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Rune Chests and probability calculation

Discussion in 'General Discussion' started by Stevie2k, Oct 25, 2018.

  1. Stevie2k

    Stevie2k Hatchling

    Hope all of you are able of a little bit of math - esp probability calculation...

    There is REALLY no need at all for the expensive two boxes - where you also must have these special keys... :

    Let's take a look at the cheapest chest, the bronze one:
    The probability for the "interesting" types of runes are:
    green rune: 1 of 6
    purple rune: 1 of 100.
    The chest costs 200 diamonds.

    Silver chest - costs 500 diamonds and 100 silver keys
    green rune: 1 of 3 (so it's twice as often as the bronze one)
    purple rune: 1 of 50 (also twice as often as the bronze one)

    Gold chest - costs 4500 diamonds and 100 golden keys
    green rune: 1 of 2
    purple rune: 1 of 10.

    Now comes the heavy part... ;-)
    What do you think are the probabilites, if you buy TWO bronze chests for 400 diamonds?
    Yeah, try it with a dice... if you have exact the same probabilites in two games the probabilites are multiplied with 2.
    So:
    green rune (on 2 bronze chest): 1 of 6 multiplied by 2: 1 of 3 (or 33%)
    purlpe rune (on 2 bronze chest): 1 of 100 multiplied by 2: 1 of 50 (or 2%)

    Do you find the funny thing? This are exactly the same probabilites as the silver chest - but you pay 100 diamonds less and do NOT need any silver key.
    It is completely insane, if you take a look at the golden chest:
    It costs 4500 diamonds, thats 22.5 times the costs of the bronze one:
    green rune (on 22.5 bronze chest): 1 of 6 multiplied by 22.5: 375% (so you definitely get more than one...)
    purlpe rune (on 22.5 bronze chest): 1 of 100 multiplied by 22.5: 22.5% or 1 of 4.44

    Did I mention that you get A LOT MORE runes (to sell or whatever) if you only take bronze chests? In the example of the golden chest you get over 40 runes!

    So... You loose sooo much diamonds if you buy any other chest than the bronze one... AND: there is really NO USE AND NEED for this silver and golden keys...
     
  2. PolliSoft

    PolliSoft Hatchling

    Hi,
    I'm sorry to say that your statistical logic is a bit off. You are correct in the analogy of the dice, but the logic is a bit off. The fundamental difference is that you are using logic for statistics without replacement (https://stattrek.com/statistics/dictionary.aspx?definition=sampling_without_replacement). Here, if you take 2 pebbles from an urn without putting the first back after you picked it, your chances of taking a specific pebble doubles.
    However, with dice and runes here, we have to use logic for sampling with replacement. This means that every time you take a ticket in the lottery of rune chests, the outcome doesn't depend on the previous. The formula for this is (where P is the probability of winning at least once after buying n tickets, and p is the probability of every win) P(n)=1 - (1-p)^n where n is the number of tickets bought.
    In your examples this gives:
    green rune (on 2 bronze chest): 1 - (1 - 1/6)^2 = 0.3056 (or 30.56%)
    purple rune (on 2 bronze chest): (1 - (1 - 1/100)^2 = 0.0199 (or 1.99%)

    The more tickets bought, the more the result between the different formulas will differ. If it's a bit difficult to wrap your head around the differences, think of the dice. By the logic of @Stevie2k, by throwing 6 dice at the same time, the result of those would always be one 1, one 2, one 3, one 4, one 5 and one 6.
     
  3. PolliSoft

    PolliSoft Hatchling

    So, the most important question is "What is the probability to get at least 1 purple rune buying the gold chest, and what probability do I get by buying a number of bronze or silver chests for the same amount of gold?"
    To get to a comparable amount of gold, we use 9000 gold (it's either gold OR keys).
    Number of bronze chests for 9000 gold = 45 => Number of runes = 90
    Number of silver chests for 9000 gold = 18 => Number of runes = 54
    Number of gold chests for 9000 gold = 2 => 6 (But here you always get at least 1 purple, so rather it is 2 purple + 4 unknown)

    Purple rune probability:
    bronze: P(90) = 1 - (1 - 1/100)^90 = 59.5%
    silver: P(54) = 1 - (1 - 1/50)^54 = 66,4%
    gold: P(4) = 1 - (1- 1/10)^4 = 34.4% (+ 2 guaranteed purple)

    This means that if you are willing to spend a lot of Gold, go for gold! If you want to spend less Gold, go for silver!
     
    Last edited: Oct 25, 2018
    Redwing likes this.
  4. Nyk

    Nyk Super Cool Bird

    Math :eek:
     
  5. A. Wolf

    A. Wolf Motherflocker

    Wait, are you saying 2+2 does NOT = 3? :confused:o_O:eek::(:D
     
  6. Gildan

    Gildan Super Cool Bird

    Disregarding your math completely, the foundational premise of your entire argument is flawed because you are operating under a massive misunderstanding regarding how those keys function: They are not an additional requirement. The price for those chests is the cost in gems or the cost in keys, not both - by collecting the keys through the various in-game methods, you can open those chests without paying gems for them.

    The only chest that always costs you gems is the one you're advocating people open instead.
     
  7. Starman.thc

    Starman.thc Super Cool Bird

    This is great info...I could never spend 4500 gems anymore. There is hope!! Would be interested in knowing where that info is noted.
     
  8. A. Wolf

    A. Wolf Motherflocker

    ??? it is noted in the game where you would spend EITHER Keys OR Gems...
     
  9. Gildan

    Gildan Super Cool Bird

    Yeah, the game doesn't explicitly use the word "or"... but it does have two different buttons each labeled "Get Chest" with different currencies, so it was just intuitively obvious to me that it was a choice between two options and not a comically large button that is divided into two distinct UI elements. Rovio is bad at internal consistency and in-game explanations, but they're not THAT bad.
     
    PolliSoft likes this.
  10. Stevie2k

    Stevie2k Hatchling

    OOoohhhkkk... The "OR" is a thing I missed too... ok, thanks! Than the bigger chest do make sense to me, not by buying with diamonds though... I am not completely sure if my math is bullshit or not - I still think I am right... But it does not matter so much any more...
     
  11. A. Wolf

    A. Wolf Motherflocker

    Anyone have a sense yet of how much boost we really get from purple Runes?
    Like, i have one that will add 80 Crit, but the concept of Crit & Front Crit are totally new in this game.
    So, i dont know what "+80 Crit" will actually do?...
     
  12. feffe

    feffe Tiny Birdy

    My understanding of the "+XX Crit" is just that, extra critical damage. In your example +80 in the base critical damage that the bird does. But I don't know if that involves both critical damage done from the birds SS or just the regular "pinball-hits" from behind.
    My understanding of the "Front Crit %" is the same. Think Annie with Early Threat evo, she does critical damage from any angle when the attack counter of a pig is 2 or less. So I think that the "Front Crit %" is supposed to mimic that behaviour the % amount of times.

    Again, I don't know if this includes any SS hit or just regular hits or both.

    My Master Matilda has 2 purple runes (top + top right), 2 greens (top left + middle) and 1 grey (bottom) and she now has the following stats:
    Power: 14890 (as you know A. Wolf, this is just SS10 + PL10. Visual - not actual power)
    Damage: 3190
    Health: 4729
    Front Crit Chance: 16,5%
    Additional Crit Damage: 83

    When I added the second purple rune to her, I had to replace a green (the top one) - and then I actually got less Additional Crit Damange, but gained Health/Damage/Front Crit Chance (if I remember correctly). So even the same runes (same position/shape that is) give different stats in different colors. Not just purple > green > grey.

    So, this rambling adds up to; No. No I don't know enough to say anything definitive. I will need much more purple runes to get some grasps.
    And finally, even with a 16,5% Front Crit Chance - I haven't seen a front critical hit from my Master Matilda yet, neither from her SS nor from regular hits.
     
  13. A. Wolf

    A. Wolf Motherflocker

    Yeah, i guess that's my main gripe... the front crit shows a % (presumably out of 100). That makes sense although still a bit indefinitive.
    BUT, the additional crit is totally undefined as it is not a % at all. So no way to know what its really adding.
     
  14. Nyk

    Nyk Super Cool Bird

    Yes and it could be 80 damage before the critical damage multiplier is added, or 80 damage after the multiplier is added. If critical damage is ~3 times regular damage, then 80x3=240 damage, plus the other miscellaneous multipliers. It's very confusing and not well explained. And I've never seen Carson do a front critical despite having ~22% front Crit chance.
     
  15. A. Wolf

    A. Wolf Motherflocker

    My maxed Master Carson w 2 purples & 96 crit wont even kill all 5 small pigs like he did before they added these dumb runes...
    Now im pissed that i wasted so much resources & the 2 purple runes on a bird that wont do what he should in my arena team.
     
    Kimo likes this.
  16. Nyk

    Nyk Super Cool Bird

    Did you swap your leader out (which may or may not have boosted Carson)? Master Carson struggles to kill all the little pigs for me unless my leader bonus boosts him. I usually keep QB, Carson, or another blackberry bird as my leader. I will admit, the arena has gotten harder since they added runes.
     
  17. A. Wolf

    A. Wolf Motherflocker

    No, i always use Claude. the first week I had him he was wiping out all 5 pigs from any angle even at P7-P8.
    Then immediately after they changed our visible power & added runes (the very next week), he cant kill them because the change boosted pig health by about 20%.
     
  18. Kimo

    Kimo Tiny Birdy

    I'm glad you posted this. I've been trying to decide what to use my purples on. It was between Master Carson, Master Matilda or, now after seeing Beast in action, Master Beast.

    Master Carson and 5* Carson just don't have the ko ability that I thought they would.
     
  19. Nyk

    Nyk Super Cool Bird

    I'm beginning to think that runes ruin birds. Not aid them. This seems to be a common problem, because master carson for me used to be stronger than matilda. Now, as you said yourself, he isn't as good.
     
  20. Gildan

    Gildan Super Cool Bird

    I've had a lot of success swapping out my objectively better, but statistically less powerful QB for a Master Beast, but that's probably mostly because I'm running Fringy as the team leader and doing that netted me an extra color on the team. Depending on the angles I can just straight 1-shot the small pigs with my opening non-powered up shots now, and most matches end (in my favor) after 2 shots total.
     

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