Subject
[Primer, Math] Why did I get four Banes from x10 elemental yellow summons or how summons, and indirectly recruit training, works in Empires
This post contains math that may be difficult. Unfortunately summons require the use of probability to explain.
==Background==
Heroes are like your skill tree, or spells, in other games. 1* heroes have attack special skills, 2* add multiple targets or secondary effects, 3* increase the power of secondary effects, 4* add tertiary effects.
5* Heroes ( and eventual 6* ) take 1* to 4* abilities and significantly scale up their power, or adds permanent effects like revive and minions. So heroes, and their special skills, are an inverted pyramid.
Just like no one wants more versions of a first level magic missile spell, no one wants more versions of 1* Heroes.
4*, 5* ( and eventual 6* ) make the Devs the most money and help the most with the current game mechanics. This can be seen by each Challenge event adding two 4* and three 5* heroes ( as of 2018-March, reflect red and reflect green remain unknown )
==Elemental summons==
We don’t know the odds for elemental summons, but we have a good idea of the odds for legendary training. If we could just pull yellow heroes from legendary training, using the known odds for 3*- 5*, the odds would probably look like this:
3* 75%- 18.75% Bane, 18.75% Dawa, 18.75% Gan Ju, 18.75% Kailani
4* 20%
5* 5%
So if we look at ten summons in a row, with the above odds, most sets of ten would have zero= 5* yellow heroes, 1-3= 4* yellow heroes and the remaining 3* yellow heroes. So if you only get 3* yellow heroes ( 1 in 18 chance ) there are not ten 3* yellow heroes so you will get duplicate Banes. It is unlikely we will get ten Banes in a row, and the odds of no Banes is 1 in 8, but we will probably get somewhere between 2- 4 Banes.
We have been told that legendary training odds are better than elemental summons odds, so the odds of getting multiple Banes is actually HIGHER than the above example. Because we can not do colored elite training or colored legendary training, this hides the odds from most users until they try an elemental summons.
==MY PERSONAL OPINION==
===3* heroes===
I would not mind if the Devs added Purple, Yellow and Blue 3* healers to the game.
I do not mind 3* heroes, unless the Devs fix +skill rolls, duplicates are your best chance of getting a 3* hero to 8/8 special skill before 3.50.
===Better Mechanic==
I don’t see the Devs ever changing the odds of summons or training camps, it keeps the game afloat. Personally I budge 3 summons per month ( about $12 USD ) to try and get the Hero of the Month. I have Peters, so I will use my 3 summons per month on Guardians or Knights. If the month is Pirates, I will use it on elemental red, since I lack Boldtusk 4* heal all with attack buff, Kelile sniper with DOT and Gormek splash damage with defense debuff.
I would actually spend more money if their was some way to see what I was getting first. I don’t know how the Devs would accomplish this, elemental summons appears to be their compromise, but I have suggested the following:
Featured Deal of the Day ( Hero, Ingredient, Ascension Item )
==DATA==
Legendary training hero 3* pool
Yellow four 3*
Red four 3*
Blue five 3*
Purple five 3*
Green six 3*
