Hello, Meerkat here, doing more maths as an attempt to procrastinate doing other, less appealing maths. After Shattered Timelines came out, I calculated the total number of possible different games (it was 71,466,240), and now we have NEW THINGS I'm going to do it again.
So, let's start with sets of 5 heroes. We now have 23 different hero decks, so that's 23C5 = 33649 teams, to start with. Now we need to take our 18 promo heroes into account, so we have 18 x 22C4 = 131670 teams with one promo, 18C2 x 21C3 = 203490 teams with two, 18C3 x 20C2 = 155040 with 3, 18C4 x 19 = 58140 with 4 and 18C5 = 8568 with 5. Add those up, we get 556908. The only problem is, this includes teams that have two of the same hero (Legacy, Bunker or Wraith); we need to subtract 3 x 21C3 + 3 x 16 x 20C2 + 3 x 16C2 x 19 + 3 x 16C3 = 21630 bad pairs - but even this takes out those pairs with two duplicate heroes twice, so we add back 3C2 x (14 + 19) = 99, giving us a grand total of 535377 five-hero teams.
Right, four-hero teams now. Similar procedure, 23C4 + 18 x 22C3 + 18C2 x 21C2 + 18C3 x 20 + 18C4 = 8855 + 27720 + 32130 + 16320 + 3060 = 88085, minus 3 x 21C2 + 3 x 16 x 20 + 3 x 16C2 = 1950, plus 3C2 = 3, equals 86138 teams of four. For three-hero teams, 23C3 + 18 x 22C2 + 18C2 x 21 + 18C3 - 3 X (16 + 21) = 9847 three-man teams. Total these up, you get 631362 hero teams.
Environments are still easy; there are 14 of them, along with 22 regular villains and two difficulty settings; 631362 x 2 x 22 x 14 = 388918992 games not against the Vengeful Five. Against them, a five-man band can play against them on two difficulties in fourteen different environments, for 14990556 games, a quartet can play against 5 different arrangements of them for a total of 12059320, and a three-piece suite can take on ten different Vengeful Threes, for 2757160 games.
Total number of deck combinations? 418,726,028. Which is a lot.