Chances of pulling 2 x Dr.Strange covers in Higher Learning

Zombionicdoom

I need 2 x Dr. Strange covers, he’s currently 3/3/5, so blue, purple or both of either. He’d be my only fully covered 5 and is soft capped at Lvl. 350

I have enough CP (390) for 15 pulls.

Should I spend or should I hoard? I’m terrible at this kind of maths so I can’t figure out if it’s worth it or not but I’m guessing I’d need to be pretty lucky!

nordhofsweden

1:7 for Hulk, Strange or X.
You should hopefully get at least two covers, but you’d have to get pretty lucky for them to be the 2:9 covers you want them to be.

shardwick

I say go for it. Maybe you'll get lucky and snag a Strange and a bonus Strange.

HoundofShadow

Approximately 42 pulls to get Strange x 2. 

With Rng being Rng, you might get him on the first two pulls or you might never get him  with 15 pulls.

How's your Mordo? He feeds Dr Strange.

Zombionicdoom

HoundofShadow said:

Approximately 42 pulls to get Strange x 2. 

With Rng being Rng, you might get him on the first two pulls or you might never get him  with 15 pulls.

How's your Mordo? He feeds Dr Strange.

Excellent point, I’m 23 covers away from a blue and purple. I’m not sure it’s worth spending the CP in that case. I’ll make sure Mordo’s a BH and there we go. 

shardwick

I just pulled a Mordo from personal rewards in the event so I'll trade you my Mordo for a Sabretooth, Black Cat or Ronin. Ahhh if only they had a trading system in place.

sambrookjm

If I'm doing the math right, your odds are somewhat better than what I would have thought at first.  Still not good, mind you.  It's early in the morning, so if anyone else wants to confirm this, go right ahead.

(assuming) Odds of getting a 5-star:  1/7
Odds of getting any Dr Strange:  1/7 * 1/3=1/21
Odds of getting one of the right covers:  (1/21) * (2/3) = 2/63
Good covers needed:  2
(assuming) Independent cover pulls: 15

You're looking at a binomial distribution.  The odds of you pulling exactly two covers in 15 pulls (or fewer) are:
(15*14/2) * (2/63)^2 * (61/63)^13 which is roughly 6.96%

The first term (15*14/2) is how many different ways you can pull the two Strange covers you need in your 15 pulls.  You could pull them on the 7th and 12th cover, the 2nd and 14th cover, or the 1st and 2nd if you're really lucky.

The second term (2/63)^2 is the chances of two of the covers being the ones you need, while the final term (61/63)^13 is the chances that the rest of the covers are *not* the ones that you need. (This includes the Dr Strange cover that you don't need, but could save.)

If you pull all 15 covers, regardless of how many good Strange covers you get, you've got about an 8% chance of getting 2+ of the Strange covers you need.

This does not take into account Bonus 5-star Heroes.  (You *do* have Strange set as your 5-star bonus hero if you're looking to cover him, right?)  The odds of getting a 5-star bonus hero in 15 pulls is ridiculously low anyway, but it would *slightly* increase your chances.

So to quote Dirty Harry:  You've got to ask yourself one question: "Do I feel lucky?" Well, do ya,punk?

JSP869

You could beat the odds. One of my Ally mates did and pulled two X5 covers from his two Tokens this morning. Several other Ally mates got one X5 cover, and I thought they'd used up all our luck, but I pulled a Blue X5 myself. I did buy out the Vault to get the token in there too though, so I made 3 pulls, and I got his cover with my 3rd pull.

Best of luck to you, too! May RNGesus smile upon you!

Zombionicdoom

sambrookjm said:

If I'm doing the math right, your odds are somewhat better than what I would have thought at first.  Still not good, mind you.  It's early in the morning, so if anyone else wants to confirm this, go right ahead.

(assuming) Odds of getting a 5-star:  1/7
Odds of getting any Dr Strange:  1/7 * 1/3=1/21
Odds of getting one of the right covers:  (1/21) * (2/3) = 2/63
Good covers needed:  2
(assuming) Independent cover pulls: 15

You're looking at a binomial distribution.  The odds of you pulling exactly two covers in 15 pulls (or fewer) are:
(15*14/2) * (2/63)^2 * (61/63)^13 which is roughly 6.96%

The first term (15*14/2) is how many different ways you can pull the two Strange covers you need in your 15 pulls.  You could pull them on the 7th and 12th cover, the 2nd and 14th cover, or the 1st and 2nd if you're really lucky.

The second term (2/63)^2 is the chances of two of the covers being the ones you need, while the final term (61/63)^13 is the chances that the rest of the covers are *not* the ones that you need. (This includes the Dr Strange cover that you don't need, but could save.)

If you pull all 15 covers, regardless of how many good Strange covers you get, you've got about an 8% chance of getting 2+ of the Strange covers you need.

This does not take into account Bonus 5-star Heroes.  (You *do* have Strange set as your 5-star bonus hero if you're looking to cover him, right?)  The odds of getting a 5-star bonus hero in 15 pulls is ridiculously low anyway, but it would *slightly* increase your chances.

So to quote Dirty Harry:  You've got to ask yourself one question: "Do I feel lucky?" Well, do ya,punk?

Wow 🤯

Fair play to you and your wizard maths skills!

I have actually managed to pull a bonus Dr. Strange before now, however, he was one of the two 5* bonus heroes I’ve acquired since the whole system began! Maybe it is my turn to be lucky?

I think though I’m just going to wait it out and earn the covers via Mordo, I’m in no great hurry to cover him really. 8% chance to get the covers seems fairly low when I’ll have them in 23 x mordo covers time!

Kolence

Chance to pull any 5* in a legendary store is 0.15
Chance to pull one of the 3 in the store is 0.05
Chance to pull 2 of the 3 covers for that one 5* is 0.033333....

Chance for a bonus hero is 0.05 for any 5* you do pull, so it's 0.15 x 0.05 or 0.0075
Chance that bonus hero cover is one of the 2 you want is 0.005

Putting those values in an online binomial calculator gives these chances at 15 tries:

probability of success on a single trial 0.03333333
number of trials 15
number of successes 1

<x, 0.60138303175

=x, 0.31106015666

>x, 0.08755681159

probability of success on a single trial 0.005
number of trials 15
number of successes 1

>=x, 0.07243103119

>x, 0.00251377223

Now, you can get 2+ covers you want from direct pulls, 
OR you can get 1 cover from direct pulls AND 1+ covers from BH pulls,
OR you can get 0 covers from direct pulls BUT STILL get 2+ covers with BH...

0.08755681159 +
+ 0.31106015666 x 0.07243103119 +
+ 0.60138303175 x 0.00251377223 =
=0.11159896

All in all, ~11% chance you succeed covering your Dr. Strange.