The computer gets one swipe and unlimited transfers. It can visit the same station over and over, but it can't repeat a segment of the subway map twice.
Rules for a Data News-approved longest subway ride
You can visit the same station as many times as you want.
You can make any station-to-station transfer that's marked as a free transfer on the subway map.
You can only ride each segment of the subway map once. A segment is basically anything that looks like one segment on the map. If any two lines go between station A and station B, and they don't diverge in between, that's one segment.
Once you've ridden a segment, you can't backtrack in the opposite direction. If you take the R north from Bay Ridge - 95 St, you can't take it back south.
Once you've taken the local, you can't take the express, and vice versa. If you take the E from 14 St to 34 St - Penn Station, you can't take the A between them later.
If there's more than one line, but they run side-by-side on the map, that's still one segment. The E, F, M and R between Jackson Heights and Forest Hills are one segment together. The B and Q from Prospect Park to Brighton Beach are one segment together.
We're choosing to ignore the existence of the West 8 St - NY Aquarium and Sutphin Blvd - Archer Av stations for simplicity's sake.
We assume that every standard line is running in its entirety, including the shuttles.
The AirTrain isn't a subway line. Don't be ridiculous.
to a new random station
Booting up...
Initializing modules...
Swiping in... 
Ready to ride. 
Routes Checked:

The Longest Subway Ride