Subject

[Play Style] +Skill Roll for heroes with ONLY farmable ascension materials [Analysis, Math]

==Background==

Same color, 1* heroes give the greatest +skill roll when leveling a hero.

Using same color 1* and 2* heroes to level a 4* hero will often take until 3.40 to 3.60, or higher, to get an 8/8 special skill.

==Simple Advice== ( see clarification below )

-If you are leveling a team hero using only farmable ascension materials, use ONLY same color 1* heroes to level the team hero until the team hero is 8/8 special skill. This applies to 3*, 4* and 5*.

-Use your spare 2* and 3* heroes to level a same color 8/8 special skill team hero.

-If you donâ€™t have a same color 8/8 special skill team hero for your spare 2* and 3* heroes, use them to level an other color 8/8 special skill team hero. You will lost 16.6% of the XP, but you will have the greatest chance to get 8/8 special skill on all your team heroes.

-If you donâ€™t have *any* 8/8 special skill heroes, use spare 2* and 3* heroes to level 3* team heroes. You will increase the chance of a 3* team hero without 8/8 special skill, but 4* and 5* Heroes have secondary effects ( Defense debuff, Attack buff, etc. ) and sometimes even tertiary effects ( looking at you Alberich and Ares ) that *cannot* be increased once they reach 4* 3.60 or 5* 2.60, while 3* 3.50 heroes can still be leveled to raise their special skill.

Edit:

Clarification: for simplicity, heroes are described as 8/8 special skill. However 3* and 4* heroes can ascend to tier 3 using only farmable ascension items. 5* heroes can ascend to tier 2 using only farmable ascension items. So a tier 1, 3* hero with 6/8 special skill is guaranteed to become a 8/8 hero. While a tier 1, 5* hero with 6/8 special skill is only guaranteed to become a 7/8 hero.

Guaranteed 8/8 heroes can be treated as already 8/8 heroes for this post.

Stars, tier, special skill guaranteed to become 8/8 using farmable ascension materials

3*, 1, 6/8

4*, 1, 6/8

5*, 1, 7/8

3*, 2, 7/8

4*, 2, 7/8

Edit 4-12

==alliance chat ==

I need to finish leveling my farms & food storage ( I want all to be level 20, with the occasional bump to mines to feed two builders ).

I am then considering raising a second train camp to 19 for extra fast training. Extra fast costs a lot of food but gives you lots of 1* heroes for raising special skills.

==Original Post==

==Complex Advice==

RNG means 3* 3.50 team heroes have a 1 in 17 chance of 3/8 special skill or never raising the special skill during leveling ( Note 1 ).

While the odds are approximately the same if you use batches of one 1* same color hero at a time or batches of ten, every time your fail a skill roll using a batch of ten 1* same color heroes you significantly increase the odds that your hero will fail all their remaining skill rolls before reaching maximum tier and maximum level with farmable ascension items.

Example:

Using batches of ten, a 5* 2.1 hero gets a maximum of 27 rolls of +20% until reaching 2.60 . After 16 rolls, if you are not 8/8, you have a 1 in 11 chance of never making 8/8. Using batches of one, the same hero gets a maximum of 270 rolls of +2%. After 16 rolls, if you are not 8/8, you have a 1 in 169 chance of never making 8/8.

You are not increasing your odds of an 8/8 special skill hero by rolling in batches of one, but you are *decreasing* the odds of a 3/8 special skill hero.

This does not normally matter since 5* Heroes take such a huge amount of XP to reach 4.80. But since we are only using farmable ascension materials, 5* heroes lose the most XP for skill rolls ( Tier 3 and Tier 4 ) and the most automatic special skill increases ( ascension to Tier 3 and Tier 4 ).

Note 1)

Data

Farmable Ascension items and max level

Star, Tier.Level, times leveled ( true level )

3* 3.50= 120

4* 3.60= 150

5* 2.60= 110

Raising a 5* hero from 2.1 to 2.60 takes 48,453 XP or 270 same color 1* Heroes

27x 20% using batches of 10 heroes

Number of rolls, rolls remaining, formula, Chance of not raising special skill at least once

4, 23= 0.8^ 23= 1 in 169

8, 19= 0.8^ 19= 1 in 69

12, 15= 0.8^ 15= 1 in 28

16, 11= 0.8^ 11= 1 in 11

20, 7= 0.8^ 7= 1 in 5

24, 3= 0.8^ 3= 1 in 2

270x 2% using batches of 1 heroes

Number of rolls remaining, formula, Chance of not raising special skill at least once

4, 266= 0.98^ 266= 1 in 215

8, 262= 0.98^ 262= 1 in 198

12, 258= 0.98^ 258= 1 in 183

16, 254= 0.98^ 254= 1 in 169

20, 250= 0.98^ 250= 1 in 156

24, 246= 0.98^ 246= 1 in 144