Verification Request

2

Comments

  • jamesh
    jamesh Posts: 1,600 Chairperson of the Boards
    MissoesRicRose said:
    OJSP said:
    You've been asking the same question since September 2017. What makes you think you'll get a different answer from the players? There is currently a player in another thread who's opened 35 tokens without getting a 5* from the same store, so your 20 is not exceptional.

    If you want to ask the developers about your pull statistics to see whether there's any problem with your numbers, send a ticket to Customer Support.

    As far as I know, the developers have never answered any questions about token pull results in the forum. Otherwise, you'll just get answers from other players telling you to keep opening tokens and record your own results to confirm if the percentage is lower than expected.
    In fact, there is no probability, the game is already pre-programmed to give you a certain character. If it were not so, the game would not give you the same characters after a backup.
    That is a simplistic way of looking at things.  The game is using a pseudo-random number generator, and generates the same pulls after a restore from backup, because it is starting with the same seed.
    A good PRNG is designed such that if you know the seed you can reproduce the same sequence of numbers, but if you don't know the seed the sequence should be indistinguishable from uniform random data.  This kind of system is quite important in cryptography: streaming ciphers effectively "add" a PRNG sequence to the plain text to encrypt, and "subtract" the PRNG sequence to decrypt.
    No one decided to initialise your PRNG to result in 20 failed pulls.  In fact, the ability to do so would make a PRNG useless for cryptography.  If I can determine the seed based on the first few numbers in the sequence, then I can predict the entire sequence.  And it seems likely that the game uses a cryptographically secure PRNG, if for no other reason than that there are many free high quality ones available and that money is on the line.
    The probability of making 20 pulls without seeing a 5* is 3.9%, so you'd expect about 1 in 25 people to get this unlucky.  That's common enough to make bad luck seem more likely than conspiracy.
  • sambrookjm
    sambrookjm Posts: 2,157 Chairperson of the Boards
    HoundofShadow said:
    The formula is this:

    Odds of drawing 4* from LT = 1 - (1/7) = 6/7 or 85%.

    Odds of drawing zero 5* out of 20 pulls in a row which is the same as drawing all 4* out of 20 pulls in a row = 0.85 ^ 20
    <math nerd hat on>

    Close, but not quite.

    You can round 6/7 off to 85% for a one-of pull without much error.  When you raise it to the 20th power, though, your answer will get considerably different.  6/7 is 0.857142 repeating, so the chances for pulling a 5-star with an LT is 1/7, or 14.285714 (with the 285714 repeating forever)%  (6/7)^20 = 0.045821.... which is about 1:21.82, or slightly worse than the odds of getting two pair in a 5-card poker hand (1:21.0).  That's about a 15% difference than 0.85^20, which comes out to 0.038760..., or about 1:25.8.

    <math nerd hat off>
  • jamesh
    jamesh Posts: 1,600 Chairperson of the Boards
    sambrookjm said:
    HoundofShadow said:
    The formula is this:

    Odds of drawing 4* from LT = 1 - (1/7) = 6/7 or 85%.

    Odds of drawing zero 5* out of 20 pulls in a row which is the same as drawing all 4* out of 20 pulls in a row = 0.85 ^ 20
    <math nerd hat on>

    Close, but not quite.

    You can round 6/7 off to 85% for a one-of pull without much error.  When you raise it to the 20th power, though, your answer will get considerably different.  6/7 is 0.857142 repeating, so the chances for pulling a 5-star with an LT is 1/7, or 14.285714 (with the 285714 repeating forever)%  (6/7)^20 = 0.045821.... which is about 1:21.82, or slightly worse than the odds of getting two pair in a 5-card poker hand (1:21.0).  That's about a 15% difference than 0.85^20, which comes out to 0.038760..., or about 1:25.8.

    <math nerd hat off>
    In-game, it lists the probability of pulling a 5* from a token as "~1:7", so all it is telling you is that it's somewhere between 1:7 and 1:6 (assuming they are smart enough not to overstate win probabilities on something they want people to gamble on).
    The devs have occasionally listed the odds at 15% in the past, so that's probably a better number to use than 14.285714.  Similarly, when they updated the support token odds recently, the numbers published on the forum were whole percentage points.
  • Yepyep
    Yepyep Posts: 952 Critical Contributor
    sambrookjm said:
    HoundofShadow said:
    The formula is this:

    Odds of drawing 4* from LT = 1 - (1/7) = 6/7 or 85%.

    Odds of drawing zero 5* out of 20 pulls in a row which is the same as drawing all 4* out of 20 pulls in a row = 0.85 ^ 20
    <math nerd hat on>

    Close, but not quite.

    You can round 6/7 off to 85% for a one-of pull without much error.  When you raise it to the 20th power, though, your answer will get considerably different.  6/7 is 0.857142 repeating, so the chances for pulling a 5-star with an LT is 1/7, or 14.285714 (with the 285714 repeating forever)%  (6/7)^20 = 0.045821.... which is about 1:21.82, or slightly worse than the odds of getting two pair in a 5-card poker hand (1:21.0).  That's about a 15% difference than 0.85^20, which comes out to 0.038760..., or about 1:25.8.

    <math nerd hat off>
    It's just been such a long, long time since I used this -- I had the formula right, but I kept multiplying the chance of pulling the 5*, as opposed to pulling the 4*, so I was getting (obviously) ridiculously small percentages.  

    This is straight up John von Neumann* game theory math stuff, right? The very, very easy part of it...  :D

    Thanks for the help, y'all! 

    *For me, JvN is on the shortest of lists of screaming geniuses of all history. I wish I could really understand more of what he was all about...
  • sambrookjm
    sambrookjm Posts: 2,157 Chairperson of the Boards
    jamesh said:
    sambrookjm said:
    HoundofShadow said:
    The formula is this:

    Odds of drawing 4* from LT = 1 - (1/7) = 6/7 or 85%.

    Odds of drawing zero 5* out of 20 pulls in a row which is the same as drawing all 4* out of 20 pulls in a row = 0.85 ^ 20
    <math nerd hat on>

    Close, but not quite.

    You can round 6/7 off to 85% for a one-of pull without much error.  When you raise it to the 20th power, though, your answer will get considerably different.  6/7 is 0.857142 repeating, so the chances for pulling a 5-star with an LT is 1/7, or 14.285714 (with the 285714 repeating forever)%  (6/7)^20 = 0.045821.... which is about 1:21.82, or slightly worse than the odds of getting two pair in a 5-card poker hand (1:21.0).  That's about a 15% difference than 0.85^20, which comes out to 0.038760..., or about 1:25.8.

    <math nerd hat off>
    In-game, it lists the probability of pulling a 5* from a token as "~1:7", so all it is telling you is that it's somewhere between 1:7 and 1:6 (assuming they are smart enough not to overstate win probabilities on something they want people to gamble on).
    The devs have occasionally listed the odds at 15% in the past, so that's probably a better number to use than 14.285714.  Similarly, when they updated the support token odds recently, the numbers published on the forum were whole percentage points.
    Interesting.  I figured that the ~1:7 was including bonus heroes, much the same way that it's ~1:43 for getting a 3-star from a standard token.  The odds of getting a single 3-star are twice as bad as that in reality, but since you always get a bonus hero 3-star from a standard token, they take that into account.
  • ssbledsoe
    ssbledsoe Posts: 52 Match Maker
    This is simple math folks.  Here's a nice link showing how streaks happen even with something w/ 1:2 odds (flipping a coin):
    https://wizardofodds.com/image/ask-the-wizard/streaks.pdf

    0/20 sucks, for sure.  No one says it doesn't, but it's simply not uncommon or even unexpected if you know how math works.
  • helix72
    helix72 Posts: 995 Critical Contributor
    As @jamesh pointed out, assuming D3 is using terminology correctly, ~1/7 literally translates to "about 1 in 7" which only means it could be between 1:6.50 (15.4%, any higher and they should say ~1:6) and 1:8.49 (11.8%, any lower and they should say ~1:8). I've heard and seen enough evidence in my own play and from more experienced players that I have been using 15% for the actual 5* pull rate for a while now.

    You'll note some probabilities are listed with the tilde (~) and some without. Getting a 4* out of a heroic pack is listed as ~1:16 but getting a 4* support from a beginner support token is listed as exactly 1:50.

    And the bonus hero chance is on top. So with a 15% draw rate and a 5% (notice it says 1/20 not ~1/20) for bonus heroes, your overall pull rate including bonus heroes will regress to the mean of 15% x ( 1 + 5% ) = 15.75%. @OJSP at 15.9% after 487 pulls is within a reasonable tolerance to support the underlying probabilities.
  • Banquetto
    Banquetto Posts: 29 Just Dropped In
    helix72 said:
    And the bonus hero chance is on top. So with a 15% draw rate and a 5% (notice it says 1/20 not ~1/20) for bonus heroes, your overall pull rate including bonus heroes will regress to the mean of 15% x ( 1 + 5% ) = 15.75%. @OJSP at 15.9% after 487 pulls is within a reasonable tolerance to support the underlying probabilities.
    As I understand it, the 4* or 5* decision is made before the 5% chance of a bonus hero. So you still have a 15% chance of getting a 5*, not 15.75% .. just than 1-on-20 of those 15% occurrences will give you two 5* covers.

  • jamesh
    jamesh Posts: 1,600 Chairperson of the Boards
    helix72 said:
    And the bonus hero chance is on top. So with a 15% draw rate and a 5% (notice it says 1/20 not ~1/20) for bonus heroes, your overall pull rate including bonus heroes will regress to the mean of 15% x ( 1 + 5% ) = 15.75%. @OJSP at 15.9% after 487 pulls is within a reasonable tolerance to support the underlying probabilities.
    Not quite: while it is true  that 5% of the time you receive a 5* cover you'll get a bonus, it is also true that 5% of the time you receive a 4* cover you'll get a bonus.  So it is still 15% with bonus heroes.
    From what the devs have said in the past, the odds displayed in game have the bonus hero odds pre-multiplied in.  This is why it shows different odds for single and 10/40 packs of heroic tokens: they have the same base odds, but different bonus hero odds.
  • HoundofShadow
    HoundofShadow Posts: 8,004 Chairperson of the Boards
    edited March 2019
    Hope this helps:

    Note: I don't know how to extract quote within quotes, so this is the best I could do.  :D
    Every time you open a pack, you will have a chance (5% for single packs and 8% per draw of a 10x/40x pack) to get a Bonus Hero. When you get a Bonus Hero, you will receive a cover of a favorite character you have chosen in rarity of the cover that you drew. For example, if you draw an Iron Man (Hulk Buster) and receive a Bonus Hero, you will get a cover from any 4-Stars you have marked as your favorite.
    *New Update* How did we arrive at 5% for single packs? Here's Anthony from Demiurge with an exclusive drop rate breakdown, using Heroic Packs as an example:


    Let's take the Heroic Pack. You have a ~71% chance to get a 2-Star, a ~23% chance to get a 3-Star and a ~6% chance to get a 4-Star. When you open a pack, you have an overall 5% chance to get a Bonus Hero. The way we get to that math is to set the chance to get a Bonus Hero per rarity that you draw. When you draw a 3-Star or 4-Star, you have roughly a 17% chance to get a Bonus Hero. When you multiply the chance to get a cover of that rarity with the chance to get a Bonus Hero, you get the [percent] chance to get a Bonus Hero from any one pull from a Heroic pack (~4% for 3-Stars and ~1% for 4-Stars).


    In other words, because 2-Stars don’t have Bonus Heroes available, the Bonus Hero drop rate is actually 17% for 3-Star and 4-Star pulls, and factoring the 2-Stars into the equation is what drops it down to 5%


    https://forums.d3go.com/discussion/60255/new-feature-bonus-heroes-updated-3-1-17/p1

  • Markot
    Markot Posts: 86 Match Maker
    I keep track of my pulls since 6/2016

    There were some tokens with 10% probability (release for new 5*, more than a year ago) and two times 25% probability by mistake. But If I count just tokens with 15% 5* probability I get the following succes/pulls ratio:
    408/2694 it is 15.14%

    During the time I had several long streaks without 5* - the longest was, I think, 46 pulls. Right now I have a streak of 36 latest legends tokens without a 5* and I don't know how many more I will need to pull to finaly get one. But in the long time average everything looks OK. 
  • abmoraz
    abmoraz Posts: 712 Critical Contributor
    OJSP said:
    MissoesRicRose said:
    In fact, there is no probability, the game is already pre-programmed to give you a certain character. If it were not so, the game would not give you the same characters after a backup.
    That is correct. So, what you should do is ask Customer Support if your tokens are pre-determined to give you a 5* at an acceptable rate or not. Doing it in the forum most likely won't give you any official or satisfactory answer, considering you've asked about this more than 3 times already.
    That is not correct.  There is absolutely probability... however, your token *IS* pre-determined.  These are not mutually exclusive concepts.

    Imagine buying a pack of baseball (or Yugioh or Magic:TG) cards.  The pack contains random cards, however, once you pick the pack you are buying, the contents are not going to change.

    Tokens in MPQ work similarly.  When you get a token, it is randomly assigned a number.  That number determines what cover/prize you get out of the pack/vault.  The only way to get a different reward for that token is to wait until the contents of the pack/vault changes.
  • Quebbster
    Quebbster Posts: 8,070 Chairperson of the Boards

    I did 400 pulls in the Favorite Legends store. The first 20 were all fourstars, then I finally got my first Purple. Once it was all done I figured out I had a fivestar rate of 16% so a bit above the displayed odds, but I definitely had dry streaks.

    On the other hand, in some special stores the first two pulls have been fivestars. Some streaks are good, others less so. Pulls being predetermined just means you need to get through the Latest Legends pulls sooner or later though.

  • sambrookjm
    sambrookjm Posts: 2,157 Chairperson of the Boards
    edited March 2019
    My son got two pulls from the Galactic Heroes vault.  Personal Progression was a 5-star Star Lord, and Alliance Progression was a 5-star Captain Marvel.  If you ask him, the chance of a "successful" pull were 100%, with a 0% chance at a Bonus Hero.

    I took 11 tokens from the vault until I got a Captain Marvel.  My two pulls from the event were both 4-stars.  That was my only 5-star pull, so my chance of a "successful" pull was about 7.7%.  But I did get a Bonus Hero (Namor, who is now 0/3/2), so the odds of getting a Bonus Hero were the same as getting a 5-star.

    Are any of these actually correct over the long term?  Of course not.  Even combining our pull rates, we get a 5-star 20% of the time, which is still considerably higher than the published value.  But thanks to the danger of Small Sample Sizes (tm) we're both correct for our respective accounts.
  • Banquetto
    Banquetto Posts: 29 Just Dropped In
    abmoraz said:
    OJSP said:
    MissoesRicRose said:
    In fact, there is no probability, the game is already pre-programmed to give you a certain character. If it were not so, the game would not give you the same characters after a backup.
    That is correct. So, what you should do is ask Customer Support if your tokens are pre-determined to give you a 5* at an acceptable rate or not. Doing it in the forum most likely won't give you any official or satisfactory answer, considering you've asked about this more than 3 times already.
    Imagine buying a pack of baseball (or Yugioh or Magic:TG) cards.  The pack contains random cards, however, once you pick the pack you are buying, the contents are not going to change.
    That's a good analogy. Once you buy a pack of trading cards, you can open it now, open it later, buy some more and open them first, open it while standing on your head.. nothing is going to change the contents of the pack.
  • KGB
    KGB Posts: 3,189 Chairperson of the Boards
    edited March 2019
    Banquetto said:
    abmoraz said:
    OJSP said:
    MissoesRicRose said:
    In fact, there is no probability, the game is already pre-programmed to give you a certain character. If it were not so, the game would not give you the same characters after a backup.
    That is correct. So, what you should do is ask Customer Support if your tokens are pre-determined to give you a 5* at an acceptable rate or not. Doing it in the forum most likely won't give you any official or satisfactory answer, considering you've asked about this more than 3 times already.
    Imagine buying a pack of baseball (or Yugioh or Magic:TG) cards.  The pack contains random cards, however, once you pick the pack you are buying, the contents are not going to change.
    That's a good analogy. Once you buy a pack of trading cards, you can open it now, open it later, buy some more and open them first, open it while standing on your head.. nothing is going to change the contents of the pack.

    Actually I think this analogy is confusing. If you buy a pack of trading cards the contents of the pack are fixed (ie the cards in the pack don't change because they are physically inside the pack).

    What you are doing in MPQ is buying a pack of numbers. Later you exchange each number for a cover. As mentioned, the numbers are fixed (don't change) but what they award you most definitely does change since pack dilution comes into play as new characters are added.

    Since most people only care about the card/cover and not the random number itself the analogy isn't quite the same.

    KGB
  • Moon Roach
    Moon Roach Posts: 2,863 Chairperson of the Boards
    KGB said:

    <snip>
    What you are doing in MPQ is buying a pack of numbers. Later you exchange each number for a cover. As mentioned, the numbers are fixed (don't change) but what they award you most definitely does change since pack dilution comes into play as new characters are added.

    </snip>
    That's why I like the idea of being able to see what the next 10 (or some other number) pulls will be using the current rewards table, even if it costs a few CP.
  • Darth_VanDer
    Darth_VanDer Posts: 4 Just Dropped In
    This thread has absolutely gone the wrong way. It should have been filled with nothing but posts of people reporting how they beat the draw rates...especially regarding 5* Carol. Even better if it's actually true. KC_Hammer, bluewolf, and sambrookjm had the right idea. Here's my contribution...

    I pulled 5* Carol with my one and only pull from Galactic Heroes...

    Let the piling on commence!

  • sambrookjm
    sambrookjm Posts: 2,157 Chairperson of the Boards
    Darth_VanDer said:
    This thread has absolutely gone the wrong way. It should have been filled with nothing but posts of people reporting how they beat the draw rates...especially regarding 5* Carol. Even better if it's actually true. KC_Hammer, bluewolf, and sambrookjm had the right idea. Here's my contribution...

    I pulled 5* Carol with my one and only pull from Galactic Heroes...

    Let the piling on commence!


    In that case, I pulled 113 tokens from the vault, and they were *all* 5-star Carols, so I could immediately max champ her with my 5M+ ISO I had lying around.  Yeah...that's it.  That's the ticket.
  • DAZ0273
    DAZ0273 Posts: 10,101 Chairperson of the Boards
    sambrookjm said:
    Darth_VanDer said:
    This thread has absolutely gone the wrong way. It should have been filled with nothing but posts of people reporting how they beat the draw rates...especially regarding 5* Carol. Even better if it's actually true. KC_Hammer, bluewolf, and sambrookjm had the right idea. Here's my contribution...

    I pulled 5* Carol with my one and only pull from Galactic Heroes...

    Let the piling on commence!


    In that case, I pulled 113 tokens from the vault, and they were *all* 5-star Carols, so I could immediately max champ her with my 5M+ ISO I had lying around.  Yeah...that's it.  That's the ticket.
    I pulled Old Man Logan and he wasn't even in the vault!

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