The chance for styx troops is 5%, which should be equally distributed for the 5 colours, so 1% chance for each colour.
So it may be something like this:
The red styx troop has 1% chance and 10 possible positions in the 10-pull.
The green styx troop has 1% chance and 9 possible positions in the 10-pull.
The blue styx troop has 1% chance and 8 possible positions.
The yellow styx troop has 1% chance and 7 possible positions.
The purple styx troop has 1% chance and 6 possible positions.
The remaining 5 positions are filled with whatever gets pulled = 100% chance.
=> To get at least one styx troop of each colour in a 10-pull:
1% x 10 x 1% x 9 x 1% x 8 x 1% x 7 x 1% x 6 x 100% x 100% x 100% x 100% x 100% = 0.0003024%
=> on average every 3307 10-pulls (edit: seems wrong by a factor 5x4x3x2)
I’m not going to say you made a mistake… but I think I recalled this as a possibility…
The first time a styx troop is pulled… it can be any of the 5 colors… so a full 5% chance… but… the second troop cannot be the first color… so the percent chance goes down to 80% of 5%, and so on all the way down to 20% of 5%.
Like I said… when I was in college… this was probably fresh… but as of now… man… not so much.
The first styx troops can be any of the 5 colours (=5%) at one of the 10 positions. The next colour goes with 4% and 9 possible positions, and so on.
Regarding my calculation, I could start with any of the 5 colours, not just red, so I need to include all the possible sequences of the colours, and multiply my calculation with „x 5 x 4 x 3 x 2 x 1“, which then gives the same result.
The (hopefully) correct calculation should be then:
5% x 10 x 4% x 9 x 3% x 8 x 2% x 7 x 1% x 6 x 100% x 100% x 100% x 100% x 100% = 0.036288%
=> on average every 28 10-pulls
Umm. .036288% is one divided by about 271,000. One in every 271,000 [edit - wrong math, one in 2756] 10-pulls gets all 5 colors of Cyclops troops (with the math in your post, idk if thats the right formula or not, I took prob&stats class like 26 years ago)
If we take as chances
5* = 2.5%
4* = 26.5%
3* = 71%
I would assume
(2.5%)^7 x (26.5%)^3 x (10!) / [(10 – 7)! x (10 – 3)!] = 1.36301 x 10^-11
=> every one in 73.367 billion 10-pulls
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Well, shouldn‘t the 5 different styx troops then be using the factorial function as well?
5% x 4% x 3% x 2% x 1% x (10!) / [(10 – 5)! x (10 – 5)!]= 3.024 x 10^-6
=> every one in 330,688 10-pulls
Looks like the gut feeling was right (and my statistics skill very rusty )
50 ETT pulls done for me… Figured I could one day dream of using these as an alternative to some of my existing magic troops (if and when I can ever get them levelled!)
Obtained:
1x Red Cyclopes - [New]
1x Green Cyclopes - [New]
1x Blue Crit - [3 Owned]
1x Purple Mana - [2 Owned]
1x Purple Crit - [3 Owned]
45x 3* troop dupes
Considering I didn’t have any +20% mana troops for Blue or Green (Purple / Yellow magic troops owned), I am happy to have at least managed to get a Green option, but I definitely could have done without the Red, since I already have 3 Magic troops in Red…
Oh well, life goes on, and back to hoarding ETT’s until the next Magic/Styx troop portal I suppose! Certainly not somewhere that I will be splashing my gems though
They take long enough to level that it really doesn’t upset me at all
Had 50 ETT this time, missing only yellow & green Styx Troops.
9 4* troops in total, with
1 x blue Styx
2 x red Styx
1 x yellow Styx
I was kinda hoping I’d get both green & yellow with those 50, preferrably without even using them all so I could save the rest for Magic Troops (missing red & purple). Well now I have enough feeder troops to get my purple & red Styx Troops to 23.