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Statistical model for 5 star latest legendary draws without customer service switch.

whitecat31whitecat31 Posts: 523 Critical Contributor
edited June 20 in Theories and Statistics

Hello all, 

Originally, I had done some statistically testing with latest legendary draws in order to determine how many pulls are needed to get the three 5 star characters fully covered so they could be champed.  

Based on the 1:7 odds of pulling a 5 star I came to the conclusion that 273 pulls should generate on average 39 five star covers.

The 39 five star covers was important because you only needed 13 covers, no matter the color, to create a five star champion, with the customer service swap. So I had a 99+% chance of a single 5 star character being covered, about a 80% chance of getting two 5 star characters being covered and a below 30% chance of getting all three covered. Basically, once thirteen numbers were counted in one set you had a 5 star character that you could champ, with the 'good customer service' model.

With the removal of the customer service switch, which I call the 'good customer service model', I have found the odds have drastically dropped.    I have three sets of numbers.  Each set has a population of 3, and it is roughly a 11.11% chance to populate any of the numbers.   There is a 33.33% chance that one of the sets will have a number within them populated and that is all we can guarantee.

With the new system, we can call this the 'bad customer service model', once I have any of the individual numbers go past a 5 count, it's value toward champing a character now drops to 1/3rd of it's value.  So in theory there is over a 50% chance that I could pull 14 covers of a character and still not have that character champed. 5 +(1/3rd) + 2 +5 (1/3rd).  

To get that guarantee of a 99+% chance for a single 5 star character being covered, I have to toss in the new 1 for 3 exchange system. This means basically 9 more draws per character to make that guarantee. Or basically 63 more pulls per characters, because guess what people, 5/0/5 models happen.  Oh and that 63 has to be multiplied by 3 (63 x3 = 189).  

So I am looking at telling people to horde 189 + 273 for a total of 462 for basically that 99+% chance to get a single 5 star character fully covered from the latest legendary.

So in a 5/2/5 model you will want 15 covers to champ that character.  Multiply 15 x3 and you get 45 total covers desired.  Although, I would like to say  45 five star pulls with a hoard size of  (45 x 7 = 315)  should get a 99+% chance for a single five star character to be champed in this scenario, I can not make that guarantee.  Because I kept getting 5/0/5 and 5/1/5 scenarios in modeling. By the way 5/0/5 and 5/1/5 cover spread models gave a horrifying performance statistically in the bootstrap models.

Let's say you have the 5/1/5 model.  You have a 33 percent chance to get the middle number. (If that character was chosen another which is another 33% chance). True odds are 11.11%.    Once you get up to 3 covers, you can't save any more, you have to use or lose. This is literally a loss of 2 post champion levels.

So at best I can say there is a 95% chance with the 315 horde pull with the 'bad customer service model' versus the 273 horde pull and the 99+% given with the 'good customer service model'.

So can anybody help me figure out the true difference between the 'good customer service model' versus 'the bad customer service model'?

Statistical update overview changed after they went from 5 to 1  to a 3 to 1 exchange model.

Comments

  • whitecat31whitecat31 Posts: 523 Critical Contributor
    edited June 20
    Of note. For a theoretical 100% chance base on the 1:7 odds, you have to work off a 5/0/0 model.  You start with 5 covers, and then you need 8 more.  Assuming all your cover colors are all the same color you would need 24 more covers. So 29 covers per character. 29 x 3 = 87.  87 x 7  = 609 pulls.  Statistical update overview changed after they went from 5 to 1  to a 3 to 1 exchange model.
  • whitecat31whitecat31 Posts: 523 Critical Contributor
    Thanks to Hadronic's tool.   Without using bonus heroes or exchanges and with no starting covers, you need 387 pulls +/- 87 pulls.  To complete all three characters.

    If you use Bonus heroes and exchanges it is 333 pulls +/- 61       
    442 pulls needed for a 95% chance. 


  • bbiglerbbigler Posts: 1,100 Chairperson of the Boards
    Why wait for a 95% chance?  You could try it with a 85% or even 65% chance, I would.  Plus, even if you don't fully cover them in 1 shot, you can continue to pull tokens until they leave Latest.  The hoard is a good jump start, but it shouldn't be a constant thing.  I'm planning to start with a hoard of 200 pulls, THEN continue to pull Latest going forward.  I may or may not fully cover the oldest 5* in the lot before they leave the pool, but the next 2 I will.  Then with a couple 5* champs, I can get better rewards along with a 4* champ farm to increase my LL pull rate and never hoard again.  Many people have done this and it works.
  • HadronicHadronic Posts: 337 Mover and Shaker
    bbigler said:
    Why wait for a 95% chance?  You could try it with a 85% or even 65% chance, I would.  Plus, even if you don't fully cover them in 1 shot, you can continue to pull tokens until they leave Latest.  The hoard is a good jump start, but it shouldn't be a constant thing.  I'm planning to start with a hoard of 200 pulls, THEN continue to pull Latest going forward.  I may or may not fully cover the oldest 5* in the lot before they leave the pool, but the next 2 I will.  Then with a couple 5* champs, I can get better rewards along with a 4* champ farm to increase my LL pull rate and never hoard again.  Many people have done this and it works.
    95% confidence interval is a common thing in statistics. No one is implying that you have to wait for that amount of tokens before pulling.
  • YepyepYepyep Posts: 395 Mover and Shaker
    This is super cool to read. I’m fully capable of consuming and appreciating it (with the explanations) but don’t have the education to do it myself. Thank goodness for specialization lol. 

    So — thank you very much!
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