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Fun math around Myth drop rates

According to taransworld.com/chest the chances of pulling Mythic and Legendary troops are:

This means that you get 1 Mythic every 1 / 0.00096 = 1041 Gem Keys (on average)

Chances of not pulling a Mythic with a Gem Key are
1 - 0.00096 = 0.99904

Chances of not pulling a Mythic (k=0) with 1000 Gem Keys are
0.99904 ^ 1000 = 0.382716

This means that chances of pulling at least 1 Mythic (k>=1) are
1 - 0.382716 = 0.617284

Chances of pulling exactly 1 Mythic (k=1) are

where np = 1000 * 0.00096 = 0.96

P (k=1) = 0.96 * e ^ ( - 0.96) = 0.3675
P (k=2) = 0.96 * 0.96 * e ^ ( - 0.96) / 2! = 0.1764
P (k=2) = 0.96 * 0.96 * 0.96 * e ^ ( - 0.96) / 3! = 0.0565


P.S. Math rules.


Math might rule… but those %’ chances suck lol

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You’ve now doomed us to a thread where someone buys 2042 gem keys, gets no mythic, and argues the RNG is broken.


Maths makes my head hurt. And I’m drunk. Ill make a seriousness comment later lol

As said on the other topic, average is nice but ask too much data. So yeah after some/a lot of trials (with one trial equal on succesful drop of one Mythic), you will be on the average, but it doesn’t help to know how much we need to be almost sure to obtain one Mythic.

So in resume, to have a 95% chance to drop one Mythic when he’s the only in the drop pool, it’s more or less x3 what you said:

And the real problem is the reduction on gems, gems keys and event keys.


I think what most people want to know is the average chance. 1:100 for VIP chests 1:1000 for gem chests and 1:10,000 for glory etc. The # of chests needed to be 95% certain of a pull is not really what we want to know imo. How many for 99%? How many for 100%?

That one is easy. Look at the name of the developer. You’ll need two fewer keys to guarantee a 100% chance that you get a Mythic. (Probability is a cold mistress.)


With 4800 gem keys chances to pull at least 1 Mythic (k>=1) are:

Yes, you need that many gem keys to be almost guaranteed to pull at least 1 Mythic. BUT.
You will be very unlucky if you pull only 1 Mythic with it. It’s only 4.5% chance. You will most likely pull 4 Mythics (18,7%).
Most surprisingly, the chances to pull either 1 or 8 Mythics are almost equal (4.5 and 5%).

With 4800 gem keys you have:
4.5% chance to pull 1 Mythic OR
10.5% chance to pull 2 Mythics OR
16.2% chance to pull 3 Mythics OR
18.7% chance to pull 4 Mythics OR
17.2% chance to pull 5 Mythics OR
13.2% chance to pull 6 Mythics OR
8.7% chance to pull 7 Mythics OR
5% chance to pull 8 Mythics OR
2.5% chance to pull 9 Mythics

EDIT: 7200 gem keys give you 99.901% at least 1 Mythic drop rate
And you will most likely pull 7 Mythics.

What players want to know is how much keys they need to be sure to drop a Mythic. 100 VIP keys is only 63% of drop chance so yeah you were right for 63% of the playerbase but what about the 37% remaining players? “We give you the average so in 5 years (60 trials) if you look at your stats in average you used 100 VIP keys” seems not that much useful…

95% seems a reasonable balance (there will be still 5% who will not get their Mythic).


If the intention is for people to buy Gems, lower the prices to something that resembles a “microtransaction”. $40 for a 50-pack of Gem chests with drop rates that abysmal is such a massive ripoff I don’t know what someone was smoking when that was considered a “good deal”.

I get it - businesses need to make money. I will happily break my now 6-month streak of not buying anything once guild task/LT rewards are re-adjusted for the artificial gameplay slowdowns that have been implemented (after nerfing the rewards in the first place on the basis of “faster gameplay”). Happy players = open wallets. In the meantime I am happily spending my entertainment dollars elsewhere.

Disclaimer - the above statements are NOT directed at the devs, as they are not responsible for the player-hostile business decisions that caused me to stop spending in the first place. They’re just doing their jobs.


Don’t get me wrong I love me some stats, the more the better. But as for what players want to know the most I think it’s the average. Let me give you an example: When playing poker people want to know the odds of getting an ace (or whatever card they’re chasing), not the odds of how many cards they’d need to have a 95% chance of getting one.

If I know the odds of VIP chests is 1:100 then when trying for a mythic and get one in 50 I know I’ve been lucky. If it takes me 100 I know that’s about average and if it takes me 150 or more then I know I’ve been unlucky this time.

When the devs are forced to show the odds for the China release I’m sure it won’t be how many chests required to 100% get one, it’ll be simply the odds of pulling one from 1 chest.

People tend to think "ok, so it’s 1 Mythic per 100 chests, why it’s 63% then, not 100% ? "
Well, that’s how math works. You get a chance to pull 2 and more Mythics with 100 chests, you know? This 37% reduction is what you “sacrifice” for these chances. You open 100 chests now and you get no Mythics. You open another 100 and you get 2. If there was some kind of algorithm that spreads Mythics evenly across all chests, then you could get 100% guaranteed Mythic from 100 chests, but at the cost of never pulling more than one.


The no math explanation: There’s always a chance to get nothing no matter how many keys you spend. :wink:

Math always wins. Luck is temporary.

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In that case math cost a lot of money if you want a complete collection.

If random requests are resolved on the server, these calculations are not really applicable to anything. Apparently, server continuously resolves multiple request using the same pRNG seed with unknown reset conditions. So, there is no cumulative chance of pulling anything, not really. So, the equation used to estimate Pn(k) cannot be used strictly. However, it might give a rough estimate just because the numbers are quite large. The trials are neither random nor independent and the equation is derived for random and independent more or less continuous sequences.

Unfortunately, since the drop rate of mythic cards is very low, getting to large numbers is essentially impossible. Well, one can say that if you buy a lot of chests, like thousands and thousands, you might eventually get something mythical out of them. :rofl:

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