The underground railway in Budapest provides a quick and cheap way of getting around. Unfortunately, not all the travel instructions are printed in anything except Hungarian, which means that you don't find out until too late about quirks, such as the fact that buying a ticket on some lines does not allow you to transfer to others without making an additional payment.
I discovered this the hard way. My daughter and I worked out how to get where we wanted to go by studying the map, but after we switched lines we were approached by two uniformed officials who demanded to see our tickets.
We were then required to pay a fine. I'm satisfied that the two officials were genuine but I suspect that they saw us - two tourists - as an easy target, because they followed us as soon as we got off the first train and on to the second.
The fine would have paid for several taxi fares, so other visitors to Budapest might wish to use that means of transport instead of the underground.
No question, the system of stamping a new ticket is silly. Hopefully within a year or two it will be replaced with a system like the Oyster one in London. But once you have worked out the ticket system, or best of all bought a season ticket, the metros and trams are the best way to get around and see Budapest, and are certainly much better recommended for visitors than taxis, which are still a risk unless ordered by phone. I agree with the above statements. You can avoid all of the unpleasantness by buying a day pass (about 1,200 forints) or a tourist pass, which gives you three days for about 2500 ft. And you can savour the looks of disappointment on the faces of the controllers when you whip out your correct documentation...all kidding aside, the public transport is generally great, so make sure you're legal to use it and all will be okay.
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The inspectors do prey on tourists. The No 2 tram along the river being a favourite trap of theirs in the summer. Don’t try to garner sympathy, they have hearts of stone. If they are genuine, they will have a red armband and should produce ID if asked.