The Flying Press Conundrum - Part 2: What if the Defending Pokemon is Dual Typed?
For any good mind journey during the night, there's a follow up the next day.
Background
As I've discussed in my previous post, there are 57 possible type combinations for another dual type move, 48 of them passed what I called the Restrictive Criterion.
In said post, I also looked for the most explosive type combination and the most reliable one. What I overlooked however, is that the defending Pokemon can also be dual typed. So, in this post, I'm redoing both question with dual typed defending Pokemon in mind.
With the added layer of complexity, the need for more assumptions arise. While previously we treated all defending types as equal, this time we're treating every single typing a defending Pokemon can have as equal, be it single or dual typed. This, of course creates an even more impractical scenario, since a lot of dual type combinations are assigned to no Pokemon. So, some people might think that the rest of this post might not be too useful.
In any case, there are actually not much work to be done from the previous one. In fact, I don't need to run a Python script again, since the number of x4, x2, x1, x0.5, x0.25, and x0 effectiveness can be derived from the single typed defending Pokemon cases. The way they're derived will be explained in the next section which can be skipped for those uninterested in the mathematical side.
Calculation
I'll go straight to give you how to calculate each of x4, x2, x1, x0.5, x0.25, and x0 effectiveness a dual typed move can have against any single or dual typed defending Pokemon, given you know how many x2, x1, x0.5, and x0 effectiveness it has against any single typed defending Pokemon. If you have the table I appended in my last post it's useful to note that the number of x1 effectiveness is 18 minus the sum of x2, x0.5, and x0 effectiveness.
Henceforth, VE is the number of x2 effectiveness, NVE is the number of x0.5 effectiveness, and NE is the number of x0 effectiveness, all in the cases of single typed defending Pokemon.
x4 effectiveness: 
x2 effectiveness: 
x1 effectiveness: 
x0.5 effectiveness: 
x0.25 effectiveness: 
x0 effectiveness: 
where E = 18 - (VE + NVE + NE) is the number of x1 effectiveness in the cases of single typed defending Pokemon.
They are basically just accounting all the cases possible to result in each effectiveness.
Result
I think most of us can agree to combine all x0.5, x0.25, and x0 effectiveness into a single quantity which we'll call resistence, you're not gonna use the move against any Pokemon that resists it anyway. But some people might argue that it's relevant that x4 effectiveness could one-hit KO what x2 effectiveness couldn't.
With x4 effectiveness as first priority, trivially the most explosive type combinations in my last post is also the most explosive here, for reference they're Ground/Ghost and Ground/Dark, with 21 defensive Pokemon typings with x4 effectiveness. But, the former edges the latter in x2 effectiveness, with 49 against 42.
If you treat x4 and x2 effectiveness as equal, then Ground/Ghost is the most explosive one with 21 + 49 = 70 of such defensive typings. However, surprisingly Ground/Fairy beats Ground/Dark to the second place, with 10 + 55 = 65 defensive typings as opposed to 21 + 42 = 63 of the latter. This is the consequence of the former having only 3 single types that resist it compared to the latter's 6.
Another surprise comes in the third place, Rock/Ghost is tied with Ground/Dark at 63. While the latter has 21 typings it's x4 effective against compared to the former's 15. The former compensated for it by only being resisted by 56 typings compared to the latter's 58.
One way to weigh x4 effectiveness against x2 effectiveness is to multiply the former quantity by 2 before adding them together, this way the ranking looks as, in order from highest to lowest, Ground/Ghost, Ground/Dark, Rock/Ghost, Ground/Fairy.
In the discussion of most reliable combination, Flying/Ground still holds a big lead with only 18 typings resisting it, namely Flying and all the 17 dual typings that include Flying.
Very interesting to note, though. The second most reliable combination is Ground/Fairy with 41 typings resisting it. If you noticed, Ground/Fairy also popped up in the discussion of most explosive combination, being the second most explosive combination when you treat x4 and x2 effectiveness as equal. So I guess we've found ourselves a new dark horse in this whole dual type move discussion.
Finally, Ground/Ghost, Ground/Dark, Ground/Fairy, Rock/Ghost, and Flying/Ground, all passed the Restrictive Criterion.
Personally I still find Flying/Ground to be the most interesting, but Ground/Fairy and Ground/Ghost have emerged as the second and third. For reference no existing Pokemon have the Ground/Fairy typing, while 6 Pokemon have the Ground/Ghost typing, namely, Golett, Sandygast, Galarian Yamask, and their evolutions, Golurk, Palossand, and Runerigus.
Thank you again for keeping up with me. I'm not posting the table since it's too big this time.