Does 50 each time or 200 each time have higher chances of getting more mythics im the end? Say we start with 1000 keys, it will be 20 draws for 50 each and 5 draws for 200 each. Which way would be better in the end?
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Technically neither, because thatâs just not how RNG works. However, calculating a cumulative probability across a specified number of ârollsâ is pretty straightforward math so letâs tackle it:
- If the probability of acquiring a Mythic from one Gem Chest is 0.1% (âPâ), then the probability of the chest NOT containing a Mythic is 99.9% (â1-Pâ).
- The probability of opening 50 (âNâ) chests without a single Mythic is (1-P) ^ N
- Thus, the probability of obtaining at least one Mythic in 50 Gem Chests is 1 - (99.9%^50), or about 4.8%.
As for 200 Gem Chests? Same formula, different inputs, 1 - (99.9%^200) = about 18%.
And since you have 1,000 keys? â oh wait, this is actually an easy one because every expected value of 100%, i.e. âNâ rolls of a â1/Nâ probability (in this case 1000 x 0.1%) always trends towards a â1/eâ cumulative probability (about 38%) of no successful outcomes (details), aka. about a 63% chance of getting at least 1 Mythic from 1000 keys.
If you want to get a little more advanced, you can also calculate the expected # of chests to achieve any given % of acquiring (at least) one Mythic. Just rearrange the formula a bit and you get:
N = log(1 - C) / log(1 - P)
where âCâ is your desired certainty (cumulative probability) and âPâ is the actual drop rate per chest. e.g. if you want an overall 50% chance of getting (at least) one Mythic then you will need to open âonlyâ 693 Gem Chests to do so! (And you have 1,000)
Isnât math fun?
Oh, wait, the question was about whether to spend your keys in what increments specifically, right? Well ⌠technically it doesnât matter (see top of post) but if you DO get a Mythic from Gem Chests then you will likely save the other keys for later, right? Obviously this wonât happen often, but in the event it does, the smaller the increment you use, the more keys you might have left, at the cost of taking that much longer to open the chests. (E.g. say that the RNG gods smile and chest #149 will contain a Mythic â you will either have 850 or 800 keys remaining after that drop.)
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Thanks for the detailed response. But we donât really know how RNG is implemented in game. From my past experience that opening 200 at a time gave me better chances of getting a mythic but then again sample size is too small.
Youâre calculating probability of a case when to expect a mythic card. Opening either 1, either 1001 chests does not change the 0.1% chance of Rolling a mythic. The only difference is your click count.
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Its better 50 at the time, so you donât waste keys. Like it could give you the legendary or mythic you want with the first 50, second 50 or the third 50. And yes you save 50 keya.
You cannot predict chest outcome probability with RNG in this form. And yet people continue to collate data, throw a bit of maths into the mix and come up with values that are practically meaningless and which conjure expectations from players who also dont understand RNG. Threads are riddled with disappointed players who feel that âxâ attempts merits favourable RNG and the desired outcome. Gems RNG does not self correct by recording player specific historic data. Its like trying to give infinity a value; it doesnt work.
That depends on what you are trying to get.
If you are opening gem chests just to get whatever random mythics then 200 at a time will be fine.
Suppose you are opening gem chests during the mythic week, trying to get specific mythic then 50 at a time is the best like what Crow says.
As for event keys (it is used to target the specific mythics), 50 at the time is the best method because you dont want to waste event keys after you get the mythic you want. Suppose you would have get the mythic at 49th chest then you wasted only one if you open 50 at the time but you would have wasted 151 chests if you open 200 chests at once.
Not specifically, of course.
But there is no âgamblerâs fallacyâ in pure math.
Like I mentioned above, even if you spend 1,000 Gem Keys the math predicts a noticeable probability (almost 2-in-5) that none of those chests will drop a single Mythic.
But the more attempts you make, the more opportunities you have for a desired outcome occurring somewhere in those attempts, by definition â thus the desired outcome is in fact âmore likelyâ.
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The desired outcome likelihood is the same on your 1st fight as your 1000th fight. Frequency of attempts does not increase the odds because there is no historical correction. Its purely down to luck and thats why data collation is misleading and irrelevant. Yes i suppose more attempts mean you may get lucky eventually but there are no guarantees and no statistics that can in any way indicate when that stroke of luck will happen. You can of course attempt to grind the favourable outcome but in reality nothing changes probability wise.
Just open your keys. Cross your fingers, close your eyes. Boom! Either try again or 
party time. The more keys you have, the more chances of getting the mythic. I normally think of how can I get more keys than how to open it.
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Of course your understanding of probability is entirely correct.
But statistical analysis and data correlation is far from irrelevant. It is used extensively to evaluate risk.
Thanks to the anecdotal and actual data gathered by players it allows us to make relatively informed decisions on how we play and the goals we set.
I for one will always respect those who gather and correlate data for the benefit of (some) others.
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I completely agree that statistical analysis is a valuable tool in the right environment and when applied correctly. I use it myself extensively in industry (SPC, lean engineering etc). But this requires constant process monitoring and data sampling. I understand that players collect data to estimate drop rates etc but the results often lead other players to âexpectâ outcomes that are in fact unrealistic. SPC will amongst other things factor in wear and tear, mean time before failure and other accumulated system factors. These are historic, gems is not historic. I think the main issue is not the fact that ppl are collecting data to try to help; it is that many many players dont quite grasp RNG conceptually as it is implemented in this game.
@Helvellyn Sorry, but I don´t understand, what you are trying to say⌠You âsuppose more attempts mean you may get lucky eventuallyâŚâ? I don´t suppose, I expect exactly that. Of course, you can never tell, when the desired event will happen, but if the chances for success are constant with every try, of course the chances to have at least one success will increase with every repetition you will do.
Given the example of a myhtic drop: Rolling for the monthly mythic is significantly different, if you are in a guild, that will give you only 100 gem keys per month or in a guild, that accumulates 10000 gem keys per month. In the first case, you will need to get lucky to get a monthly mythic, in the second case, you can almost guarantee, that you will get at least one copy. Of course, there is always the (very small) chance for this one veeery long streak of bad luck and you will burn 10000 gem keys and still don´t have a mythic drop. But if the stated drop rate of 0.1% is correct, this should not happen on a regular basis and if it does, either the drop rate is simply wrong or the RNG isn´t really giving random numbers, but is biased (due to programming issues).
You also say that âmany many players dont quite grasp RNG conceptually as it is implemented in this gameâ. This makes me want to know, what you think, how RNG is implemented in this game? I would expect, that for every roll of a key, the drop rate is unchanged and every key has the same chance to give a mythic. And if I understood you correct, then this is also what you would expect. But then I don´t understand your conclusions⌠If this is true, I can for sure expect to get one mythic for every 1000 gem keys - on average. And for sure, on average is the important thing here. I can´t open 1000 gem chests and scream âFRAUD!!!â, if I don´t see a mythic drop. Sometimes it takes more than the 1000 keys, and yes, sometimes significantly more than 1000 keys. But I will also not scream âFRAUD!!!â, if the drop happens already on the first 50 keys I spend - and this also happens 
So, as a summary: If I had the chance to open 1 billion gem keys right now, I would expect the absolute number of mythic drops somewhere around 1 million and the relative frequency more or less exactly at 0.1%. Small (really small) deviations are of course ok, but if there is a significant deviation from the expected value after such a huge number of tries, then the RNG isn´t working correctly. Period.
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Short version, your chances donât change if you open 200 chests one by one or in bulk. The only difference is that if you really open one by one you can stop right when youâve found what you were looking for.
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When you use the term "expectâ in relation to RNG of this nature you immediately illustrate that RNG is beyond your comprehension. Perhaps infinity would be something you would have more chance to understand. Way too many ppl think that if they do more grind then your chance will improve. But no, the chance is always the same regardless of attempts. Ive made this point many times and yet still get this kind of response because of naivety.
Arenât those two statements a little imprecise? It feels like youâre conflating two definitions of âchanceâ with each otherâŚ
1 - âIf you grind more chests then your chance will improveâ is TRUE in the context of at least one desired outcome after N repeated attempts. This is mathematically and statistically provable (and you know it is), e.g. if I open 200 Gold Chests I tend to get about 48-52 Traitstones because their drop rate from these chests is 25%.
2 - âThe chance is always the same regardless of attemptsâ is TRUE on a per-attempt basis. Regardless of whether I open 1 chest, 10, 50, or 200, a 1% drop rate of something means a 1% probability from each chest.
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Ok, I will keep it short hereâŚ
Example: Next week Friday we will see a new mythic. Assume we have player A, a low-level player that has just started to play the game and is in a low-level guild. And we have player B, absolute endgame player with fully maxed account in a high-end guild. Assume, player A has 50 gem keys and 500 glory keys available to gamble for the new mythic. Player B has 8000 gem keys and 20000 glory keys available to gamble for the new mythic. Are you trying to tell me, that A and B have the same chance to get the new mythic, because âthe chance is always the same regardless of attemptsâ?
If this is really your opinion, then MY comprehension of whatever is for sure not the problem here 
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On a chest by chest basis where A and B open 1 chest at a timeâŚyes.
Nice try, but that was not my question The question is, is the overall chance for finally getting the mythic the same for A and B? They can´t be compared chest by chest, when A has spent all of his 50 gem keys, B has 7950 more gem keys left to continue⌠I hope, that we can agree, that the massive number of keys for player B is a huge advantage in the hunt for at least one copy of the monthly mythic. I think, avoiding an answer to my question and retreating to the âchest by chest basisâ already shows, that you know, I am right here. This is just a perfect example, why the number of attempts DOES matter.
And I myself am proof for this example. Until September 2020, I was playing in a guild, that finished the basic guild tasks every week, not more. After that I put my game to another level and joined a guild, that does about 30-40 legendary guild tasks every week. The number of keys I have available since then just exploded. I could see the consequences immediatelly. Before September 2020 I took a close look at every mythic and decided, if I wanted to roll for it or not. If it was too bad, I just didn´t, as I didn´t want to waste keys. However, there were several mythics I would have liked, but didn´t get due to lack of keys. Amarok is an example I remember quite well. After September 2020 I never wasted a second for thinking about if I should try for a mythic or not. I got them all, some with 200 gem keys, others with 4000 gem keys, but in the end, I got them all. My key stacks always were just too big to fail.
By the way, if increasing the number of attempts on an experiment, where every result is independent from the others and the chance for success remains the same on every attempt, would NOT increase the chance of having at least one success, it would mean, that the theory of the Bernoulli chain is wrong. That would be nothing less than a mathematical sensation, this theory exists since the 17th or 18th century. Needless to say, it has never been falsified.
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Iâve been getting this impression too (and in fact was planning to ask a similar question as this, but you beat me to it)âŚ
When a player decides to open a batch of chests (hoping for whatever desired outcome) yes any two chests in a batch have the same drop table as each other but please do NOT confuse the per-chest drop rate with the statistically expected / mathematically predicted drop rate for the batch as a whole.
Iâll concur that, technically speaking, this is the correct answer to the wrong question â but in your defense, they didnât specify just how many keys each player was actually spending to open Chests.
If I open a batch of 50 Gem Chests I donât have âaâ 0.1% chance of getting a Mythic, I have fifty 0.1% chances of getting a Mythic.
Right? Right.
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