One Star to Five Star Thought Experiment

chrisH

For those of you that like thought experiments and theory crafting considering getting average odds how many one star packs would you need to open to end up with a 5 star with 13 covers.

For this let's use Wolverine as he has a clear path from 2-5.
Consider:
one star pack has 1 in 8 chance for a 2 star
There are 13 available 2 stars.
63 covers needed to champ and recycle a 2 star
8*13*63= 6552 one star covers just to champ and recycle one 2 star wolverine netting Three 3 star Patch covers. 

This process could be repeated to champ and recycle 3 star into 4 star X Force Wolverine covers and eventually into 5 star covers. 
Assuming you have all Wolverines as bonus heros. And use all tokens and CP gathered along the way to best effect of the goal of a 13 cover Old Man Logan how many one star packs would you need to bust to get there? 

Dormammu

I tried using my smartphone's calculator to figure it out but it didn't have enough digit placements.

jamesh

You're also getting heroic tokens from your 2* champ rewards, and legendary tokens from 3* champ rewards.  That gives you chances to get 3*, 4*, and 5* Wolverines either directly or through bonus heroes.

bluewolf

Some rough math:

You get 3 Patches from your first 46 2* Wolvies, so that means about 16 2Wolv = 1 Patch.

You get 3 XFWs from 113 Patches, so about 38 Patches = 1 XFW

You get 6 OMLs from 113 XFW's, so about 19 XFWs = 1 OML

(Ignore the weird spacing between some covers here.)

16x38x19 = 11,552  2* Wolvie covers per OML cover.

Now... 8 standards for a 2, and 13 2's is 104 Standards on average per 2 Wolvie.

So if you opened around 1,201,408 Standards, you should get an OML out of that.  Eventually, assuming you didn't get stuck with a bad spread.

EDIT:  I realize it sounds like a lot of tokens to open.  But wait!  You should also get a 5HE, 5DD, 5CM, and Cap IW from that finger-numbing exercise.

MoonKnight

It would be interesting to do the math on all the iso it would require to get there too. It’s no small feat to roster and champ multiple XFWs...

Nabistay

Don't forget those heroic tokens also have a chance to give colossus, who gives x-force, so there is another (super tiny) boost from the heroic token rewards you get from championed 2* wolverine

bluewolf

I realized that my post may not have been clear.....you get a single OML cover from opening those 1.2 million standards.  (and the other 5's).  So it's like 15.6 million Standards to get a complete OML (which you would eventually have since it's all going to be champ rewards so your spread will be perfect).

Kolence

It must be shorter than that because for every 3 5* covers you get from flipping a 4*, you also get 250 cp from other champ rewards. So, at least, you could buy an extra 5* cover every 3 maxed 4*s.

bluewolf

I was pretending you could only use Standards....just for fun.  Obviously you'd get lots of better resources you could use to accelerate things.

Ptahhotep

The calculations so far haven’t taken into account the three stars that standard tokens give. I don’t remember the exact drop rate, but you get a guaranteed bh every time.

AXP_isme

I think it’s in the region of 2-2.5% based on a relatively small sample (a few thousand) and my anecdotal recollection. I could check if anyone is interested but for these back of the envelope calculations that should be enough. 

Steel_Colt

So, I did some Excel magic, and unless I messed up something major along the way, it’s actually a lot less than has been calculated so far.

It’s quite a bit of text, including a lot of numbers, so you can skip to the end for a TLDR, if you want.

 

Based on in-game odds, I drew the following conclusions:

 

Every 8 standard tokens yield a 2*.

Every 43 standard tokens yield a 3*.

Every 3* gained from a standard token yields a bonus hero. We’ll set our bonus hero to 3* Wolverine of course, for this experiment.

 

So, every 43.000 standard tokens gives you 5.375 random 2*s, of which about 413 are Wolverine.

These 43.000 standard tokens also give you 1.000 random 3*s, of which about 21 are Wolverine.

These 1.000 random 3*s also give you 1.000 bonus heroes, which of course, are all Wolverine.

 

Then we get to champ rewards.

Every 63 covers you get for 2* Wolverine gives you three 3* Wolverine covers.

These 43.000 standard tokens give out about 20 covers for 3* Wolverine by way of 2* champ rewards.

Every 113 covers you get for 3* Wolverine gives you three 4* Wolverine covers.

These 43.000 standard tokens give out about 27 covers for 4* Wolverine by way of 3* champ rewards.

Every 113 covers you get for 4* Wolverine gives you six 5* Wolverine covers.

These 43.000 standard tokens give out about 1,5 covers for 5* Wolverine by way of 4* champ rewards.

 

Totals for all Wolverines, directly from tokens and from champ rewards, are:

2* Wolverine --- 413 covers

3* Wolverine --- 1.041 covers

4* Wolverine --- 1,5 covers

 

If we add all these covers and keep opening standard tokens until we come up with 13 covers for 5* Wolverine we need to open 380.943standard tokens.

 

Apparently, thanks to the guaranteed bonus hero when drawing standard tokens the brunt of the Wolverines you’ll pull are 3*, instead of the higher-odds 2* variant.

 

Also, along the way we champed 2* Wolverine 59 times, costing about 4,4 million Iso-8.

We champed 3* Wolverine 82 times, costing about 10,4 million Iso-8.

We champed 4* Wolverine 3 times, costing about 1,1 million Iso-8.

 

If we sold all the 1* covers we got from opening these tokens, we got about 32,4 million Iso-8, more than enough to cover the champing costs.

 

All this is not accounting for the other 2*s, 3*s, 4*s and 5*s gotten along the way, as well as all the other champ rewards from the Wolverines we farmed, or the Iso-8 and Hero Points gotten for selling them as max-champs.

 

 

TLDR:

You need to pull 380.943 standard tokens to fully cover Old Man Logan.

Steel_Colt

Also, to add, while I didn't take into account whatever champ rewards we got along the way, I did account for maximum rewards, so I went for max-champed every time, instead of scrapping a characters once the last cover champ reward was given out. You could get your Old Man Logan a lot faster by scrapping your 3* at level 183 and starting a new character. That way you get one 4* Wolverine every 30 covers, instead of 3 every 113 (or one every ~38.)

Steel_Colt

OK, so I took into account scrapping a character at it's optimal level when only going for the cover rewards, getting a champed OML as fast a possible. 
This means scrapping 2*s at level 127 (last cover reward).
Scrapping a 3* at level 183, this will take 30 covers, the next cover reward takes another 40 (level 223), so starting anew is better when only going for covers. 
Scrapping a 4* at level 360 (last cover reward). 

Going this route means only opening 274.637 standard tokens. 

AXP_isme

Surely you can’t scrap the 3* at 183. If you do that you end up getting the same 4* cover over and over. If you’re not opening any other tokens then there’s no chance to get covers in other colours for 4* wolverine so he can never be champed and never deliver covers for OML. I think you’ll have to let the 3* wolverine get to 265 three times and to 223 twice more before you can start scrapping them at 183. 

Steel_Colt

AXP_isme said:

Surely you can’t scrap the 3* at 183. If you do that you end up getting the same 4* cover over and over. If you’re not opening any other tokens then there’s no chance to get covers in other colours for 4* wolverine so he can never be champed and never deliver covers for OML. I think you’ll have to let the 3* wolverine get to 265 three times and to 223 twice more before you can start scrapping them at 183. 

Ah, you're right, I didn't realise that oversight at the time. But seeing how we'll have to champ 3* Wolverine 82 times in the original calculations, you'll still save yourself a lot of token pulling if you take the scrapping route after getting the initial 13 covers for 4* Wolverine. 

Steel_Colt

And thank you @AXP_isme for actually reading my wall of text, so I didn't type all for nothing.

AXP_isme

You’re welcome @Steel_Colt, good analysis btw. I really enjoy this kind of theorycrafting. It appeals to the maths geek in me.

As as an aside, I think you would have to write a simulator to get a real result here given the amount of randomness involved. 

Steel_Colt

AXP_isme said:

You’re welcome @Steel_Colt, good analysis btw. I really enjoy this kind of theorycrafting. It appeals to the maths geek in me.

As as an aside, I think you would have to write a simulator to get a real result here given the amount of randomness involved. 

Same here, I like messing around with Excel and trying to calculate things like this, taking various variables into account. Writing a simulator is a bit out of my league. Best I've done in excel is designing a medium pressure steam boiler powered by waste gas, based on three years of data and regression analysis. But that was for work/school final assessment. Took me about 6 months. 😂 

chrisH

I like your logic here. I think for the sole goal of getting a 13 cover OML you would probably end up with some number of bonus 5 stars from opening the LL tokens as well as enough CP from all the camp recycles to buy one for the 720 price tag cutting down on the total number of one star tokens needed to be opened. 

AXP_isme

The idea is that you only open standard tokens. If you start down the road of tracking all the items you get as rewards you need to start tracking everything so you can work out when the rest of the 2*s flip and then into 3*s etc... along with the heroic tokens you get as rewards, the CP and the HP that you would probably have to spend on heroic tokens (but at what price?) and it gets very complicated. You need some simplifying assumptions or it becomes so complex as to become a bit meaningless.