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 don’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 don’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