04 %
1 Four-Stroke Engine 7.04 %
1 Serial Racing Engine 7.04 %
1 Mid-Tech 7.04 %
1 Hybrid Engine 7.04 %
1 Electric Engine 7.04 %
1 Class A Part 7.04 %

Novice Bundle
2 items:
1 guaranteed
1 random
75 87.5 % Blueprint Boxes
12.5 % Pro Kit Boxes
1 BP BMW M2 SE 100 % 1 BP BMW M2 SE 75 %
1 i5 Engine 3.57 %
1 i4 Engine 3.57 %
1 V6 Engine 3.57 %
1 Class B Part 3.57 %
2 Early Tech 3.57 %
2 Initial Tech 3.57 %
1 V8 Engine 3.57 %

## How many coins can I earn?

• Quests: There are 30 quests with three levels rewarding  15,  25 and  35. If you accomplish all quests you get a bonus reward of  750, so the total number of coins you can get from quests is  3,000.
• On track: As some quests require a huge amount of finished races, it is also possible to collect about  100 per day automatically on tracks when playing races, which would result in  1,000.

We'll take this total of  4,825 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  4,825 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  7,700.
• 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  13,300—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  4,825 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:

Blueprints P
1 96.57 %
2 84.36 %
3 63.33 %
4 39.97 %
5 21.15 %
Blueprints P
6 9.44 %
8 1.17 %
10 0.08 %
12 0.0033 %
15 0.000011 %

## Can I build a BMW M2 SE with those coins?

Yes.

The car needs 70 blueprints to be assembled. For  4,825 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:

Boxes P
8 67.85 %
9 83.43 %
10 92.19 %
12 98.57 %
15 99.92 %

## Other probabilities

Each box is calculated with the above-mentioned  4,825.

### Expert Bundle

What you can expect from 13 boxes:

Item Amount P Amount P Amount P
Special Offer – i6 Engine Box 1 64.66 % 2 26.39 % 3 7.26 %
Legendary Engine, Advanced Tech 1 64.66 % 2 26.39 % 3 7.26 %
Tokens  50 74.58 %  100 37.87 %  150 13.39 %
Credits  30,000 99.99 %  48,000 99.91 %  72,000 62.13 %

### Specialist Bundle

What you can expect from 32 boxes:

Item Amount P Amount P Amount P
Rare/Motorcycle Engine, Mid-Tech 1 90.33 % 2 66.89 % 3 39.38 %
Tokens  40 28.87 %  80 2.10 %  120 0.06 %
Credits  12,500 89.74 %  25,000 19.45 %  37,500 0.30 %

### Novice Bundle

What you can expect from 64 boxes:

Item Amount P Amount P Amount P
Common Engine 1 90.24 % 2 67.11 % 3 40.13 %

## How can I calculate this myself?

The maths 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 next posts 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.

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