For busses, the B stop on the way out may be in another zone as the B stop on the way back because they're geographically displaced. For busses and trains, depending on your type of ticket (2-8 zones, 8+ zones, commuter card) and whether the zone intersection is on or between stops/stations, you may have to pay for that zone one way but not the other. Those are edge cases.

But the most confusing part is the ring topology (here shown with the zone-ring center being the actual city center):

https://passagerpulsen.taenk.dk/sites/default/files/styles/f...

When buying 2-8 zones you don't pay for individual zones, but rather rings from your origin zone. Going one way, the zone rings look one way. Going back they look different, because the origin zone is different.

A practical example of this peculiarity:

You go from Hellerup (zone 2) to Friheden (zone 33) via the central station (zone 1). Your ring 0 is zone 2, and zone 1 and 33 are both in ring 1, so you only pay for two zone(-ring)s: https://dinoffentligetransport.dk/media/1413/svanemollen-fri...

You go back from Friheden to Hellerup via the central station: Your ring 0 is zone 33, zone 2 is in ring 1, but zone 1 is in ring 2 this time, so you pay for three zone(-ring)s: https://dinoffentligetransport.dk/media/1411/friheden-svanem...

Your origin zone on the way out was adjacent to both other zones needed (needing only 1 ring), but your origin zone on the way back was not (needing 2 rings).

So they're not just different prices: The graph that spans train stations via zones in the ring topology is not metric. So getting a return ticket is not the inverse of getting the ticket out. And while you have a ticket that's valid for the timespan of your return, it may not be valid for your return path.

What the... that was painful to read and comprehend. Was this kind of complexity really necessary? Did someone get a promotion for coming up with this?

I copied and translated a quite limited subset of the official traveller guidelines.

There are several reasons why it ended up like this, and I don't know all of them.

But two reasons I can think of:

1) With the introduction of RFID-based commuter cards, the zone system was revised for traditional ticket types as well. It appears convenient that a price can always be determined by knowing the check-in point, the check-out point and the shortest path in the graph. Unfortunately, with the old ticket types, you have to perform the calculation instead.

2) It is the odd shape of zone 2 that causes some tickets to not work on the way back, even though the trip goes in a straight line. But for a large part of all trips, you only need zone 1 and 2, or zone 2 and zone (30, 31, 32, 33). Only the ones that start in zone 2, go through zone 1, go back into zone 2 and farther into another zone (or vice versa) have the anomaly. (Trips that actually bend can have this too, but it is slightly more intuitive.)

Other possibilities: Trains going in different directions don't make the same stops (express vs local), and time-based fares applying to a specific direction based on commuting patterns.

In the US, on Amtrak, a ticket is specific to an exact train, like buying a plane ticket. There's no generalized "I want a ticket from DC to NYC."

Some of the shorter ones have unreserved coach class tickets that aren't restricted to a specific train. So, while there is no generalized, "I want a ticket from DC to NYC", there is a generalized, "I want a ticket from Chicago to Milwaukee."

Another possibility is that there is more demand in one direction.

You might have a major city, A, a center of finance and law and full of corporate headquarters, and a smaller city, B, where many of the companies whose headquarters are in A have their engineering and manufacturing facilities.

Someone making a deal with one of those companies may need to visit both engineering to work out technical details first and then visit headquarters to work out business, financial, and legal details. They will travel from home to B, and then travel to A, and then when done travel directly home from A. This may happen much more than the other direction--people needing to visit headquarters first and then going to visit engineering and manufacturing, without needing to go back to headquarters.

Net result: more passengers needing B to A than A to B. This can result in A to B trips having empty seats. It might even result in some trips with no passengers at all! They can't simply cancel those trips, because they need to get the vehicles to B to handle the B to A traffic, so they sell seats cheap.

Chicago has a minor version of this, even without zone fares: The entry fee to get on a train is $2.50 everywhere except O'Hare Airport, where it's $5.

Interesting, thanks!

The tourist fee.

Nah. Most the people I see on that train are people commuting to/from work, and locals who live along the blue line corridor. Some tourists, but I think most of them are opting to pay a driver 8x as much to take even longer to get them downtown.

They use a zone system, and you don’t have to pay for a zone if you get off at the first stop after entering it.

This creates the asymmetry

thanks