Average amount of epics required for a T4 or T5

*WARNING* mathematics ahead

So, miika posted at some point that the average amount of epics you'd need to obtain from a pool of 35 to get 6 the same ones (which you need for a tier 5 epic), is 72. I decided to do a little calculation. I don't have enough probability background to do it with "clean" mathematics, but I do have enough coding background to simulate it, so that's what I did. I created a script that makes a vector with 35 elements, draws a random integer between 1 and 35 and then adds 1 to the index equal to that random integer. Repeat this until one of the elements of the vector becomes 6, then find out how many iterations it took. Repeat that many times, find the average, and we are done.

Spoiler: MATLAB code

Code:

x = 10000;
F = zeros(x,1);

for i = 1:x

    A = zeros(35,1);

    for n = 1:200
        I = randi(35,1);
        A(I) = A(I) + 1;
        M(n) = max(A);
    end

    F(i) = find(M==6,1);

end

mean(F)

Results:

On average, you need 73 epics to get 6 copies of some epic, and be able to create your first tier 5
On average, you need 36 epics to get 4 copies of some epic, and be able to create your first tier 4

Conclusion: @Miika 's 72 was WRONG you need 73!!!!

P.S. Yes, I know I take games too seriously sometimes

 

What?! It's 73 instead of 72?!

Let's burn that witch!

 

Worth remembering that your first t5 is just as likely to be Gear Lube as Sniper Cannon And that even if you acquire 50 epics pr there is a 22% chance of not seeing a specific epic even once.
Heck even if you gather 100 epics you have a 5.5% chance of not getting a single Sniper (or whatever your heart desires).

Some amount of guaranteed progress to look forward to would enhance my desire to play (and spend) - Whether that be an option of spending 3000pearls once a month on buying a single duplicate epic or w/e.

 

You raise an interesting question, what if you get a Gear Lube and have to wait for your 2nd chance to get 6 of the same? I modified the script:

Spoiler: modified code

Code:

x = 10000;
F = zeros(x,2);

for i = 1:x

    A = zeros(35,1);

    for n = 1:200
        I = randi(35,1);
        A(I) = A(I) + 1;
        M(n) = max(A);
     
        if M(n)==6
            A(I) = 0;
        end
    end

    F(i,:) = find(M==6,2);

end

mean(F)

This tells us that the second occasion that 6 epics are achieved is, on average, at 90 epics. So you'd only have to wait for 17 more after your gear lubes.

Note: I did not exclude the fact that in those 17 items could be another 6 gear lubes, so that the second occasion is for the same item as the first, but that chance is of course tiny
Extra note: you are of course right about no guarantees. It is a random system after all, and all we can calculate to get a feeling of how long stuff takes is averages.

 

It took me exactly 73 epics to get 6 grenades, well done MATLAB

 

Averaging 7-8 epics a month for active f2p players like me, it’ll take around 10 months average to get my first tier V epic

 

I'm at 73 epics aswell. 1 useable epic at T4, Repair Pulse at t2 (bought one of those for 3k pearls), Repair Bolt T1, Repair Box would have been t2 if I had kept them.

Might have scrapped enough Standard Mortars and maybe Triple Torpedo for t5 though.
---
@Miathan Educate me please. Assuming that 4/35 epics acquired are green, how long before my t2 Repair Pulse will reach mk5?

 

I'm pretty sure my next T5 will be tritorps haha, that would have made me so happy once.

 

Well, since acquiring a specific item from the random draw is only 1/35 chance, you could go hundreds of draws without getting one, so this answer is going to be depressing

I rewrote the code to start with one specific element of the vector at 2, and then check when it reaches 6

Spoiler: new code

Code:

x = 100000;
F = zeros(x,1);

for i = 1:x

    A = zeros(35,1);
    A(1) = 2;
    V = zeros(700,1);

    for n = 1:700
        I = randi(35,1);
        A(I) = A(I) + 1;
      
        V(n) = A(1);
          
    end

    F(i) = find(V==6,1);

end

mean(F)

This results in a value of 140. That's right, if you're average, you will need another 140 epics to finish that pulse. If you're worse off than average... I'll leave that to your imagination

 

If you're looking for a specific item this math doesn't take into account the probability of getting an epic of any color and getting an epic of a chosen color from pieces.

 

It does take into account randomly acquired pieces, since those follow the same distribution, but it does not take into account specific color pieces purchased directly from the shop. I don't think they would make a noticable difference though. The rate at which epic pieces appear in the shop is far too low for that.

 

Cheers! Maybe Ill make it before 2020 then thanks

 

@Miathan You should probably modify it now! Achievements give 1 specific epic dupe now! (just in case you already had 1st epic)

Edit (I know someone who would be interested)--> @Snapshot

 

Can you make a script to throw out like 10 random (but constant) integers to account for those standard mortars, gear lubes, carronades, frost blasters, etc... we threw out to make room in inventory? Like throw out all of #'s 6, 9, 13, 18, 21, 26, 32?

 

Well, this only works for weapons (and healing items). If we single out weapons: those are 19 out of 35 items, so if I modify the script a bit, it shows that the average amount of random epics needed to be able to create your first T5 epic weapon is 85. Now, if I set the required amount to 5, to account for the 1 obtained from an achievement, the number becomes 63. If I set it to 3 (to make a T4) it becomes 26.

So on average, only 26 randomly drawn epics are required to be able to make your first T4 epic weapon, provided you do the matching achievement for a duplicate.

Spoiler

x = 10000;
F = zeros(x,1);

for i = 1:x

A = zeros(35,1);

for n = 1:200
I = randi(35,1);
A(I) = A(I) + 1;
M(n) = max(A(1:19));
end

F(i) = find(M==5,1);
G(i) = find(M==3,1);

end

mean(F)
mean(G)

 

That's easy, all I need to know is how many items you consider useless

 

Nice thead! I didn't saw the Miika thread you talked, then I never heard about any of it. Thanks for the information

 

Really cool thread man...envious of your skillz and creativity.

 

Love this thread. Very nicely done @Miathan !

 

Oh well! That explains why I haven't received a single epic rail gun in 10 months. It's just sad.