I like to do 50 at a time.
Thatâs what she said! Sorry, I just had toâŚ
I didnt read all of your answer tbh. So if player A gets the desired outcome having opened his limited number of keys but B spends significantly more keys to get the desired outcome then thats down to the luck of the draw. Of course there are numerous possible outcomes as to success based on RNG (or lack of). Having a sackful of keys i agree gives you more bites at the cherry but does not necessarily provide the desired outcome. Only an infinite number of keys can give what you describe as the âexpected outcomeâ. Anyway this is getting way off topic so I have no more to say on the matter. I have kind of agreed with you other than the terminology used in quotes above.
I still donât fully understand what youâre trying to say.
For example, I have a few D20 die in my hand, and I want to row each dice only once. If I want to get a single 20 value result, how many die do I have to roll?
According to you, itâs impossible, as I canât own infinity die? 
You have 1/20 chance to get it on the first dice. Then 1/20 on the 2nd. And so on. Chances youâre getting no D20 become less with more dices, yet the chance to see 20 is still the same. Your current result (chain of results) is what you measure with percentage. Regardless how many heads you had, even if you had 50, 500, infinity heads in a row, the next flip still has 50% chance for heads or tails.
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âAs many as it takes.â
20d20 has a ~62% chance of seeing at least one die roll a 20. Otherwise, every roll must necessarily be 19 or less which is a (19/20) ^ 20 = ~1/e (about 38%) probability.
Incorrectly phrased, and THIS is the problem we have with your arguments: your reasoning is correct but your conclusions are poorly written (even to the point of misleading). Consider how the statement reads if we invert the claim:
âCan notâ, as in âhas no capability ofâ or âis NOT possibleâ. You see the problem now, right?
Any finite number of keys âcanâ i.e. âhas a possibility ofâ producing a desired outcome, though any specific batch âmayâ or âmay notâ actually do so, depending on the size of the batch, and it is obviously incorrect to claim that any specific batch âwillâ or âwill notâ produce a desired outcome (at least well outside its calculated rate of probability and statistically expected outcome).
This is why precision wording matters.
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Too bad schools no longer require everyone to take a logic class.
I glad no one give me an exact number, because thatâs not possible and not how statistics work. 
I was kinda disappointed no one say âYou canât compare dice to RNG, itâs not a same thing!â, because it actually is. RNG is referred to random number generator program, while dice is a physical number generator.
I bring up dice because talking statistic can be so abstract, so real life situation is easier to be visualize.
And as from answers above, we can all agree on that the more die you roll, the more likely one of them will land on 20 face result.
And that can be apply to Gems Of Warâs keys opening too, thatâs why a lot of players want to be in guild that finish a few Legendary Tasks every week, so they can have more keys, thus more resources and more attempt they can try to get the troops they want. So grinding for more keys is not a useless waste of time.
And to the main question, as a lot of people answer already, chance are the same, what youâre trying to optimize is resource management, and if itâs worth the time.
Back to the dice example again, If I have 1,000 dice in a box, how many should I bring out and roll to get 20 face result?
Doing one at the time will be slow and might make your hand tired (like opening Gold Keys. 
), but on average, you will row less die, and wonât make a huge mess that you have to clean up later, because you didnât roll more die than you absolutely need. (More keys saved)
Doing 50, or 200 at the time, result will be the same, but they will be a lot of die laying around, and more mess to clean up (troops to disenchant), but you save time, at a cost of mass rolling. (More keys might be spend than necessary)
So itâs up to each person preference, I guess, and depending on how many keys do you have, and can you afford to spend more to save time.
Personally, I have too many keys, so I always spend maximum amount of keys possible on monthly Mythic chase. Event keys though, itâs limited and hard to farm, but I still spend 200 at the time to chase new Legendary. Because I find 50 at time annoying, and I might rage spending more than 200 if I didnât get in the first few batches of 50, so I rather spend 200 once and be done for a week, as it rarely fail.
Beside, I donât care how many copies I will get, just one is fine, as I will use Minor Ascension on it anyway, and there is no rush to get 4 copy of every Mythic, base or not, as I will get there eventually when I chase monthly new Mythic anyway.
The other physical analogue is a deck of cards - with the important caveat that drawing cards from a deck (without replacement) DOES bias the next draw and eventually yields all possible outcomes, so the âgamblerâs fallacyâ isnât necessarily a fallacy (e.g. Blackjack card counting).
And technically, many programmatic RNGs essentially have a fixed sequence of outputs ⌠which just so happens to be millions of entries before it repeats (and for practical purposes is reduced to such a smaller range that youâre never looking at the raw output anyway).
(Heck, when learning BASIC one of the things I remember growing a little annoyed with was my inability to reliably seed its RNG function, e.g. have separate RNGs running in isolation from one another.)
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no. the context of my terminology relates to another forum post using the phrase âexpected outcomeâ. RNG does not have an expected outcome unless historical correction is employed. Here it is not. Statistical process control is my bread and butter so saying i dont understand logic (not you but someone else) is not going to cut it here. SPC is a far more data representative tool than a handful of players with no life trying to guide us on drop rates etc. Thats why you are continuing the discussion while i make a living. Enough. Schoolâs out. I graduated and some of you failed. Thats why you grind and i donât.
I am not trying to win anything. I play my way and others play theirs. Why the witch hunt?
Then what good are the posted drop rates if not to map the RNGâs raw output to some specific outcome, thus a player can âexpectâ that when aggregated across multiple draws, approximately some % should be a particular outcome?
Every time, your explanation is fine but the conclusion feels like "every analysis you made is wrong because RNG will not be analyzed" and I hope Iâm just reading the tone wrong.
Also, I donât âgrindâ. Iâm content to mostly just play daily/weekly events, cool down with a few runs of Treasure Hunt, then spend all the keys at once and see if I can make some upgrades. (I donât even have free scouting.)
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So, should you open 50, Or 200, At a time?
Ultimately it doesnât really matter. If youâre going to spend 200 keys regardless, the only difference between doing it as a batch of 200 vs. four batches of 50 is the time required to click the corresponding buttons on the UI.
If you are looking for a specific drop (e.g. newly released Mythic) batches of 200 will give you overall better probability per batch, while batches of 50 might save you a few keys if you actually get that drop early; but this doesnât say anything about the next time.
Personally I would have loved being able to snag Flame of Anu, Pan, or Ishtara when they released, but no, I donât have the resources for that sort of grind.
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Well, then thanks for taking a break of making a living and wasting your precious time on âdiscussingâ with us inferiors, Your Grace 
Joking aside, you have a quite rude way of communicating, that makes a conversation rather uncomfortable. The quoted passage is not the first example, you also told me, that RNG is âbeyond my comprehensionâ. You have no idea of the educational background of other participants in this thread. Just because you are using this ominous statistics tool doesn´t mean, that all the others are uneducated and are just talking nonsense.
To be honest, I had this impression on most of your replies to my posts. Why read all of it, after all, you are a SPC user, so why think about other arguments and maybe understand them, right? Time to end the discussion here. I don´t want to waste time trying to explain rather basic math to someone, who then refuses to read my whole argument, just picks out the points he likes and then proceeds to say âbut I know so much better than all of youâ.
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Same. Helvellyn, it is not difficult to state applicable experiential background without also insulting other users in the process. This discussion is about the underlying math, not âSPC master race vs. console peasantsâ.
Then I apologise for how I have phrased my contributions and any insult or condescendence that may have been caused. That was not my intention and thats why I withdrew from the discussion. I will try to be more diplomatic henceforth.
Iâll open 50 chests at a time during the fist week of a mythicâs release forevermore⌠I somehow pulled FOUR of The Gemini at once when using 200 keys.
(link is timestamped)
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Genki going for 4 of every mythic 
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Gem keys? Still, DANG.
Let's see if I got this math right...
So thatâs 0.1% ^ 4 (aka. 1/10^16) for the four Mythic dropsâŚ
multiplied by 099.9% ^ 996 for the other chestsâŚ
multiplied by C(200,4) because the Mythic drops could have occurred at any 4 points during 200 chestsâŚ
âŚ
~5.87 ^ 10^-5 or (1 / ~17,000) probability!