What rarity of items do you have a full set of?

Discussion in 'Card Hunter General Chat' started by BlackVoidDeath, Feb 16, 2015.

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What rarity of items do you have a full set of?

  1. None

    23.9%
  2. Common

    67.0%
  3. Uncommon

    52.3%
  4. Rare

    44.3%
  5. Epic

    22.7%
  6. Legendary

    4.5%
Multiple votes are allowed.
  1. BlackVoidDeath

    BlackVoidDeath Guild Leader

    I had 1 of every Uncommon and Rare before i got my last Common (Rowan Magestaff)
     
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  2. Sir Veza

    Sir Veza Farming Deity

    It's been about 3 months of farming and shopping since my last post here, and today I picked up Aork's Vial Of Memories from the DD.
    I still need Reap The Whirlwind (L18), Ichabod's Buckler (L9), Bynzer's Weighted Club (L12), Godtouched Mace (L18), and Heartripper (L18) to complete my collection.
    I also picked up my 12th Acidic Gland from the DD to complete my "Max Usable" for common through rare. I have a max usable of 72% for epic, and 28% for legendary. In the past few months I've sold more epics and legendaries as excess than I've kept. There are certainly worse in-game problems to have, but I do wish the RNG would shift a bit and give me more I could use.
     
    Last edited: Jun 9, 2015
  3. Bandreus

    Bandreus Thaumaturge

    Whoa :eek:

    Hopefully Randi is reading this and blesses you with exactly those few items you need for your collection before EttSC hits.

    Anyway, I don't think the RNG can be blamed. When you get that close to 100%, the odds of you rolling exactly what you need naturally get astronomically low.

    Anyway, good luck with your endeavors. You really are the resident Farming Deity
     
    Sir Veza likes this.
  4. Scarponi

    Scarponi Moderator

    It definitely gets more and more difficult to pull what you need the closer you get to completion. That said, with 5 legendaries left, statistically you should see one of them in 52 legendaries (drops or shops). At 17 legendaries a week just from shops, it should theoretically only take about 3 weeks to see one of Sir Veza's remaining even if he doesn't play a single map.

    I myself still needed 49 legendaries and 2 epics as of three months ago. Today my list is:
    Cobalt's Chalice (E)
    Lewin's Boots
    Beater
    Mindless Aggression
    God's Rage
    Darkblood Glaive
    General Jelom's Helm
    Absolem's Leather Shoes
    Yancley's Boots

    My max usable from common to legendary is:
    100%
    99% (need 1)
    99% (need 3)
    77%
    28%
     
    Last edited: Jun 9, 2015
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  5. Bandreus

    Bandreus Thaumaturge

    Wow, that made me want to dig into the math behind the odds of @Sir Veza scoring those few missing items, which involved dusting my knowledge about combinations off. Man, has it been a while since I last put that stuff to use.

    Now, I have no clue about the specifics for the algorithm used in DD/Randimar's, but assuming uniform distribution of probabilities.

    I think there's a grand total of 261 Legendary items in CH? That'd be excluding treasures and items not normally available at the shops (halloween/holiday specials).

    So for the DD it's quite easy, Veza has a whooping 5/261ths chance to score one of those 5 items, on any given day. That's roughly equivalent to a 1.9% chance.

    I'll list all possible outcomes for Randi's under spoilers (the math is quite fun, but prob not very interesting. to most human beings at least :p).
    Given random selection of 10 legendary items available at randi's each week:
    • The chance of Veza not getting any of the items he needs = 0,82128759405585656291630786059438 (i.e. ~82%)
    • Him getting exactly 1 of the items he needs = 0,16625254940401954714905017420939 (i.e. ~16%)
    • Him getting 2 of the items = 0,01206671729545303164791493199907 (i.e. ~1%)
    • Him getting 3 of the items = 3,8768569623945483206152391964879e-4 (i.e. ~0.3%)
    • Him getting 4 of the items = 5,427599747352367648861334875083e-6 (i.e. ~0.0005%)
    • Him scoring the jackpot and getting all 5!!! = 2,5948684051087016647942636852987e-8 (i.e. ~0.000002%)

    Simply put, each week Veza has a chance of ~17.9% of finding one of the items he needs at Randi's. It's not that bad at all.

    Now, if we want to estimate the weekly chance of him getting an item from both either DD or Randi's, we need to take a slightly more refined approach. Namely, we need to take repetition into account.

    For the 7 items available in the DD over the course of any given week, Veza has about a 12.5% chance of getting (at least) one of the items he needs.

    We're almost there: combining the results from Randi's and a full week worth of DD, the (approximate) chance of Veza adding one more item to his collection is ~= 30.4%

    Which is to say, as @Scarponi pointed out, more or less a 3 weeks wait (more like 3.2 weeks to be nitpick-y). But this was definitely more about me spending hours destroying my self esteem over how rusty my math-skills got, rather than me expecting to arrive at a different result :p
     
  6. Sir Veza

    Sir Veza Farming Deity

    So when I needed 6 and didn't see one for 13 weeks, it was a bit on the unlucky side, statistically speaking? If only this improved my chances for the next few weeks, but alas, I don't think probabilities actually work that way.
     
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  7. Rebel7284

    Rebel7284 Ogre

    correct and indeed probabilities do not work that way (a coin you flip now doesn't care what it landed on last time.)
     
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  8. Bandreus

    Bandreus Thaumaturge

    The point being (as far as we know, at least) the algorithms for determining what's available in DD/Randi do not factor-in what has been available in the past days/weeks.

    I.e. in probability theory terms, the event of any given item to be available in the shops is statistically independent from previous events. (I'm unsure if, in English, this wording is true to what I'm trying to say, but hopefully you do understand).

    When we talk about probabilities for anything happening (in this instance, any item missing from anybody's collection to be on offer at the shops) that has to always be intended in the sense of expected value. This is why lucky streaks (getting tons of epics/legendaries out of a few chests, or scorying 3 legendary items from a signle drop) and long-lasting draughts (getting minimum or very poor drops many, many times in a row) are not that uncommon. Probability has it's own way of making fool of all of your most reasonable expectations.

    Regarding Veza's 13 weeks wait: to make things easier on me, I'll assume he only limited himself to checking what was up in the DD and Randi (i.e. not opening other chests from Campaign/Loot Fairy/Leagues/etc), but I'll conversely assume his weekly chance of getting an item from the shops to be 40%, i.e. significantly higher than what I previously elaborated for the 5-items-missing version of the problem. I don't pretend this to be a good approximation, but this is only for the sake of painting me ridiculous for talking this stuff on the forums.

    This is equivalent to saying each week Veza had 2 out of 5 chances to grab a new item for his collection.

    On the first week, his chance of getting an item he needed was 40%. Conversely, he had a 60% chance of not getting one of those missing items. Since he did not get anything good out of that first week, we keep going on.

    On the second week, his chance still was 40% (individual events are independent), but the overall chance of him getting an item he needed on the second week exactly was 24% (40%, the chance of "success" times 60%, because he did not get a "success" on the first week).

    Third week, chance of success still 40%, but chance of succeeding on the third week exactly was 14.4% (40% times 60% times 60%).

    Rinse and repeat for thirteen consecutive weeks, at which point the chance of him getting an additional item into his collection (and doing so on the 13th week exactly) was a whooping 0.08%.

    At first, when you look at things in this perspective, probabilities can start getting pretty confusing, so let's put things another way.

    Again, assuming each week Veza's chance to add another item to is collection was 40% (I need to reiterate this is only an approximation)

    The chance of Veza getting that additional item at any point during the first 12 weeks was ~99.78%
    While the chance of him not getting another item during the first 12 weeks was, unsurprisingly, ~0.22% (which is to say, a chance in 459)

    So yeah, in all likelihood, Veza was a bit on the unlucky side... statistically speaking ;)

    I'd really appreciate if anybody skilled in probability theory could confirm/deny if my approach was correct with this. At this point, it has been too many years since I did this sort of stuff at school for me to be confident about my method :p
     
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  9. Scarponi

    Scarponi Moderator

    In English your wording is indeed mathematically rigorous and correct.
    Looks fine to me :).
     
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  10. Pawndawan

    Pawndawan Champion of Cardhuntria

    All this random math talk reminded me that I got my last rare earlier this month. :) Missing one uncommon (Acolyte's Healing Ring), 38 epics and 176 legendaries, treasure excluded.
     
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  11. Bandreus

    Bandreus Thaumaturge

    I'm only 7 items away from completing my epics set. Legendaries are going to take some more time still: 115 to go!
     
  12. Sir Veza

    Sir Veza Farming Deity

    So what I really need is a million to one shot. At least they always work in the movies. :cool:
     
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  13. Sir Veza

    Sir Veza Farming Deity

  14. Scarponi

    Scarponi Moderator

    Last edited: Jul 10, 2015
  15. Sir Veza

    Sir Veza Farming Deity

    Are leagues and MP paying off for you, or are the shops playing nice? Little of both? Either way, good show!
     
  16. Scarponi

    Scarponi Moderator

    This particular one was in the purple chest in the MP reward track.
     
  17. BlackVoidDeath

    BlackVoidDeath Guild Leader

    Pretty sure that right now (at this point in time), everyone doesnt have a full set of everything (if you do then... wow) ;)
     
  18. Jayce

    Jayce Hydra

    Crazy dedication. I approve =D
     
  19. Scarponi

    Scarponi Moderator

    Well at the moment, I need 1 uncommon, 2 rare, 1 epic and 20 legendaries.

    EDIT: Oh, and I also have 19K in gold of excess I need to sell now. :)
     
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  20. Bandreus

    Bandreus Thaumaturge

    I'll get back in a couple days when I get some free time to play the new SP content and open my 300-something chests and let you know
     

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