I’m one of the unlucky players who already crafted 15 eggs and still needs a single dragon.
My collection: 4x Amethialas, 2x Garnetaerlin, 2x Rubirath, 5x Sapphirax and x2 Topasarth.
You may are in the same postion and ask yourself: How BAD is my luck to not pull the last missing dragon, even with the initial 1/6 chance? This list shows you how likely it is to not pull your last needed dragon. As you can see with my last crafting attempt (number 15) the chance was 6,49% to still miss out this card. Unlucky, but unfortunately in a realistic room. I just wish they would filter out dragons after 4 copys, but anyway: How many eggs you had to open for a full set or how many do you opened at the moment without having a full set? Comment below!
If you had already used 14 eggs and pulled 5 different dragons, then the chance of a 15th egg not pulling the missing dragon is 83.33%.
If after your 14 eggs you had another 15 eggs to open, then your chance of missing with all 15 would be 6.49%.
It does not matter how many eggs have already been opened. If you still have one dragon to get, the chance of missing it with the next egg is 83.33%, missing it with the next two eggs is 69.44%, etc.
In my scenario i gave all dragons a number from 1 to 6, so it’s like throwing a dice and not hitting number 6 (the specific number doesn’t matter, it’s just the number/dragon that never ended as a result) - but to keep it simple: the odds for not hitting a 6 with 6 throws are 33,49% as example and i see no problem to replace the dice scenario with dragons?
Just going to note that the probabilities you stated are the CUMULATIVE values for the stated outcome – not the probability for that attempt individually (which is always X / 6, X being the number of unowned dragons)
I’ve plotted this data myself previously, here is your probability of owning X dragons after N eggs, charted in various ways:
Stacked plot (all outcomes sum to 100%):
Non-stacked plot (easier to compare each outcome):
Y-logarithmic plot (each outcome trends towards an exponential decay of *(X/6):
Sure, after pulling other dragons over and over i care more how likely this outcome is. I know in the end it’s still the same 1/6 chance for the last dragon every time, but i need something that gives me (false) hope in such frustrating times.
Thank you very much for sharing your nice graphis. I have to admit it gives your a even better idea/look at things. Fingers crossed egg number 16 - 20 gives me more luck.
The odds for not hitting a 6 with 6 throws are 33.49%, but only if you have not rolled the dice yet. If you have rolled some of the dice already and not got a 6, then the chance of still not having a 6 after the 6th throw is increased. You should ignore the previous rolls and use the table above with the number of remaining rolls. So if you are doing 6 rolls, and have not got 6 with the first 4 rolls, you have two rolls remaining and the chance of not hitting a 6 is now 69.44%.
If you look at Stratelier’s second graph (above), you’ll see it’s about a one-third chance to have five dragons after 15 eggs, about two-thirds to have all six, and a small chance to have four or fewer.
I like JamesDurning’s approach here. His post includes precise probabilities, and a description of how the numbers are derived. That gives the probability of exactly 5 distinct dragons after 15 eggs as 32.27% and having all 6 as 64.42%.
More than 3% of players still have only four of the dragons after 15 eggs. You have not been lucky, but your luck is not extreme.
Random dragons from eggs is unfun and unfair. I agree that the system needs some reworking (capping at 4 copies, or an ability to craft specific dragons for a larger amount of dragonite).
There’s a well-known phenomenon where an expected value of 100% (aka. N independent rolls of a 1/N probability) actually converges to a roughly 1/e chance (~37%) of a complete losing streak across all attempts.
If you have 4 dragons: in the next 7 eggs you have about a 50/50 chance of having all 6.
There’s still a >1% chance that it’ll take you more than 29 eggs to get the last 2. Pray to RNGesus!
Update 9/14/23: Another egg, another Garnetaerlin. Very good system. Very cool.
Update 10/1/23: Sapphirax #7, do I win a prize when I have a full useless set of four?
Update 11/1/23: Rubirath #2
Update 12/30/23: It took nearly 18 months and 14 eggs, but we finally have 5 of the 6 dragons. Never forget the devs’ unbelievably moronic comment from their announcement video for the new cosmic eggs, that they are totally delusional and think people actually enjoyed these first ones.
Update 1/14/23: Another Topasarth. Just got my first two weeks ago after 14 eggs, and now they’re taunting me with a dupe instead of the last one!
