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## Comments

2,642Chairperson of the Boards941Critical ContributorThank you! I've been telling everyone for years that the RNG is fishy.

1,668Thanks so much!!!

7,757Site Admin395Mover and Shaker150Tile TopplerYup I'm sitting at 60/300, end of 2017 I'll finally be able to jump into 5* land

941Critical Contributor771Critical ContributorHow does that change the estimates?

Operating under the assumption that customer service will help with duplicates it doesn't seem like the number would be that much higher.

I tend to assume I have worse than average luck so I know when this says 230 for one then the answer for me personally becomes 275-300 in order to play it safe.

338Mover and Shakerlook at the plots in the OP. the third one is most obvious.

In every one the fitted gaussian underpredicts the data below the mean and over predcts the data above the mean. This is because a gaussian distribution ranges from negative infinity to positive infinity and is symmetric. Basically saying that there is a non zero probability that you could cover max a 5* opening some negative number of tokens. Which isnt possible.

The very nature of this test is not symmetric. it is impossible to open 1 token and have a max 5* starting from nothing, on the contrary it is very possible that you need to open 2000 covers even though the mean is only 230ish.

the data only has a tail above the mean. the data is zero for all negative values, the poisson preserves these features.

the gaussian is a decent approximation to a poisson distribution if the mean is large, but the closer the mean is to zero the worse the approximation gets.

math is kinda my thing.

474Mover and ShakerMy 20LT and 450cp stockpiled, only got me 1 and 1

other that that, 3 3 2 2

the rest is only garbage ( 3 2 and other irrilevants covers)

I don't know if I should feel lucky or disappointed

762Critical ContributorI calc. ~95% confidence around 300 LLT, good luck. To max all 3 from nothing

@10% I'd feel sightly disappointed. It's a pretty small sample, but that's what the rate use to be.

762Critical ContributorI'm so happy to learn new things, here is a Poisson Distribution

Given we've met the 3 criteria

- The interval of the observation is fixed
- The rate of the event is constant
- Occurrences are independent

I've add a shaded (x-Value) Probability of >230 pulls97Match MakerLong story short (9 months long, that's how long it took me to save up enough CP), I had saved 5577 CP (and a few tokens) when Dr. Strange was added to the Latest Legendary token. Add in champion rewards (CP, Tokens) I got from the 4*s I pulled with my hoard, and I ended up with exactly 250 pulls. Yay for round numbers!

The end result: 11 Black Bolts, 21 (!) Black Widows, and 10 Dr. Stranges. Fortunately, I already had 2 Black Bolts, so he ended up at a perfectly championable 553. My Widow pulls were 2 Purple, 9 Red, 10 Black. Fortunately CS was accommodating to my request to flip one of the duplicates to the needed 3rd purple and I didn't need to sell the extra 10 covers I couldn't use (I already had 1 cover on Widow from a previous Red Room token.) I was a tad disappointed that I

onlypulled 10 Dr. Strange covers, but he'll be in the latest for a while longer, so I'm confident I can scrounge up the 3 more I need before he leaves.Overall, 42 of my 250 pulls were , so 16.8%. Better then expected, but not earth-shatterly so.

So consider this a testimonial. This method worked for me. Past performance isn't indicative of future results and all that, and of course this "evidence" is anecdotal, but whatever,

I'mhappy, right?**a quick aside, I hoarded CP, but opened Latest Legendary tokens as I got them. This allowed me to cover 4* characters, and I always had something to work on while I was hoarding. I currently have 29 championed 4*s, since they were my focus for a long time. This worked out really well for me because nearly 2/3rds of the 4* covers I pulled when cashing in my huge CP stash went right into champion levels.

995Critical ContributorUnfortunately I only saved for 2 months, have 150 pulls, and a mere 9.9% draw rate. The difference is staggering. "luckily" my pulls were skewed toward strange and at 390 he is actually usable in PvE for me so it's not a total waste, but the difference between being 5% low vs. 5% high on your pull rate is well within the realm of possibility and makes for a HUGE difference in progression based solely on RNG.

I encourage others wanting to whale latest characters to very strongly look at the confidence bands for getting what you want, because while 250 pulls gives you close to even odds to get what you want, you could also end up with 3 unusable 5*s that quickly vanish into the diluted classic pool destined never to be finished.....

4,731Chairperson of the BoardsI wish I had taken stats at all. I'm pretty good at math, but never taken a statistics class ever I always have some trouble understanding the finer points.

258Mover and Shaker338Mover and Shakeryes, typically whenever you are counting occurences within a set interval the probability distribution function (PDF) will be poisson shaped. great job on your analysis.

338Mover and Shakerwell if he had always opened the same number of tokens, say 500, and asked how many 5s i get, that would lead to a binomial distribution. Since its impossible to get less than zero or greater than 500. Given that we know the odds are 15% that distribution would be centered on 75.

90Match Maker762Critical ContributorI've shaded the left tail with 150 tokens with 99% confidence you'll finish that single featured character at 10% rate.