Standard Tokens required to champ 5* Wolverine

MadScientist

Recently, there was a discussion here how long it would take to champ 5* Wolverine using only standard tokens.

Just for fun I wrote a program to simulate this task.

The rules were as follows:

• The bonus heroes were fixed as 3* Wolverine, 4* Wolverine and 5* Wolverine
• If you have a Heroic Token, open it
  
• If you have a Legendary Token, open it
  
• If you have 20 Command Points, buy a Classic Token
  
• Otherwise, open a Standard Token
  
• Sell all 1* covers
  
• Recruit all other characters. If they can be champed, champ them. If they have reached maximum champ level, sell them and recruit a new one.
  
• Once 5* Wolverine can be champed, stop.
  

Example result from one random simulation:

It took 152941 Standard Tokens. In the process, 1793 Heroic Tokens, 330 Legendary Tokens, and 240 Classic Tokens were used. All extra tokens were gained from champion rewards.

5* Wolverine ended up 4/4/5. Of these covers, 7 were from champion rewards, 5 were from bonus rewards via legendary tokens and 1 was directly from a classic token.

4* Wolverine ended lvl 280 with one full champion sold. Cover breakdown: 3 from heroic tokens, 3 from bonus via heroic tokens, 5 from legendary tokens, 9 from bonus via legendary tokens, 1 from classic tokens, 15 from bonus via classic tokens, and 100 from champion rewards.

3* Wolverine: 32 full champions sold. Cover breakdown: 83 from standard tokens, 3542 from bonus via standard tokens, 9 from heroic tokens, 16 from bonus via hoeroic tokens, and 74 from champion rewards.

Full champions from all 2* characters were sold 24 or 25 times. 

The whole process required 40,743,451 iso8 with 7,898,199 iso8 left over. A total of 210,925 hero points were produced (none were used, it was assumed there were enough roster slots available).

tiomono

Rerun it adding colossus as an additional bonus hero? I am curious if that would slow it down or speed it up. This is only counting tokens though right, no accounting for event rewards?

It's looking like with patch you got 96 xforce covers. But had 100 champ reward covers total for xforce. So either the last patch had gotten you 4 additional covers with colossus adding nothing, or colossus did not max out one time while patch maxxed 32 times.

Borstock

240 Classic Tokens pulled and you got 1 five-star Wolverine.

Yikes.

AXP_isme

Excellent analysis and a good read. Interestingly it ended up playing out slightly differently from how I imagined. I had predicted that the 3* BH into 4* progression would come to dominate how you got the covers for OML. It was interesting that the BH component of the LTs and CP came into play getting earning over 1/3 of the required covers. I would have thought that you would struggle to generate large enough quantities of LTs or CP to pull a significant number of 5* BHs. 

What was also interesting, though not statistically significant given the sample size, is that 5 BHs were earned from 330 latest legends but none from the classic legends. 

How many times did you run the simulation and how did the distribution of standard tokens drawn compare to what was predicted in the original theorycrafting?

Kolence

Ooooh, this is very interesting. Thank you for making this and sharing here.

I'm curious about a few more things if it's not too much to see? 

- When champing 4*s, did the simulator take into account some give 6 covers (5*) and 4 tokens, and some give 10 tokens?

- Would opening legendary tokens but saving cp for direct buying of targeted 5* (OML) reduce the number of standards it takes?

- HP earned along the way from champ rewards could also be used to speed it up even more, buying heroic tokens? Single pack for 400 HP? with 1 in 20 bonus rate, or buying in bulk with 1 in 12 bonus rate. Though it looks like the most 4* feeder covers came from direct 3* BH opening standards and their champ rewards, anyway. So probably not worth the hassle...  

MadScientist

I repeated the simulation 5000 times. Here is a histogram of the result:

https://imgur.com/LbrTqRq

The average is 166,993.6
The standard deviation is 26,222.5

MadScientist

tiomono said:

Rerun it adding colossus as an additional bonus hero? I am curious if that would slow it down or speed it up. This is only counting tokens though right, no accounting for event rewards?

I repeated the simulation using Colossus instead of Patch as bonus hero and noticed no obvious difference.

tiomono said:

Rerun it adding colossus as an additional bonus hero? I am curious if that would slow it down or speed it up. This is only counting tokens though right, no accounting for event rewards?

It's looking like with patch you got 96 xforce covers. But had 100 champ reward covers total for xforce. So either the last patch had gotten you 4 additional covers with colossus adding nothing, or colossus did not max out one time while patch maxxed 32 times.

The four extra covers were from the current versions of Patch and Colossus.

Kolence said:

- When champing 4*s, did the simulator take into account some give 6 covers (5*) and 4 tokens, and some give 10 tokens?

- Would opening legendary tokens but saving cp for direct buying of targeted 5* (OML) reduce the number of standards it takes?

- HP earned along the way from champ rewards could also be used to speed it up even more, buying heroic tokens? Single pack for 400 HP? with 1 in 20 bonus rate, or buying in bulk with 1 in 12 bonus rate. Though it looks like the most 4* feeder covers came from direct 3* BH opening standards and their champ rewards, anyway. So probably not worth the hassle...  

Yes, I did take in account the different champion rewards for the different characters.

The other two points are beyond the scope of the simulator right now.

tiomono

MadScientist said:

tiomono said:

Rerun it adding colossus as an additional bonus hero? I am curious if that would slow it down or speed it up. This is only counting tokens though right, no accounting for event rewards?

I repeated the simulation using Colossus instead of Patch as bonus hero and noticed no obvious difference.

tiomono said:

Rerun it adding colossus as an additional bonus hero? I am curious if that would slow it down or speed it up. This is only counting tokens though right, no accounting for event rewards?

It's looking like with patch you got 96 xforce covers. But had 100 champ reward covers total for xforce. So either the last patch had gotten you 4 additional covers with colossus adding nothing, or colossus did not max out one time while patch maxxed 32 times.

The four extra covers were from the current versions of Patch and Colossus.

Interesting numbers, thanks for the work.

I was meaning having both patch and colossus as bonus 3*'s. So colossus did not max out even 1 time while patch hit max 32 times just as bonus hero? Wow. Bonus heros doing work.

Also interesting was only 1 xforce from classic tokens. While 5 from latest legends. Poor classics getting some rough numbers.

TPF Alexis

@MadScientist You're really living up to the screen name here! Great stuff!

ZootSax

MadScientist said:

I repeated the simulation 5000 times. Here is a histogram of the result:

https://imgur.com/LbrTqRq

The average is 166,993.6
The standard deviation is 26,222.5

So, if Standard Tokens were still purchasable for 500 Iso-8, it would take, on average, 83,496,800 Iso-8 to buy your way to an OML.  If you were to purchase that in USD (Mother Lode is 78,000 Iso-8 for $99.99), it would cost $107,089.29, not including taxes/fees (with a surplus of 41,200 Iso-8, again ideally; the standard deviation is ~168 Mother Lodes, or ~$16,800).  This gives a typical expectation to spend between ~$90,250 to ~$124,000 to cover the range of one standard deviation either way form the average.  In car terms, that's the difference between a base 2019 Lotus Evora and a base 2019 Corvette ZR1.

Anyway, silly musings aside, this was really interesting.  Thanks for sharing, @MadScientist

Brigby

@MadScientist MRW I saw all of your calculations and work.



Well done! Quite interesting seeing the results of your experiment!

DeNappa

This is pretty awesome. Nice work!

Although I'm still curious about the two variables mentioned by @Kolence .

With the first one (buy covers with CP directly) I guess you would only start spending the CP until after you unlocked all colors with XFW champ rewards covers.

MadScientist

I did new simulations with a slight rule change:

• instead of buying classic tokens with CP, all are saved and used to buy 5* Wolverine covers directly (for 720CP)

Here are the results of 5000 simulations:

• 131,047 +/- 13,366 Standard Tokens were needed
• 5.67 +/- 0.60 5* Wolverine covers were from champion rewards
• 1.99 +/- 1.16 5* Wolverine covers were bonus heroes
• 5.35 +/- 0.71 5* Wolverine covers were bought with CP

Punter1

Great work.

What I spotted from the sample - only 6x 4* XFW naturally pulled from 570 tokens (legendary & classic).  Sure the BH and Champ system works well, but that puts dilution problems in perspective.  Good luck to those that are trying to get caught up these days.

Ares76

Good name for this threat could have been "Old Man Logan had a farm - E - I - E - I - O".