Announcement Announcement Module
Collapse
No announcement yet.
Some Shop Probabilities Page Title Module
Move Remove Collapse
X
Conversation Detail Module
Collapse
  • Filter
  • Time
  • Show
Clear All
new posts

  • Some Shop Probabilities

    Hey all! Another player and I worked out the probability of getting mythics and legends for some of the sales. This probability may not work for future sales since it all depends on percentages for specific Curios and enhancements, but it works for some. I bolded and underlined the final probabilities and the important stuff in case you don't feel like looking at the math. I'm only doing probability for 5 and 10 disc (if this option is available) sales since the probability for 1 disc is exactly what's listed in the sale.

    Current (at least when I put them in here) Sales:

    For promo sales that show a 2% chance for mythics and a 12% chance for legends for 5 discs, these are the chances for a mythic or legend:
    • For 5 discs, the shown chance of getting a mythic or legend for one of these discs is .14 (14%). So, the chance of not getting a mythic or legend (which is so much easier to calculate than the opposite) is .86 (86%). To calculate the chance of not getting a mythic or legend, you multiply .86x.86x.86...until you are multiplying it 5 times (.865). This'll give you .4704270176 (47.04270176%), which is the probability of not getting a mythic or a legend. So, subtract this from 1 and you'll get .5295729824 (52.95729824%), which is the chance of getting a mythic or legend. This is basically a 53% chance.
    For boost sales with a 6% chance to get a heroic boost and a 24% chance to get a ultimate boost for 5 discs here's the probability of getting a heroic or ultimate boost:
    • The chance of getting a heroic or ultimate boost in one of these 5 discs is .3 (30%) so the chance of not getting a heroic or ultimate boost is .7 (70%). Multiple .7x.7x.7...until you are multiplying that number 5 times (.75), which gives you .16807 (16.807%). Wow...this is such a nice decimal... Anyway, subtract that number from one and you get .83193 (83.193%), which is the final probability. This is basically 83%.
    Since the premium sale has only one disc with the chances listed and the ultimate sale has a guaranteed mythic and all legends for five discs, I think this is all the calculating I have to do for now.

    Older Sales:

    For promo sales that show a 2% chance for mythics, these are the chances for only a mythic:
    • For 5 discs, the shown chance of getting a mythic for one of these discs is .2 (2%), so the chance of not getting a mythic is .98 (98%). So, multiply .98x.98x.98....until you are multiplying it 5 times (.985). This'll give you .9039207968 (90.39207968%). Subtract this from 1 and you have the chance of getting a mythic, which is .0960792032 (9.60792032%). Basically a 10% chance.
    For promo sales that show a 1.5% chance for mythics, a 3.5% chance for legends, and a 7.2% chance for epics for 5/10 discs with a guaranteed epic or better for 10 discs, these are the chances for a legend or mythic:
    • For 5 discs, the shown chance of getting a mythic or legend for one of those 5 discs is .05 (5%). So, the chance of not getting a mythic or legend is .95 (95%). To calculate the chance of not getting a mythic or legend, you multiply .95x.95x.95....until you are multiplying it 5 times (.955). This'll give you .7737809375 (77.37809375%), which is the probability or not getting a mythic or legend. So, to finish, subtract that number from 1 (or 100 if you're using percents) and you'll get the probability. .2262190625 (or 22.62190625%). Basically a 23% chance.
    • For 10 discs, it's a bit trickier (meaning a lot trickier). I have no clue how that guaranteed epic or better Curio affects the rest of the probability. Do 9/10 discs have normal probability and the last one has special probability? And would that special probability have the same ratios for epic and above Curios as the ones listed in the sale (the ratios being out of 1 instead of .122).? Or would the 10/10 discs have normal probability if one of the earlier ones gave you an epic? If anyone does know, please tell me. I'd like to have the correct probability. For now, I'll give the probability of 9/10 discs with normal probability and the last one with special probability with the same ratios as listed in the sale. The shown chance of getting a mythic or legend of those 10 discs is .05 (5%). So, the chance of not getting a mythic or legend is .95 (95%). For the 9 normal probability discs, you use a similar method as above with the 5 discs. You multiple .95x.95x.95...until you are multiplying it 9 times (.959). This'll give you .6302494097 (or 63.02494097%). Now for that extremely annoying 10th disc.*groans* So, once again, the chance for a mythic or legend is .05 (5%). All of the probabilities of epic Curios and better adds up to .122 (12.2%). The chance of the mythics or legends for the disc where only the epic or better probabilities exist is .05/.122, which is .4098360656 (40.98360656%). Then, the probability of not getting a mythic or legend for this special disc is that long decimal subtracted from 1, which is .5901639344 (59.01639344%). So, the probability of not getting a mythic or legend in these 10 discs (9 normal and 1 special) is .6302494097x.5901639344, which is .3719504713 (37.19504713%). Subtract this from one and the probability of getting a mythic or legend is .6280495287 (or 62.8049587%). Basically a 63% chance.
    Let's say you really want to get a mythic and don't care about legends. Well, here's the probability of getting a mythic for promo sales with a 1.5% chance for mythics and a 10.7% chance for epics and legends for 5/10 discs with a guaranteed epic or better for 10 discs:
    • For 5 discs​, the shown chance of a mythic for one of those 5 discs is .015 (1.5%). So, the chance of not getting a mythic is .985 (98.5%). So, to find the chance of not getting a mythic in the 5 discs, multiply .985x.985x.985...until you are multiplying it 5 times (or .9855). This'll give you .9272165024 (92.72165024%). Subtract this number from 1 and this'll give you .0727834976 (7.27834976%), which is the chance of getting a mythic in the 5 discs. This is basically 7%.
    • For 10 discs for mythics, there is the same problem with the guaranteed epic. I'll calculate the same way as I did for the previous 10 disc, 9 normal discs and 1 special disc with the same ratios for the odds of epic and above Curios as the ones listed in the sale (out of 1 instead of 12.2). So, for the 9 discs, the probability of getting a mythic in one of the discs is .015 (1.5%). This makes the probability of not getting a mythic .985 (98.5%). So, to find the chance of not getting a mythic in the 9 discs, multiply .985x.985x.985...until you are multiplying it 9 times (.9859). This'll give you .872822784 (87.2822784%). Now for the special disc, the probabilities for epic and better Curios add up to .122 (12.2%). The mythics make up .015 (1.5%) of that. So, the chance of getting a mythic from this special disc with only epic or better Curios is .015/.122, which is .1229508197 (12.29508197%). Subtract that number from one and the chance of not getting a mythic from this is .8770491803 (87.70491803%). So, the probability of not getting a mythic in these 10 discs (9 normal and 1 special) is .872822784x.8770491803, which is .7655085073 (76.55085073%). Subtract this from 1 and you get .2344914927 (23.44914927%), which is the odds of getting a mythic in the 10 discs. This is basically a 23% chance.
    For premium sales with a 4.5% chance for a mythic and a 10.5% chance for a legend for 5 discs, here's the probability of getting a mythic or legend:
    • Since the chance of getting a mythic or legend in one of these 5 discs is .15 (15%), subtract that number from 1 and you'll get the probability of not getting a mythic or legend, which is .85 (85%). So, to find the probability of all the discs combined, multiply .85x.85x.85...until you are multiplying it 5 times (.855). This'll give you .4437053125 (44.37053125%). Then, subtract that long decimal from 1 and you'll get the final probability, which is .5562946875 (55.62946875%). Basically 56%.
    For premium sales with a 4.5% chance for mythics, here's the probability of getting a mythic for 5 discs:
    • Since the chance of getting a mythic in one of these 5 discs is .045 (4.5%), the chance of not getting a mythic is that number subtracted from 1, which is .955 (95.5%). Multiply .955x.955x.955...until you are multiplying that number 5 times (.9555) to get the chance of not getting a mythic for all 5 discs. This'll give you .7943590686 (79.43590686%). Subtract that number from 1 and you'll get .2056409314 (20.56409314%), which is the final probability. This is basically a 21% chance.
    If any part of my calculations is wrong, PLEASE tell me. I want to make sure I have the right probabilities. I'll try to continue adding to this as the Curio odds change in the shop. I need to finish the boost stuff as well. But for now, good luck.

    Oh! I almost forgot something (meaning I forgot it twice in previous edits and decided to do another edit to put it in ). If anyone wants me to find a probability for a specific Curio, just let me know in the comments below or in the game and I'll try to get back to you as soon as possible (I'm *MOD*Starlight if you didn't know). Make sure you tell me what type of sale it is and if you plan to do 5 or 10 discs to get that Curio.
    Last edited by Starlight; April 27th, 2016, 10:36 PM. Reason: Organization. Yay! Sorry I haven't updated the boost shop. Too lazy to grab my calculator .-.

  • #2
    You need like RNGod to get everything amirite
    Last edited by BronzerTheGuyYouKnow; April 5th, 2016, 06:10 AM. Reason: not really a huge edit but ayy

    Comment


    • #3
      Wow lots of math, it seems right though, good job.
      Last edited by Roshen; April 6th, 2016, 02:06 AM. Reason: i was raised by wolves

      Comment


      • #4
        I posted that in promotional sale odds from Landerz :

        "Actual promo for 500 and 1000 gems pack is :
        1.5 myths, 3.5 legs and 7,2 epics
        When you spend for the 1000 gems pack of 10 discs you got one special discs (part of the 10 which means only 9 are normal) that you can consider to be x/12,2 (basically /(1,5+3,5+7,2)).. instead of x% (basically /100) so that's basically your magic discs where the odds gets crazy but that doesn't mean we should discard the other discs from the equation.

        AT LEAST ONE 4* or 5*
        9 discs where the odds of getting 4/5* is 5% or 0,05 per discs and one where the odds is 5/12,2
        We need to work with the complementary because if we get the odds that NONE of them drop over the 10 discs then we can just use the complementary of that value to obtain the odds that AT LEAST ONE of them drop, logic!
        which makes (0,95^9)*(7,2/12,2) = 0,372 =37,2% to NOT get ANY 4* or 5*
        so basically 62,8% to get AT LEAST ONE 4* or better

        And that's not the same result as above so I am going to try with a real calculator.. well i don't see the problem on my part maybe the post above forgot to factor the 1 epic or better disc or maybe the odds changed since then..

        AT LEAST ONE 5* now
        so this time it's significantly lesser we have 9 discs at 1,5% so a complementary (chance that it doesn't happen) of 98,5% or 0,985 AND one disc at 1,5/12,2 which has a complementary of 10,7/12,2..
        So the operation goes as follow :
        (0.985^9)*(10,7/12,2) = 0.7655 or 76,55% To NOT have any mythic dropping which means that the complementary (Having at least one dropping) is 23,45% chance that at least one will drop...

        At first i only wanted to give an explanation to ppl for how you calculated it but since we don't have the same number I suppose I'll have to go through the 3000 gems equivalence ..

        I also need to say that for premium odds I got the same result using the same method I used for promo odds so I suppose one of us got something wrong.

        So spending 3000 gems in promo you get (0.985^27)*((10,7/12,2)^3)= 0,4486 or 44,86% to NOT get any mythic and thus 55,14% to get AT LEAST ONE mythic

        as for the 3000 gems spent on premium, you get 0,955^10=0,631 or 63,1% to NOT GET ANY mythic so only 36,9% chance to get AT LEAST ONE mythic.. (weird, this time we don't have the same number despite that I had the same result than you for one premium)

        So my conclusion is totally different, Promo is the way to go..


        I hope I have been clear enough in my explanation on the logic behind my math.

        If anyone hasn't understood, I'll be happy to give a more thorough explanation with actual demonstration of the process.


        02/28/2016 EDIT
        NEW ODDS : 3% mythic over 9 discs and 3/13,7 over one disc
        using the same process than above I got 40,6% to get at least 1 mythic "

        It's a response to someone that didn't have the same odds..
        I think we have similar results, Star.

        I made the comparaison for 3000 gems spent in promo and premium though.
        Last edited by Mjoern; April 13th, 2016, 08:49 PM.

        Comment


        • Starlight
          Starlight commented
          Editing a comment
          Yup. We have the same results.

      • #5
        We would need a new shop math probabilities for the new sales format, anyone care to do the maths as im not good at that... thanks!

        Comment


        • Starlight
          Starlight commented
          Editing a comment
          I put the new shop stuff in the original message
      Working...
      X