Sunday, July 1, 2012

Math vs. Capcom

So now that I have Ultimate Marvel vs Capcom 3, it still seems... incomplete. It's not that I'm good at the game or anything – I haven't even faced Galactus in single player yet althought I suspect that perhaps my son playing LEGO Batman 2 may have something to do with part of that. It's just knowing that there are two more characters available, and they're characters that were available in Marvel vs Capcom 2. I never found myself using Shuma-Gorath that much in the previous games, but I did use Jill once in a while as a rushdown character and to supply my teammates with health.

Ultimate Marvel vs Capcom 3 is the expanded version of Marvel vs Capcom 3, part of Capcom's 'Vs' series fighting games. Many popular characters from the Street Fighter series are present in the 'Vs' games, along with other characters from their action franchises Devil May Cry, Okami, Mega Man, and Resident Evil. The 'Vs' series games differ from the standard Street Fighter series games in that there are teams of multiple characters, and while each player only directly manipulates one character at a time, they are allowed to call their partners in to do 'assist' moves, or tag out to one of the other characters if needed.

Should I get the two downloadable characters? Well, let's do the math.

The math is a little funny, though. Interpreted purely in terms of the number of characters, it seems crazy that the first 48 characters cost you $40 which is $0.83 each, and the next two characters cost you $5 each. Of course, if you bought the original version of Marvel vs Capcom 3 when it came out, paying $40 to get 12 more characters than what you originally had (which is $3.33 apiece) then the DLC (DownLoadable Content) pricing doesn't seem as far off.

However – let's ignore the original MvC3 for a moment and look at the math in terms of the number of possible teams. In UMvC3, without the two DLC characters, there are 48 characters and three characters on a team. Realistically, it doesn't matter what the order of the characters are – if you have a team with Spiderman, Hulk, and Wolverine, it's the same as if you had picked Wolverine, Spiderman, and then Hulk. As it turns out, for three characters, there are six different ways you could pick the same team. (This will be important in a moment.) So, since the game does not allow repeat characters on the same team, the number of possible teams works out like so:

There are 48 possible characters you could pick first.

There are 47 possible characters you could pick second, because the character you picked first cannot be picked again.

There are 46 possible characters you could pick third, since the first two characters cannot be picked again.

Which gives a preliminary figure of 48 * 47 * 46 = 103,776. However, since a bunch of those teams are repeats of each other, just with a different order of characters, we divide by 6 (See, I said it would be important later...) to get the total number of unique teams. That gives us 103,776 / 6 = 17,296 possible teams.

This is the part where the kid in the back of the room raises his hand and says "Isn't this just C(48,3)?" to which I would remind him that we're not all math majors and maybe it would be nice to show the steps instead of just cramming the problem into a formula straightaway.

So, if we figure in the two downloadable characters, the total number of possible teams increases to 50 * 49 * 48 / 6 = 19,600. That's 13% more teams, with just 4% more characters.

Phooey. I still don't know if it's worth five bucks.