General Discussion

What are the chances?

OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭

I don't know if anyone has ever done this before, but I'd like to share some interesting calculations with you. It's been a while since I learned probability theory, so I'm not a 100% sure (pun intended) that my calculations are correct. So anyone who is an expert at this, feel free to correct me.

What got me thinking was that many of us complain a lot about a certain car missing from his collection, and just not being able to pull one. For me it's the RQ20 Ford Escort Rally, but I'm sure all of us have something. So I was wondering what the chances were to get that missing car, and comparing it to some other events' chances.

I hope the chart speaks for itself. The only thing that needs to be explained a bit is the Hungarian lottery thing. That means you have to guess 5 numbers out of 90, and if you guess right you win an unimagineable amout of money.

Here's the whole chart, to put everything into perspective:

And the chart of events with probability under 1%:

So yeah, seems like pulling that Escort from a CF is harder than pulling a legendary from a Ceramic, harder than pulling two Super Rares from an Alu pack. And the numbers get worse with every new Ultra Rare added to the game. That's why we all have unicorns.

Comments

  • TimButTimBut Member Posts: 840 ✭✭✭✭✭
    already 20 Ford CFs and about 15 offroad tyres ceramic and no Ford escort for me.  

    How did you calculate chances for a certain car? Using Ford as an example? Like 1 escort from N other fords?
  • RawelRawel Member Posts: 789 ✭✭✭✭✭
    Thing about missing a certain car (lets say the escort rally is) is that you've probably never pulled a lot of ultra rares, but you only miss that one bc it's useful
  • OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭
    TimBut said:
    already 20 Ford CFs and about 15 offroad tyres ceramic and no Ford escort for me.  

    How did you calculate chances for a certain car? Using Ford as an example? Like 1 escort from N other fords?
    There are 160 different Ultra rares. So to get the chances for a certain UR, you divide the droprates by 160 everywhere. It's the same for any UR, Escort is just my unicorn.
  • HeissRodHeissRod Member Posts: 4,584 ✭✭✭✭✭
    Interesting that it's way easier to pull a Legendary from a CF compared to a Ceramic.
  • Hutch_TimHutch_Tim Administrator, Hutch Staff Posts: 600 admin
    This is great!

    I would also note that the average late-game player opens roughly 5 to 6 Ceramics or Premiums for every one Carbon Fiber. I think this is why it can feel like you get more good cars from Ceramics - the sheer force of numbers overcomes their individual lower probability.
  • hillclimberhillclimber Member Posts: 2,095 ✭✭✭✭✭
    edited January 15
    @Ozzman, I'm sorry but I think your numbers are off! (or I'm missing something)
    your graphic say's the chance to pull two S from one ceramic is 0.00065% but...

    the chance to pull a legendary with the second last card is 0.1% than the last card is automatically a legendary too (let's neglect the Audis for a moment) . So one 1 ceramic out of 1000 should give a double legendary not 1 out of 153'846.
  • evilprofesseurevilprofesseur Member Posts: 1,202 ✭✭✭✭✭
    @Ozzman, I'm sorry but I think your numbers are off! (or I'm missing something)
    your graphic say's the chance to pull two S from one ceramic is 0.00065% but...

    the chance to pull a legendary with the second last card is 0.1% than the last card is automatically a legendary too (let's neglect the Audis for a moment) . So one 1 ceramic out of 1000 should give a double legendary not 1 out of 153'846.
    I don't think that this is the way it works. If card 2 was a legend you'd simply see it as the last one. Card 1 is still selected randomly and could be a lowly rq15.
  • Hutch_TimHutch_Tim Administrator, Hutch Staff Posts: 600 admin
    @Ozzman, I'm sorry but I think your numbers are off! (or I'm missing something)
    your graphic say's the chance to pull two S from one ceramic is 0.00065% but...

    the chance to pull a legendary with the second last card is 0.1% than the last card is automatically a legendary too (let's neglect the Audis for a moment) . So one 1 ceramic out of 1000 should give a double legendary not 1 out of 153'846.
    I don't think that this is the way it works. If card 2 was a legend you'd simply see it as the last one. Card 1 is still selected randomly and could be a lowly rq15.
    That's correct. Each card is generated according to those probabilities, and then you are shown them in order of increasing RQ.
  • OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭
    @Ozzman, I'm sorry but I think your numbers are off! (or I'm missing something)
    your graphic say's the chance to pull two S from one ceramic is 0.00065% but...

    the chance to pull a legendary with the second last card is 0.1% than the last card is automatically a legendary too (let's neglect the Audis for a moment) . So one 1 ceramic out of 1000 should give a double legendary not 1 out of 153'846.

    Yes, that made me think a bit when I did the calculations, but I came to a conclusion that it doesn't work like that.

    When you open a pack the cards are always sorted ascending by RQ, but that doesn't necessarily mean that the first card you turn comes from "Card 5", the second from "Card 4"... and so on. So when you pull a legendary, you can get that from either "Card 2" or "Card 1". I think the card flippings are totally independent events, just like rolling a dice 5 times (but different number of outcomes and probabilities). So to pull two legendaries, you have to pull one from both cards, meaning the probability is 0,65% * 0,1%.

    Maybe @Hutch_Tim can confim this.

  • bantel_catbantel_cat Member Posts: 756 ✭✭✭✭
    Ozzman said:Yes, that made me think a bit when I did the calculations, but I came to a conclusion that it doesn't work like that.

    When you open a pack the cards are always sorted ascending by RQ, but that doesn't necessarily mean that the first card you turn comes from "Card 5", the second from "Card 4"... and so on. So when you pull a legendary, you can get that from either "Card 2" or "Card 1". I think the card flippings are totally independent events, just like rolling a dice 5 times (but different number of outcomes and probabilities). So to pull two legendaries, you have to pull one from both cards, meaning the probability is 0,65% * 0,1%.

    Maybe @Hutch_Tim can confim this.

    Yes that is the way I see it and the way I calculated in my spreadsheet
    2 S = 0.65 x 0.1 
    1 S = 0.65 + 0.1 = 0.75

  • hillclimberhillclimber Member Posts: 2,095 ✭✭✭✭✭
    thanks for helping me understand. And it explains a lot, if it would be 1/1000 than we should see frequently double Legendary pulls here in the forum posted but it never happens.
    However the graphic says the second last card gives you a 0.1% chance for a legendary (and we know the 5th card is never lower than the 4th). not you get 5 draws to a legendary with 3x 0%, 1x 0.1% and 1x 0.65%.
    ...and now I keep my nose out of trouble and no trouble will come to me 🤐
  • OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭
    edited January 15
    Ozzman said:Yes, that made me think a bit when I did the calculations, but I came to a conclusion that it doesn't work like that.

    When you open a pack the cards are always sorted ascending by RQ, but that doesn't necessarily mean that the first card you turn comes from "Card 5", the second from "Card 4"... and so on. So when you pull a legendary, you can get that from either "Card 2" or "Card 1". I think the card flippings are totally independent events, just like rolling a dice 5 times (but different number of outcomes and probabilities). So to pull two legendaries, you have to pull one from both cards, meaning the probability is 0,65% * 0,1%.

    Maybe @Hutch_Tim can confim this.

    Yes that is the way I see it and the way I calculated in my spreadsheet
    2 S = 0.65 x 0.1 
    1 S = 0.65 + 0.1 = 0.75

    The "1 S" is a bit more complicated though. You can't just add up the probabilities. If you had 50% chance on "Card 1" and 50% on "Card 2" as well, that would not mean a 100% chance for a Legendary right? Wish it would. :)

    The chance to get at least 1 S from a Ceramic = the chance to get an S from "Card 1", but not "Card 2" + the chance to get an S from "Card 2", but not "Card 1" + the chance to get an S from both "Card 1" and "Card 2"

    So in numbers: 0,0065*(1-0,001) + 0,001*(1-0,0065) + 0,0065*0,001 = 0.0074935 (0,74935%)

    Because the chances are so little, it's close to your calculations, but with higher chances (like 50%, 50%), it makes a big difference.

    And it explains a lot, if it would be 1/1000 than we should see frequently double Legendary pulls here in the forum posted but it never happens.
    Well it just happend a few days ago to @SubaruLover04, and now we can appreciate it even more. :)
  • bantel_catbantel_cat Member Posts: 756 ✭✭✭✭
    Ozzman said:The "1 S" is a bit more complicated though. You can't just add up the probabilities. If you had 50% chance on "Card 1" and 50% on "Card 2" as well, that would not mean a 100% chance for a Legendary right? Wish it would. :)

    The chance to get at least 1 S from a Ceramic = the chance to get an S from "Card 1", but not "Card 2" + the chance to get an S from "Card 2", but not "Card 1" + the chance to get an S from both "Card 1" and "Card 2"

    So in numbers: 0,0065*(1-0,001) + 0,001*(1-0,0065) + 0,0065*0,001 = 0.0074935 (0,74935%)

    Because the chances are so little, it's close to your calculations, but with higher chances (like 50%, 50%), it makes a big difference.

    You are right of course, I was just using it as an approximation for calculating how many you are likely to get, not the individual chances of a pack

    If you opened 1000 Ceramics, you could 'expect':

    6.5 S from Card 5 and 1 from Card 4, i.e 7.5 in total
    Which would be the same as using a 0.75 'compound' chance

    Combining like this falls down as you say for higher odds and for low samples
  • antonyhopantonyhop Member Posts: 102 ✭✭✭
    Recorded this from the in-game forum (could not think of a faster way to save that video)
    Damn luck !!
    https://streamable.com/c9ajc
  • hillclimberhillclimber Member Posts: 2,095 ✭✭✭✭✭
    Mister Luckbox himself. Who else? 😂
  • CharlieRCharlieR Member Posts: 498 ✭✭✭✭
    Mister Luckbox himself. Who else? 😂
    Mister Luckbox himself. Who else? 😂
    This really needs some explanaition - no way this dude is on the same drop rates as us... he is always pulling sick stuff...
  • O__VERO__VER Member Posts: 1,397 ✭✭✭✭✭
    CharlieR said:
    Mister Luckbox himself. Who else? 😂
    This really needs some explanaition - no way this dude is on the same drop rates as us... he is always pulling sick stuff...
    Yeah surely he has worked out a way to manipulate the pulls.
  • TimButTimBut Member Posts: 840 ✭✭✭✭✭
    Can you calculate how the drop rates also decrease after getting Legendary? 

    I just wonder what are the chances to get 3 Legendaries in a row.  Is it like you boosted your chances to 70% - you got S, then your droprate is 55% you got another S, then your droprate is already 25% but you were lucky to get another S. 

    I just had such situation 2 times.  And how does it mix when you open CF and Ceramic in the meantime.  Usually it take 40-50 Ceramic and 15 Cfs for me to get S. 
  • HeissRodHeissRod Member Posts: 4,584 ✭✭✭✭✭
    Ozzman said:

    Just wanted to share a chart I find interesting with you guys.

    So in case you wondered what chances you have of pulling a legendary as you open more and more packs, here it is. These lines never reach the 100% of course, just get very close to it.

    And this also explains why you feel like it's easier to pull a legendary from a Ceramic. To reach 50% chace of pulling at least one you have to open 93 Ceramics. If you smurf properly, you can open 3-4 Ceramic per day. That means you can reach that treshold in 24-31 days. How many CF pack do you usually open a month? Well as a F2P I open 1-2 perhaps. To have the same feeling of legendary droprates, you'd need to open at least 23 CF packs during that time.

    Whose chart is that?  Wouldn't this mean that Hutch is keeping track of your pack openings and slightly increasing your chances to pull a Legendary each time you don't?  I can pretty much guarantee that doesn't happen.  It's been something requested before and Hutch said it would take some significant work.
  • ppedrasppedras Member Posts: 1,005 ✭✭✭✭
    I know someone in this forum that opened 6 Ceramics in a row yesterday and got 2 Legendary.
  • OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭
    HeissRod said:
    Whose chart is that?  Wouldn't this mean that Hutch is keeping track of your pack openings and slightly increasing your chances to pull a Legendary each time you don't?  I can pretty much guarantee that doesn't happen.  It's been something requested before and Hutch said it would take some significant work.
    Well it's mine, I just made it. :) You might be mistaken what it really shows though. The drop rates are the same of course each time you open a pack. So your chances of getting a legendary from a Ceramic does not really depend on the number of previously opened packs where you did not get any. What this chart shows you is the chaces of getting at least one legendary at least once, if you open 1, 2, 3... 100, 500 packs. Of course the higher number of packs you open, the higher the chance is to get a legendary, but it'll never reach a 100%, just getting closer and closer.
  • OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭
    TimBut said:
    Can you calculate how the drop rates also decrease after getting Legendary? 

    I just wonder what are the chances to get 3 Legendaries in a row.  Is it like you boosted your chances to 70% - you got S, then your droprate is 55% you got another S, then your droprate is already 25% but you were lucky to get another S. 

    I just had such situation 2 times.  And how does it mix when you open CF and Ceramic in the meantime.  Usually it take 40-50 Ceramic and 15 Cfs for me to get S. 

    That's a tough one. :) The best I can do is add two dashed lines to the chart, that shows your chances of pulling at least one legendary twice, from the same number of packs. My example earlier showed that to have a 50% chance for a legendary you need to open 93 Ceramic packs. Now you can see on this chart that the chances of 94 Ceramic packs giving you legenary(ies) twice is only 15,7%. So that's sort of the decrease you're asking probably.

    Pulling 3 legendaries in a row is easier (more precisely, pulling at least 1 legendary three times, from three consecutive packs):
    Ceramic: 0,000042%
    CF: 0,002666%

    Mixing packs would be way too hard, that's enough calculating for today. :)

  • AndreasSimmerAndreasSimmer Member Posts: 514 ✭✭✭✭✭
    good to know im well overdue for a legendary
  • OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭
    Twinkie said:
    What do you exactly mean by "twice"?
    I mean pulling legendary(ies) from two separate packs.
  • OzzmanOzzman Member Posts: 1,055 ✭✭✭✭✭
    Twinkie said:
    Ozzman said:
    Twinkie said:
    What do you exactly mean by "twice"?
    I mean pulling legendary(ies) from two separate packs.
    So you mean 2 or more legendaries out of x packs?
    I know it's a bit confusing. Well you can pull 0, 1 or 2 legendaries from a Ceramic or CF pack. So pulling "at least one legendary" means 1 or 2 from the same pack, while doing this "at least twice" means that you find "at least one legendary" in at least two separate packs (not just one).
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