So You want to Whale Latest Legendaries

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Comments

  • mpqr7mpqr7 Posts: 2,642 Chairperson of the Boards
    I'm slowly but surely gaining some of the old 5*s, so I guess I'll stick to the 20 cps for now. But eventually I'll try waiting 6+ months to get 6000 cp and hoard the LTs as well. We'll see...
  • Stax the FoyerStax the Foyer Age Unconfirmed Posts: 941 Critical Contributor
    Hadronic wrote:
    these really should be poisson distributions not gaussian.

    Thank you! I've been telling everyone for years that the RNG is fishy.
  • TLCstormzTLCstormz Age Unconfirmed Posts: 1,668
    I love this kind of data. ESPECIALLY with visual aides.

    Thanks so much!!!

    icon_e_smile.gif
  • BrigbyBrigby ADMINISTRATORS Posts: 7,757 Site Admin
    I feel like I should have paid more attention in Statistics class... icon_e_confused.gif
  • spectatorspectator Posts: 395 Mover and Shaker
    500 classic pull is now right? I take it the number goes up every two months when a 5* is moved into the pool. Any idea what the number is?
  • blargrxblargrx Posts: 150 Tile Toppler
    TxMoose wrote:
    edit: my target is 300 pulls. wondering where that falls in the curve...

    Yup I'm sitting at 60/300, end of 2017 I'll finally be able to jump into 5* land

    icon_e_sad.gif
  • Stax the FoyerStax the Foyer Age Unconfirmed Posts: 941 Critical Contributor
    Brigby wrote:
    I feel like I should have paid more attention in Statistics class... icon_e_confused.gif

    post-58615-Chevy-Chase-no-math-SNL-gif-Im-IvKX_zpshbuadxro.gif?w=280&h=210&fit=crop
  • babinrobabinro Posts: 771 Critical Contributor
    If I'm saving for 6+ months I want to get ALL 3 cover maxed.

    How 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.
  • HadronicHadronic Posts: 338 Mover and Shaker
    You left off the "why"...? I disagree. Convince me?

    look 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.
  • WEBGASWEBGAS Posts: 474 Mover and Shaker
    RNGesus is THE ONE that rules the pulls.

    My 20LT and 450cp stockpiled, only got me 1 icon_blackwidow.pngredflag.png and 1 drstrange_icon.pngblueflag.png
    other that that, 3 icon_katebishop.png 3 icon_spidergwen.png 2 icon_blade.png 2 icon_wintersoldier.png
    the rest is only garbage ( 3 icon_mrfantastic.png 2 icon_invisiblewoman.png and other irrilevants covers)

    I don't know if I should feel lucky or disappointed icon_e_confused.gif
  • HendrossHendross Posts: 762 Critical Contributor
    babinro wrote:
    If I'm saving for 6+ months I want to get ALL 3 cover maxed.

    How 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.

    I calc. ~95% confidence around 300 LLT, good luck. To max all 3 from nothing
    WEBGAS wrote:
    RNGesus is THE ONE that rules the pulls.

    My 20LT and 450cp stockpiled, only got me 1 icon_blackwidow.pngredflag.png and 1 drstrange_icon.pngblueflag.png
    other that that, 3 icon_katebishop.png 3 icon_spidergwen.png 2 icon_blade.png 2 icon_wintersoldier.png
    the rest is only garbage ( 3 icon_mrfantastic.png 2 icon_invisiblewoman.png and other irrilevants covers)

    I don't know if I should feel lucky or disappointed icon_e_confused.gif

    @10% I'd feel sightly disappointed. It's a pretty small sample, but that's what the rate use to be.
  • HendrossHendross Posts: 762 Critical Contributor
    Hadronic wrote:
    You left off the "why"...? I disagree. Convince me?

    look 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.

    I'm so happy to learn new things, here is a Poisson Distribution
    Given we've met the 3 criteria
    1. The interval of the observation is fixed
    2. The rate of the event is constant
    3. Occurrences are independent
    I've add a shaded (x-Value) Probability of >230 pulls
    LT_Token_Stats_CS_Poisson_zpssjdph6gd.jpg
  • johnnyzerojohnnyzero Posts: 97 Match Maker
    I feel like this is as good a thread as I'm going to get to weigh in on this...but I did what was described above. I brute forced the Latest Legendary token all the way to a maxed Black Bolt, Widow, and 10 covers on Dr. Strange.

    Long 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 only pulled 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 token_legendary.png , 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'm happy, 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.
  • FightmastermpqFightmastermpq Age Unconfirmed Posts: 995 Critical Contributor
    johnnyzero wrote:
    I feel like this is as good a thread as I'm going to get to weigh in on this...but I did what was described above. I brute forced the Latest Legendary token all the way to a maxed Black Bolt, Widow, and 10 covers on Dr. Strange.

    Long 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 only pulled 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 token_legendary.png , 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'm happy, 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.
    This is awesome and the story I had hoped to tell from my hoarding experience.

    Unfortunately 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.....
  • brollbroll Posts: 4,727 Chairperson of the Boards
    Brigby wrote:
    I feel like I should have paid more attention in Statistics class... icon_e_confused.gif

    I 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.
  • AwebermanAweberman Posts: 242 Tile Toppler
    We've also seen special stores for Black Widow and Doctor Strange, where I believe the chance of pulling one of those specific covers was 10%. How does that change the model, in the event that future 5* releases also get special stores?
  • HadronicHadronic Posts: 338 Mover and Shaker
    Hendross wrote:
    I'm so happy to learn new things, here is a Poisson Distribution
    Given we've met the 3 criteria
    1. The interval of the observation is fixed
    2. The rate of the event is constant
    3. Occurrences are independent
    I've add a shaded (x-Value) Probability of >230 pulls

    yes, typically whenever you are counting occurences within a set interval the probability distribution function (PDF) will be poisson shaped. great job on your analysis.
  • HadronicHadronic Posts: 338 Mover and Shaker
    Hadronic wrote:
    You left off the "why"...? I disagree. Convince me?

    look 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.

    Ohhhhhhh, yes, you're right, I was not getting that, I'm glad you added this clarification! I thought you were misunderstanding the nature of Hendross' runs, that you were thinking each the same # of pulls or something. Treating the # of pulls as though it were a unit of time. It's tracking phenomena like that (# instances per std. unit) where I have used Poissons before, thus a bias on my part. I wasn't making the leap that his test (# of pulls to reach a desired condition) could be looked at as 'standard'. And maybe I'm still not getting it icon_lol.gif In the maths, I am not classically trained, only a dirty, amateur user.

    So, yes, the asymmetric tails and the 'implied' negative probability. When I was tracking legendary pulls, and tracking the # of drops of individual covers per X pulls, I noticed the same. That it would take some multiple of the # of possibilities in the tokens in order to "mathematically guarantee" a non-zero chance of any and all covers. That is, to achieve a high confidence of the desired result by getting the peak of the distribution enough std. deviations from 0 to have no 0s.

    It was sharing those observations with Stochasticism that lead to his formula I posted above, which depressingly illustrates the evils of pairing RNG distribution with a distribution model features ongoing dilution of token odds.

    I meant to go back and demonstrate how dilution drives the # of pulls for a desired result upward exponentially ... maybe I'll get back to that, make it my next mega-post icon_lol.gif

    well 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.
  • Team_JacobTeam_Jacob Posts: 90 Match Maker
    So, how many draws for 12 covers? At some point giving up 25 draws makes sense, right? For sure with classic 5*?
  • HendrossHendross Posts: 762 Critical Contributor
    Aweberman wrote:
    We've also seen special stores for Black Widow and Doctor Strange, where I believe the chance of pulling one of those specific covers was 10%. How does that change the model, in the event that future 5* releases also get special stores?
    Great question. I got a mean of 120 with CS assistance. For completing a new featured character vault at 10% rate
    LT_Token_Stats_CS_Poisson_Featured_zpsbhncmphy.jpg
    Short version: It makes a huge difference, having a 10% shot at the same character, and only 1 character to work on. I hope Hendross runs this case for you. Factoring in friendly CS, it should 'only' take average of 130 pulls. The only variation would be whatever delta from the 10% rate each run produces.

    Without CS help, should be around 150. Up to 190 depending how high you wanted to drive confidence (190 pulls should be ~99% confidence).

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