What are the odds of getting a max covered Silver Surfer...

Unknown

What are the odds of getting a max covered Silver Surfer on your first try? In other words let's just assume someone was able to earn/buy 13 legendary tokens, What are the odds that they all pop up as Silver Surfer tokens? Is it 5% to the 13th power? I'm thinking it would be lower than that because this doesn't even factor in that you might get covers in the color that you don't need, e.g. a 6th red.

simonsez

mpqstooge wrote:

What are the odds of getting a max covered Silver Surfer on your first try? In other words let's just assume someone was able to earn/buy 13 legendary tokens, What are the odds that they all pop up as Silver Surfer tokens? Is it 5% to the 13th power? I'm thinking it would be lower than that because this doesn't even factor in that you might get covers in the color that you don't need, e.g. a 6th red.

Correct, but since not accounting you color distribution gets you to 1 in 100,000,000,000,000,000, it's pretty safe to just call it zero.

Chrono_Tata

So this is maths problem and I like maths so I'm gonna attempt to solve it for you.

Yes, as you said, not accounting for the colour distribution, the chance of opening 13 Silver Surfers in a row is 5% to the power of 13, which is about 1.2207031e-17 = 0.000000000000000012207031 = 0.0000000000000012207031%

To take into account the colour distribution, first we have to assume that the colour distribution is even for all three colours, which may not be the case. The devs has skewed the colour distribution before, with Devil Dinosaur draw rate during the Anniversary Week, which was heavily skewed towards purple. Assuming even distribution though the chance of drawing a particular cover of Silver Surfer is 5%/3 = 1.666....%

So now we have to look at all the possible draw combinations which will result in getting a fully-covered Silver Surfer after 13 draws. Not taking into account the draw order, these are (in order of Blue/Red/Black):

5/5/3
5/3/5
3/5/5
5/4/4
4/4/5
4/5/4

So 6 possible combinations. For each of these combinations, there are quite a lot of potential orders to pick out those covers, for example, to pick 5/5/3, you can draw:

blue,blue,blue,blue,blue,red,red,red,red,red,black,black,black
blue,blue,blue,blue,blue,red,red,red,red,black,black,black,red
blue,blue,blue,blue,blue,red,red,red,black,black,black,red,red
etc., etc., etc.

Basically, a lot more than I can can write down. Thankfully, you can use a simple formula to calculate the number of potential permutations you can draw 5/5/3, which is:

(number of potential ways you can arrange 13 draws)/((number of ways you can arrange 5 blue draws)*(number of ways you can arrange 5 red draws)*(number of ways you can arrange 3 black draws))

or (13!)/(5!*5!*3!) = 72,072 possible permutations

So, since it doesn't matter in which order you multiply a series of numbers, you can see that the numbers of permutations for 5/5/3, 5/3/5 and 3/5/5 are the same. Likewise, the numbers of permutations for 5/4/4, 4/5/4 and 5/4/4 are the same.

The numbers of possible permutations for 5/4/4 is (13!)/(5!*4!*4!) = 90,090

So the possible numbers of ways you can draw Silver Surfer covers from 13 draws in order to fully cover him is 90,090*3 + 72,072*3 = 486,486 different ways

The possibility of drawing each permutation is (0.05/3)^13 = 7.656561e-24

So to answer your question, the possibility of fully covering Silver Surfer from 13 consecutive draw is 7.656561e-24 * 486,486 = 3.7248097e-18 = 0.0000000000000000037248097 or 0.00000000000000037248097%

For comparison:

0.0000000000000012207031% = the possibility of drawing 13 SS covers in a row
0.00000000000000037248097% = the possibility of drawing the correct 13 SS covers in a row in order to fully cover him

You're welcome.

(People who are better at maths than me please feel free to correct if I'm wrong)

GMadMan040

The equation is so much simpler than all of that. Just divide zero by itself. Because the universe has a better chance of imploding on itself in the next 5 minutes and reducing all matter to its original pre big bang state than someone nabbing 13 straight perfect pulls in a row to fully cover SS.

(Side Note: I totally appreciate that someone went to the trouble to not only work out the math, but to explain the process, that's always valuable.)

Druss

The odds are 0%

Why?

There are only 3 covers available:

Invisible Woman Yellow,
Invisible Woman Blue and
You guessed it! - Invisible Woman Green.

Unknown

Chrono_Tata wrote:

So this is maths problem and I like maths so I'm gonna attempt to solve it for you.

Yes, as you said, not accounting for the colour distribution, the chance of opening 13 Silver Surfers in a row is 5% to the power of 13, which is about 1.2207031e-17 = 0.000000000000000012207031 = 0.0000000000000012207031%

To take into account the colour distribution, first we have to assume that the colour distribution is even for all three colours, which may not be the case. The devs has skewed the colour distribution before, with Devil Dinosaur draw rate during the Anniversary Week, which was heavily skewed towards purple. Assuming even distribution though the chance of drawing a particular cover of Silver Surfer is 5%/3 = 1.666....%

So now we have to look at all the possible draw combinations which will result in getting a fully-covered Silver Surfer after 13 draws. Not taking into account the draw order, these are (in order of Blue/Red/Black):

5/5/3
5/3/5
3/5/5
5/4/4
4/4/5
4/5/4

So 6 possible combinations. For each of these combinations, there are quite a lot of potential orders to pick out those covers, for example, to pick 5/5/3, you can draw:

blue,blue,blue,blue,blue,red,red,red,red,red,black,black,black
blue,blue,blue,blue,blue,red,red,red,red,black,black,black,red
blue,blue,blue,blue,blue,red,red,red,black,black,black,red,red
etc., etc., etc.

Basically, a lot more than I can can write down. Thankfully, you can use a simple formula to calculate the number of potential permutations you can draw 5/5/3, which is:

(number of potential ways you can arrange 13 draws)/((number of ways you can arrange 5 blue draws)*(number of ways you can arrange 5 red draws)*(number of ways you can arrange 3 black draws))

or (13!)/(5!*5!*3!) = 72,072 possible permutations

So, since it doesn't matter in which order you multiply a series of numbers, you can see that the numbers of permutations for 5/5/3, 5/3/5 and 3/5/5 are the same. Likewise, the numbers of permutations for 5/4/4, 4/5/4 and 5/4/4 are the same.

The numbers of possible permutations for 5/4/4 is (13!)/(5!*4!*4!) = 90,090

So the possible numbers of ways you can draw Silver Surfer covers from 13 draws in order to fully cover him is 90,090*3 + 72,072*3 = 486,486 different ways

The possibility of drawing each permutation is (0.05/3)^13 = 7.656561e-24

So to answer your question, the possibility of fully covering Silver Surfer from 13 consecutive draw is 7.656561e-24 * 486,486 = 3.7248097e-18 = 0.0000000000000000037248097 or 0.00000000000000037248097%

For comparison:

0.0000000000000012207031% = the possibility of drawing 13 SS covers in a row
0.00000000000000037248097% = the possibility of drawing the correct 13 SS covers in a row in order to fully cover him

You're welcome.

(People who are better at maths than me please feel free to correct if I'm wrong)

Wow, thank you. You sir are scholar and a gentleman.

puppychow

Chrono_Tata wrote:

(People who are better at maths than me please feel free to correct if I'm wrong)

Is that even possible?

snlf25

Dragon_Nexus

Chrono_Tata wrote:

So this is maths problem and I like maths so I'm gonna attempt to solve it for you.

Yes, as you said, not accounting for the colour distribution, the chance of opening 13 Silver Surfers in a row is 5% to the power of 13, which is about 1.2207031e-17 = 0.000000000000000012207031 = 0.0000000000000012207031%

To take into account the colour distribution, first we have to assume that the colour distribution is even for all three colours, which may not be the case. The devs has skewed the colour distribution before, with Devil Dinosaur draw rate during the Anniversary Week, which was heavily skewed towards purple. Assuming even distribution though the chance of drawing a particular cover of Silver Surfer is 5%/3 = 1.666....%

So now we have to look at all the possible draw combinations which will result in getting a fully-covered Silver Surfer after 13 draws. Not taking into account the draw order, these are (in order of Blue/Red/Black):

5/5/3
5/3/5
3/5/5
5/4/4
4/4/5
4/5/4

So 6 possible combinations. For each of these combinations, there are quite a lot of potential orders to pick out those covers, for example, to pick 5/5/3, you can draw:

blue,blue,blue,blue,blue,red,red,red,red,red,black,black,black
blue,blue,blue,blue,blue,red,red,red,red,black,black,black,red
blue,blue,blue,blue,blue,red,red,red,black,black,black,red,red
etc., etc., etc.

Basically, a lot more than I can can write down. Thankfully, you can use a simple formula to calculate the number of potential permutations you can draw 5/5/3, which is:

(number of potential ways you can arrange 13 draws)/((number of ways you can arrange 5 blue draws)*(number of ways you can arrange 5 red draws)*(number of ways you can arrange 3 black draws))

or (13!)/(5!*5!*3!) = 72,072 possible permutations

So, since it doesn't matter in which order you multiply a series of numbers, you can see that the numbers of permutations for 5/5/3, 5/3/5 and 3/5/5 are the same. Likewise, the numbers of permutations for 5/4/4, 4/5/4 and 5/4/4 are the same.

The numbers of possible permutations for 5/4/4 is (13!)/(5!*4!*4!) = 90,090

So the possible numbers of ways you can draw Silver Surfer covers from 13 draws in order to fully cover him is 90,090*3 + 72,072*3 = 486,486 different ways

The possibility of drawing each permutation is (0.05/3)^13 = 7.656561e-24

So to answer your question, the possibility of fully covering Silver Surfer from 13 consecutive draw is 7.656561e-24 * 486,486 = 3.7248097e-18 = 0.0000000000000000037248097 or 0.00000000000000037248097%

For comparison:

0.0000000000000012207031% = the possibility of drawing 13 SS covers in a row
0.00000000000000037248097% = the possibility of drawing the correct 13 SS covers in a row in order to fully cover him

You're welcome.

(People who are better at maths than me please feel free to correct if I'm wrong)

https://www.youtube.com/watch?v=IRsPheErBj8

Seriously though, that was a fun read. I learned much =)

Omega Blacc

Hate to be a cynic, but I've never felt something like this was worth fussing over...you know, with artificial rarity and all.

tiomono

So i hate math and am not overly concerned with the stats. The number one player in my simulator for this season has a 2-2-5 surfer level 390. Whales gonna whale. So much for anyone else having a shot at spot 1 without 5 stars.

Chrono_Tata

Omega Blacc wrote:

Hate to be a cynic, but I've never felt something like this was worth fussing over...you know, with artificial rarity and all.

Well, you're right. The chance is pretty absurdly small that it's pretty much impossible.

Just for comparison, the chance of winning the jackpot for the Powerball lottery is 1 out of 175,223,510 or 5.70699674e-9, so the chance of winning 2 jackpots in a row is 3.2569812e-17.

So at 3.7248097e-18, the chance of fully covering Silver Surfer in one go is actually lower than the chance of winning the lottery jackpot twice in a row.

Chrono_Tata

OJSP wrote:

Chrono_Tata wrote:

the chance of fully covering Silver Surfer in one go is actually lower than the chance of winning the lottery jackpot twice in a row.

So, considering the expenses for both, which one would be cheaper? Silver Surfer or winning the lottery twice?

Actually, I was trying to figure out the expected number of tokens you have to open to fully cover Silver Surfer but it's more tricky than I thought. I think some people have worked it out approximately by running simulations though.

It's easy enough to figure out how many tokens you have to open to get 13 covers (it's 300-something, I don't have the calculation with me right now), but this isn't taking into account the possibility that you are "overdrawing" certain covers.

Anyway, buying the lotto gives you back monetary returns as well, so taking into account the net money lost, I'm pretty sure buying tickets is cheaper lol. Taking into account total utility, I guess it depends on how much you "value" having a Silver Surfer.