Buying VIP chests one at a time is more economical than 50?

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1 
TLDR: Buying 50 VIPs at a time results in 5722 gems
spent on pulling a new Mythic, not 4500 gems.
This means buying 1 VIP at a time which
costs 5000 gems per Mythic is far better!

We know that Mythics drop every 100 VIP chests on average.
And we know that 100 VIP = 4500 gems and crafting a Mythic is 8333 gems (daily 50 gem offer).
What is more economical? Of course VIP keys! you will tell me.
Not so fast.

Taking a closer look we learn that chances of pulling a Myth with 100 VIP are not 100%, no. It’s actually 63.4%. You may wonder how is that possible. Does it mean that if I open 100 x 100 VIPs, I will get only 63 Myths, not 100?

The thing is that when opening 100 VIPs, you still have a chance to pull more than one Myth, namely 18% to pull 2 and 6% to pull 3, and so on. So in the long run you will get 100 Myths per 100 x 100 VIPs.

36.6% to miss a Myth with 100 VIPs is sort of “punishment”, “backlash” for those moments of glory when you pull 2+ of them. It has nothing to do with devs, it’s just how math works.

Ok, that sounds fine you may say. But think about it. You spend 4500 gems when Mythic A comes out. Nothing. Spend another 4500 on Myth B. Same. Myth C. Same. And then you finally pull 4 copies of Undine.

Are you fine with that? Do you need 4 copies of him? Probably not. You just spent 18000 gems to get 1 unique Myth. This is waaay worse than crafting.

Now tell me, what’s more economical, VIPs or daily 50 gems? With what we just observed the answer is not so clear. Beware, strong math incoming, skip it if you want to.

We open 50 VIPs at once. This corresponds to:

Myths pulled k =1 k = 2 k = 3 k = 4 k = 5
50 VIPs 30.3% 7.6% 1.3% 0.16% 0.016%

What does it mean? It means that

  • 60.5% to pull nothing;
  • in 30.3% cases you will pull 1 copy every 50 VIPs;
  • in 7.6% cases you will pull 2 copies every 50 VIPs;
  • in 1.3% cases you will pull 3 copies every 50 VIPs;
  • in 0.16% cases you will pull 4 copies every 50 VIPs;
  • in 0.016% cases you will pull 5 copies every 50 VIPs;

Let’s spend 10’000 x 50 VIPs (during exclusive periods). We will pull:

  • 3031 unique myths;
  • 757 unique myths;
  • 126 unique myths;
  • 16 unique myths;
  • 2 unique myths;

3932 myths total for 10’000 x 2250 gems = 22’500’000 gems.

5722 gems per a Myth. Not bad.
Still better than crafting.

Now let’s pull 10 VIPs at once.

Myths pulled k =1 k = 2 k = 3 k = 4 k = 5
10 VIPs 9.0% 0.45% 0.015% 0.0004% 0.000008%

Again:

  • 904.0230 unique myths;
  • 45.1559 unique myths;
  • 1.5037 unique myths;
  • 0.0375 unique myths;
  • 0.0008 unique myths;

950.7209 myths total for 10’000 x 475 gems = 4’750’000 gems.

4996 gems per a Myth. Wow.

When opening 1 VIP at once it’s obviously 5000 gems per a Myth.

To sum it up:
VIP chests are still the best tool
for pulling Mythics.

1 VIP at a time is way superior than
50 VIP and even 10 VIP. Firstly,
you can pull a Myth in, say, 7 tries
and stop, saving 43*50 gems for the
next one.

Secondly, 50 VIPs will require you to
spend 5722 gems on each new Mythic,
whereas with 1 VIP it will be 5000.

However, this only applies to Mythics
which you dont want extra copies of,
dupes of Myths like Champion of Anu
are actually favorable. Use 50 VIPs
instead.
Outside of exclusive periods 50 VIPs
are preferable, too.
11 Likes
2

This is pretty good information for when I get VIP keys in like 4 months.

1 Like
3

I didn’t spend them all on Undine. Those are atemporal events.

Can you really add probabilities like that? And why not take into account the Sunday diamond pack? Waiting on the math mages to take a look at this post, but…

4

It’s actually 5722 gems, not 6510. Spotted a mistake in the post.

In that particular case player spent 18’000 gems over 4 months, and it so happened that he pulled 4 Undines. This means he spent 18’000 gems to get 1 unique Myth.

Sunday diamond packs are out of question. It’s a must buy. Daily packs, however, are different. You need 166.66 of them to gather 4000 diamonds. 166.66 x 50 = 8333 gems.

5

I do think the math here is really fiddly and you have to consider what constraints you’re putting on the situation to know what is and isn’t “worth it”.

First, “most efficient” is always a weird thing with these pools. There are a lot of ways to look at it.

Let’s say there’s two mythics in the pool, and you want one specific one. On top of the “chance to pull a mythic” percentage, there’s only a 50% chance you’ll get the one you want. You spend 45 keys and get the one you didn’t want. Do you keep going, or do you wait?

Well, imagine a Mythic Friday comes and a new mythic arrives. Now you have the same chance to get “a mythic”, but only a 33% chance of getting the specific one you want. Your odds went down, just from waiting!

But: it’s also possible that third new mythic is ALSO one you want. Now you want 2 of the 3 mythics in the pool. Suddenly, the odds of getting “a” mythic you want are 66% instead of 33%, and that’s better than the original 50%!

So pretty much any time you get a new mythic, the “worth” of future keys goes down because the number of “mythics you want” has gone down. When new mythics are introduced, your probabilities may go up or down, depending on if you want the newest mythic.

Also, when you spend keys in bulk there’s always “waste”. Let’s say I want exactly 2 mythics. If I buy keys 1 at a time, I’m going to stop exactly when I get the 2nd mythic. If I spend 50 keys at a time, the odds are very high I’ll spend at least 10 more keys by the time I’m done because I can only “stop” at multiples of 50.

So if we factor in that every mythic we get changes the value of the keys, and we decide that “a new, specific mythic” is the only desirable outcome from keys, I think it’s intuitive without much probability study that spending 1 key at a time spends the fewest keys and lets you make the “best” decisions about whether to keep spending.

And since all of this is based on probability, we’re never going to get “the best” deal anyway.

6

Please note that my post only applies to exclusive periods, when there is only 1 mythic in the pool. 50 keys offer you discount: 45 for a VIP key. However, when you spend keys in bulk you’re always risking to overkill it, pulling 2+ Myths at once.

So what’s the balance, pull 50 keys 45 gems each OR take a risk at pulling it with one single key, possibly saving 2000+ gems? My post mathematically proves that taking risk is ALWAYS better than chasing 50 - 45 = 5 gems discount.

EDIT: During exclusive periods, of course.

1 Like
7

Ah, OK! I didn’t understand that constraint. In that case yes, I agree, but I might argue the gem cost of overshooting is worth overcoming the tedium of opening that many single-shot keys :wink:

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@netwizard nice post, here you go.

TL;DR Version of opening VIP Chests

ALWAYS Open 50.
Unless both are true: Its an Excusive week AND the Mythic is garbage, then open 1.

1 Like
9

In the post 3.3 Patch world, with tasks being nerfed, bounties, raids, invasions introduced… Gems are very scarce. Look at my stash, image

Well, I definitely don’t mind

Cause it’s just 1-2 taps for me :wink:

10

Even if the Mythic is NOT garbage, I will probably want to have 1 copy of him. 2 copies of Infernus? 1 is enough for me. 50 VIPs at once will often overkill it, and I will waste 1000-2000 gems on a useless extra copy of it.

I could’ve spent 1-15 keys, pull a Myth, and save a bunch of gems.
EDIT: Thx for the advice though. Appreciate it.

11

Hmmm interesting viewpoint. But if I can borrow your words:

In the long run of opening those same chests 1 at a time you will still get 100 Mythics but at a larger cost of gems. So from that viewpoint 50 at a time is better, it all depends on how you choose to look at it.

Also, I would never open 100 get nothing then stop. I’ll always spend another 50 till I got it.

Don’t forget, it’s not just Mythics in VIP chests. Buying 50 at a time still gets you all the other stuff at a discounted price.

12

Let’s spend 10’000 x 50 VIPs. We will pull:

  • nothing in 6050 tries;
  • 1 Myth in 3031 tries;
  • 2 Myths in 757 tries;
  • 3 Myths in 126 tries;
  • 4 Myths in 16 tries;
  • 5 Myths in 2 tries;
3031 + 757*2 + 126*3 + 16*4 + 2*5
= 4997 Myths (3 myths missing because we cut off 6+ cases).

See? We pulled 5000 copies total with 5’000 x 100 VIPs.
But we only have

3031 + 757 + 126 + 16 + 2 = 3932 unique copies!

1068 of them were completely useless for us, because we didn’t need an extra copy.

13

Come on man, the vast vast majority of us will never open more than 100 x 50 chests in our gow lifetime. Meaning almost always 1 copy, perhaps once a year 2 copies. Never have I got 3, 4 or 5. Your math is correct but just doesn’t relate to real life experience. 99% of us will never see 3 or more. You can’t set spending habits assuming you will.

2 Likes
14

Well, here’s what you CAN do.

These numbers use ridiculous amounts of chest openings to show us what the average expectation may be. If we assume there’s not a lot of variance, it’s right to assume you’ll see numbers near this model for your much smaller chest openings.

This won’t be completely right. Someone out there is going to see 10 mythics from a 50-key pull. Someone else is going to open 100 x 50 and never see a mythic. Sometimes Lady Luck isn’t much of a lady at all.

But you can’t be blamed for rolling with the average as your guideline.

15

That’s totally true. But the smaller your sample size gets the less you should rely on averages and the more should rely on what’s more likely.

Here’s another interesting point. Buying 50 at a time gives a 10% discount so every 11th opening is “free”. I think this more than makes up for the occasional double pull. Ironically 1:11 is about how often you get a double pull lol. So I’m getting my double pulls for free anyway. All depends on how you want to look at it.

3 Likes
16

Thanks for the INFO! I’m going to continue to open 50 at a time to save time which is more important especially in this game. You can do what you want.

1 Like
17

I for one appreciate this post. It took some math and time to write out the experience he’s had with VIP chests. Everybody can do what they want, but there is nothing wrong with the OP. It is great information.

2 Likes
18

Ok, let’s do some math for smaller samples.
You pull 50 VIPs at once, and I will pull 1 at a time. Deal?
Let’s see who saves more.

My price is 50 gems a key, yours is 45. On my first pull, I have 1% chance to save 2200 gems. And I pay 5 more gems to have this chance.
1% chance to save 2200 gems.
99% risk to lose 5 gems.

I saved

2200*0.01 - 5*0.99 = 17.05 gems

On my second pull:
1% chance to save 2150 gems.
99% risk to lose 5 gems.

I saved

2150*0.01 - 5*0.99 = 16.55 gems

On the contrary, with my 40th pull:
1% chance to save 2250 - 40*50 = 250 gems.
99% risk to lose 5 gems.
I lost

250*0.01 - 5*0.99 = -2.45 gems

Do you see the pattern?

№ 1 2 … 40 … 50
Gems saved 17.05 16.55 … -2.45 … -7.45

Total savings = 240 gems

19

It takes 5-10 minutes to open 50 chests one by one.
And you will save 5722-5000 = 722 gems by doing so.
I doubt you can farm 722 gems in 10 minutes.

2 Likes
20

I’ll be interested to see how long it takes to farm 722 gems.

Not including key openings, events, raids, guild tasks, maps etc.

I’m thinking it’s a loooooooong time.

2 Likes