# KD's Egg drop rates analysis (with tips)

## Preface

People are always coming to the forum wondering whether it's worth to spend gems on the eggs currently offered in the game. Various statistical analysis has been done on the as well as a lot of opinionated advice. This thread hopes to offer that in a digestible way, for mathematicians or not. This is all my own analysis and tips so if you get advice from others then choose to listen to whoever you like. This guide is split into 3 sections:
1. Picking which eggs to hatch (gem budgeting)
2. Analysis of the drop rates (comparing the eggs)
3. Summary of the analysis (things to learn from it)

## Picking which eggs to hatch

Itâ€™s very easy to get tempted but the various eggs, especially those releasing new monsters. Unless youâ€™re happy to start pouring money into the game then you have to be very strict with yourself.

What you HAVE to do is save up 300 gems to spend on one egg. When thereâ€™s a 1st pack guaranteed legendary then thatâ€™s a good place to dump 50 gems but otherwise the goal is 300.

What you do with the 300 is wait for a time when thereâ€™s a good combination of monsters featured, a monster youâ€™d like lots guaranteed in the 6th pack (typically the main factor) and chance for legendaries is either 1.5x or the featured ones are boosted. When you select to roll an egg you expect to spend 300 gems but if you get the monster/s you want or one of the 6th pack guaranteed monsters early then you should probably stop where you are and be happy you now have less time before youâ€™ll have 300 gems saved again.

Here are some â€śconditionsâ€ť that must be met in order for you to decide an egg is a good choice for spending 300 gems on (in my opinion):

• You really like all the monsters guaranteed in the 6th pack and have none of them.
• If the featured monsters donâ€™t have boosted chance (e.g. 3x, 6x)â€¦ there are at least 7 being featured.
• If legendaries are not 1.5x chanceâ€¦ the featured monsters are either boosted loads (e.g. 8x, 10x) so thereâ€™s a good chance to get one for fewer than 300 gems, youâ€™re willing to spend 300 gems for just a featured alone or thereâ€™s some other appealing bonus.

In general, the â€śspecial festivalsâ€ť with 1st pack guaranteed can be a great place to get lots of legendaries. However, the festivals (1.5x chance) can typically be better for getting more limited legendaries of the type you want. Special eggs appear to offer you the lowest rate on your gems but can be good for picking up particular legendaries and more frequently give you them for fewer than 300 gems.

The later sections of this guide will repeat a bit of this information, but only after proving it with some statistics. If you are not interested in the match I recommend you read the third section too (right at the end). It raises a few more points which may help in your decision making.

## Analysis of drop rates

The "1,3,6" guaranteed festivals are definitely the ones to go for to begin with, they give you the most legendaries for your gems as well as a limited monster that's brand new to the game and likely to be very strong (you can judge beforehand). However, they have no boosted chance on the featured (limited) monsters so even though you're getting more legendaries you'll be getting slightly less featured ones for your gems. This is offset slightly by them featuring lots at once, but it's still lower than some of the best other festivals. Let's call them:

A) â€śSpecial eggâ€ť = 4% chance legendary, boosted chance featured, featured in 6th pack
B) â€śLegend festivalâ€ť = 6.1% chance legendary, boosted chance featured, featured in 6th pack
C) â€śSpecial festivalâ€ť = 6.1% chance legendary, 1st & 3rd pack guaranteed, new monster in 6th pack

A - Typically special eggs have fewer featured monsters (1-3) but the highest boosted chance (6-10x). These are the cheapest way to get a specific legendary, but obviously worse in every other regard.
B - Typically legend festivals feature a medium collection (3-6) and a reasonable boosted chance (3-6x). It varies between festivals whether theyâ€™re good and if you have any of the collection it becomes far less valuable to you but some offer as high as 1/3 chance of each legendary being a featured one, so they can offer a good opportunity to grab a couple of the featured legendaries.
C - Typically special festivals feature lots of monsters (6-8). There is a similar issue to legend festivals where if you have some of the featured already (and itâ€™s more likely here due to the number) that it lowers your chances of gaining some new limited monsters. Additionally, the chance of each legendary being a featured is lower than the other eggs but you get more. If you have fewer legendaries, and none of the featured, these are usually the best.

### The number of legendaries

From 300 gems in each egg you get: Special egg = 2.3 + 1* Legend festival = 3.6 + 1* Special festival = 5.5 + 1**

In raw numbers you get double the number of legendaries in a special festival compared to a special egg and 1.4x the number you get from a legend festival. However, letâ€™s now assume the special egg and legend festival are good ones, e.g. 2 featured with 10x chance and 3 featured with 6x chance respectively. You donâ€™t get much better than that.

The normal egg pool includes 32 legendaries. Hence:
Special egg = (2* 10) / (32 + 2* 10) = 20/52 = 38.5% chance of any legendary being featured
Legend festival = (3* 6) / (32 + 3* 6) = 18/50 = 36% chance of any legendary being featured
Special festival = 8 / (32 + 8) = 8/40 = 20% chance of any legendary being featured

So multiply that by the number of legendary eggs you get from 300 gems:
Special egg = 2.3 * 0.385 + 1 = 1.89 featured legendaries
Legend festival = 3.6 * 0.36 + 1 = 2.30 featured legendaries
Special festival = 5.5 * 0.2 = 1.10 featured legendary (+1 new)

### The chance of getting the featured legendaries

[Bear in mind that each egg is different and this is comparing specific examples. Most special festivals feature 7 monsters, not 8. Also, the other two eggs I've used the best cases as examples too... most legend festivals have 3x chance of featured instead of 6x and the number featured is 3-4.]

Special eggs
These give the least, but theyâ€™re from a very small pool so you get one guaranteed and a relatively good chance at getting the other. Here are the numbers from the example egg above (2 featured, 10x chance):
Any (1+) featured in first 3 packs = 37% chance (0.37195)
A specific one of the two in first 5 packs = 32% chance (0.32032)
A specific one of the two in 6 packs = 68% chance (0.68301)
Both in first 5 packs = 9.5% chance (0.09288)
Both in 6 packs = 36% chance (0.35937)

Legend festivals
These give the most featured and are from a relatively small pool so you can expect to get the ones that are featured there but can annoyingly get the same one multiple times. Youâ€™ll get one of them guaranteed so what youâ€™re looking for specifically is if you can get two or more. Here are the numbers from the example egg above (3 featured, 6x chance):
Any (1+) featured in first 3 packs = 49% chance (0.48631)
A specific one of the three in 6 packs = 57% chance (0.56795)
Exactly two featured in 6 packs = 52% chance (0.52314)
All three featured in 6 packs = 2.4% chance (0.02355)

With 6 featured, 3x chance:
Any (1+) featured in first 3 packs = 49% chance (0.48631)
A specific one of the six in 6 packs = 33% chance (0.32880)
Exactly two featured in 6 packs = 45% chance (0.44975)
Three or more featured in 6 packs = 20.5% chance (0.20652)

The second example shows what itâ€™s like if the pool size is larger. The chance of a specific featured legendary in 6 packs drops from 57% to 33% but the chance of having 2+ featured from 6 packs increases from 55% to 65%. This second example is far rarer, legend festivals usually have smaller pools of featured monsters, but anything is possible.

Special festivals
These give the most legendaries by far but without boosted chance to the featured ones you will get them less than in legend festivals. However, you will get one of the two new monsters guaranteed in the sixth pack (or IT if there is only one). Here are the numbers from the example egg above (8 featured, 1x chance, 2 new monsters):
Any (1+) featured in first pack = 28% (0.28367)
Any (1+) featured in first 3 packs = 65% (0.65089)
A specific one of the eight in 6 packs (not new) = 13% (0.13279)
A specific one of the two new monsters in 6 packs = 57% (0.56640)
Exactly two featured in 6 packs = 27% (0.26984)
Three or more featured in 6 packs = 36% (0.35984)
Both new monsters in 6 packs = 13% (0.12760)

If you compare this example of a special festival to the examples of the others youâ€™ll see the chance of getting 2+ featured monsters is on par with the best alternative (legend festival: 6 featured and 3x chance) with the special festival being 63% and the legend festival being 65%. However, a special festival is more likely to include some legendaries you already have in the featured list as well as the ones you get being less predictable and many legend festivals will focus around a particular strategy so gaining 2-3 monsters there could help you create a strong team. To highlight the â€śless predictableâ€ť bit take a look at the â€śspecific one in 6 packsâ€ť on the legend festival examples and the special festival example. With 3 featured in the legend festival you can expect to have a specific one at 57% chance, when there are 6 featured this drops to 33% (still quite reasonable) but in the special festival it drops to 13%. You can rely on getting the new monsters because one is in the 6th pack guaranteed but itâ€™s a lottery for what other featured monsters you get. Even when there are 6 featured in a legend festival any particular one has a reasonable chance of being obtained, because theyâ€™re all possible to get in the 6th pack guaranteed. In legendary festivals where itâ€™s a particular monster in the 6th pack then the chance of getting a specific featured in 6 packs that isnâ€™t this one drops but is still significantly higher than in a special festival.

Also, itâ€™s important to note that these are simply examples Iâ€™m using and you cannot rely on the results completely. The eggs offered in-game may be quite a bit different to what Iâ€™m using as examples here. Each egg should be rated at the time based on its merits. I hope that the theory Iâ€™ve shared here creates a good basis for valuing eggs for yourself, specifically helping you see how having some of the featured already may affect whether itâ€™s worth it to you.

## The main things to take away from the analysis:

• Special festivals give you the most legendaries and one of the best opportunities at getting multiple featured legendaries for 300 gems
• Since special festivals do not have boosted chance for a featured the chance for any specific featured legendary is very small compared to the others
• The more featured legendaries in an egg, the greater chance of getting multiple featured legendaries from 300 gems (because you will get fewer duplicates)
• Legend festivals, especially ones with fewer featured monsters, offer a great chance to focus on picking up specific legendaries without compromising much on the number of featured legendaries you are getting
• Special eggs offer the cheapest way to get particular legendaries and have a reasonable chance of giving you the one you want before spending all 300 gems
• If you have some of the featured legendaries in a special festival already it does not matter too much (13% chance in 6 packs of you getting it - in my example) but in the other eggs it drastically affects the value of what you will get (33% or far more as a chance of getting it in 6 packs - in my examples).
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