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