# What are the chances?

**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

840✭✭✭✭✭How did you calculate chances for a certain car? Using Ford as an example? Like 1 escort from N other fords?

789✭✭✭✭✭1,055✭✭✭✭✭4,584✭✭✭✭✭600Hutch Staff › adminI 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.

2,095✭✭✭✭✭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.

1,202✭✭✭✭✭600Hutch Staff › admin1,055✭✭✭✭✭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.

756✭✭✭✭2 S = 0.65 x 0.1

1 S = 0.65 + 0.1 = 0.75

2,095✭✭✭✭✭However the graphic says the second last

cardgives you a 0.1% chance for a legendary (and we know the 5th card is never lower than the 4th). not you get 5draws toa 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 🤐

1,055✭✭✭✭✭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.

Well it just happend a few days ago to @SubaruLover04, and now we can appreciate it even more.756✭✭✭✭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

102✭✭✭Damn luck !!

https://streamable.com/c9ajc

2,095✭✭✭✭✭498✭✭✭✭1,397✭✭✭✭✭1,055✭✭✭✭✭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

feellike 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.840✭✭✭✭✭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.

4,584✭✭✭✭✭1,005✭✭✭✭1,055✭✭✭✭✭1,055✭✭✭✭✭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.

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