Whether you buy the card or not, be sure to download the official app, CPH Card. There’s a map of every attraction on the card so you can see where attractions are in proximity to one another.
Everyone wants to know... will this thing pay for itself? If you like to stay active and cram in A LOT, yes, you will definitely get your money's worth. We paid 1858 DK for two 4-day cards. Nearly every attraction in Copenhagen is on it. The value of the attractions we visited was 3466 DK and the value of the transport we rode was 946 DK, so we saved 2554 DK (about $355 US at the time.) That's the up side.
The downside is that you may feel you MUST run around like crazy and do a lot to get your money's worth. We did Kronborg Castle and the M/S Maritime Museum in Helsingor AND the Louisiana Museum in Humlebaek on the same day. They were all a way out and on the same train line so it was easy to visit a lot of high value (830 DK) attractions plus trains in one day. But it was a very full day and we did not do the Louisiana justice.
If you are not keen on lots of attractions, don’t buy this for the ease of transport. It is not a good value for that. Just buy individual tickets or multi-day passes for the number of zones you need – it IS very easy with the ticket machines in every station which have a button for English. Ignore other reviews and do NOT ride the metro or trains without a ticket. They absolutely do check, especially at peak hours, just not every time. We were checked numerous times. If caught without a ticket, the fines are steep.
Be sure to pay attention to when you activate the card, because the card is good for a set number of hours, not days.. So if you activate a four day card mid-day on a Tuesday like we did, you might be able to squeeze in an attraction on the morning on the fifth day (Saturday.)