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2019 Dhampir Crystal Question
JChanceH9
Posts: 771 ★★★
Does the 2019 crystal have a 20% drop rate or 20.88% as it was in the past? I was running the numbers, and even though the .88% seems insignificant, it is the difference between probably and probably not pulling Blade in 3 tries (50.5% vs 48.8%), which is coincidentally all I have been able to save!
I also ran the numbers for how many of each crystal you would need to spin/pop to get greater than 50% odds of pulling your desired champ, and hopefully you can see that in the picture I’ve attempted to post.
Edit: I also hope this helps those on the fence about whether they want to go for Blade, the featured 5* crystal, or the basic. The main thing is realizing that 3 shots with a 20% chance does not equal a 60% chance of pulling Blade, just as 5 shots does not guarantee you will 100% pull him.
I also ran the numbers for how many of each crystal you would need to spin/pop to get greater than 50% odds of pulling your desired champ, and hopefully you can see that in the picture I’ve attempted to post.
Edit: I also hope this helps those on the fence about whether they want to go for Blade, the featured 5* crystal, or the basic. The main thing is realizing that 3 shots with a 20% chance does not equal a 60% chance of pulling Blade, just as 5 shots does not guarantee you will 100% pull him.
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I know, and I’m hoping that can change since it has not yet been released.
What makes you think it was 20.88% in the past?
Also, I think you're a little hung up on unnoticeable differences between slightly higher and slightly lower than 50/50 odds. The reason why the odds of getting Blade aren't 60% when you pull three times is because there is a small chance of pulling more than one Blade. When you pull three crystals there are four possibilities: you pull zero, you pull exactly one, you pull exactly two, and you pull exactly three.
The odds of pulling zero are 51.2%. The odds of pulling exactly one are 38.4%. The odds of pulling two are 9.6%. And the odds of pulling three are 0.8%. If you actually sum up the average amount of Blades you'd expect to pull, it actually comes out to exactly 0.6 - the percentage chance of pulling one times the number of crystals.
This is important to remember: the value proposition of the crystals is linear if you value every single Blade pull identically. In other words, if pulling two is twice as good as pulling one. The crystals only have diminishing returns if you value any number greater than one as having the same value as pulling one: in other words, if your only goal is to avoid missing him entirely.
The value proposition of a crystal with 20% drop odds and one with 20.88% drop odds is only 4%. You are not going to notice a one percent higher drop odds in three crystals.
https://us.v-cdn.net/6029252/uploads/editor/g0/2w9ps4uhhv4g.jpeg
The equation is -x/100=(.80^n)-1 with x being the actual percent chance and n being the number of tries. Been a while since I’ve been in high school to write that out, but I think that’s it. I stand by my original numbers unless you can show and explain the math you’re using.
Not sure what the context of that pic is, but my recollection is that the drop odds feature in the game came out after the Blade rerun. I guess someone saved the original crystal and waited until the feature showed up, but I never saw that.
The probability of a set of independent events occurring is the product of their odds. The odds of getting Blade are complicated to calculate directly, but the indirect calculation which calculates the odds of not getting Blade are more straight forward because there is only one sequence of events for which that happens: the sequence where every single pull is not Blade. The odds of not getting Blade are 80% or 0.8. Therefore the odds of not getting Blade in all three pulls is 0.8 * 0.8 * 0.8 = 0.512 or 51.2%. Therefore, the odds of getting Blade at least once is 48.8% which is 100% - 51.2% (because the odds of getting Blade plus the odds of not getting Blade must add up to 100%, because that represents all possibilities). That's more or less the formula you remember.
But the odds of getting Blade at least once includes the odds of getting Blade once, plus the odds of getting Blade twice, plus the odds of getting Blade three times (since those are the only three possibilities for getting Blade at least once). The odds of getting Blade exactly once are essentially the odds of getting Blade in the first crystal and not in the second, plus the odds of getting Blade in the second but not in the other two, plus the odds of getting Blade in the third crystal but not the first two. Alternatively, the more direct statistical formula, if the odds of getting Blade are b and the odds of not getting Blade are (1-b), is [ b * (1-b)^2] * 3!/2! ; the odds of the three individual events occurring multiplied by the number of possible distinct combinations/sequences of those events. That's 0.2 * 0.8 * 0.8 * 3 = 38.4% Repeat for the other two.
Also, the odds of getting Blade at least once should be the sum of the odds of getting him once plus twice plus three times. And you get 38.4% + 9.6% + 0.8% = 48.8%, which agrees with the calculation that directly calculates the odds of not getting Blade and assuming the odds of getting Blade are 100% minus that.
The text states that starting on Feb 22nd the crystal is avail, but in the summary it says to open them starting Feb. 28th? So which is it?