Clive Page wrote:

My sample journey was one I actually do from time to time: King's
Cross St Pancras to Richmond (Surrey). It tells me the three options
a

Oyster
peak £3.90 off-peak £2-80
(But no route is specified, does that mean using London Underground
all the way? I've no idea. And does "Oyster" imply London
Underground only, that implication is not spelled out, and does not
seem very logical now that Oyster cards are valid on a much greater
variety of trains).

That is the default fare, which will be charged for any route you
choose to take that is not specifically listed as an exception. So as
long as you do not pass through the gatelines at Waterloo, Victoria or
Vauxhall you will be charged that fare.

Changing at Waterloo or Victoria and Clapham Junction:
Peak £5.40, off-peak £4.20

Changing at Vauxhall
Peak £5.00 off-peak £4.20

So if my assumptions are right it costs more to mix NR and TfL
trains, but why are the two off-peak fares the same but peak fares
different? Baffling.

Then the route I might well take is Thameslink to West Hampstead and
then West Hampstead Overground to Richmond. That route isn't likely
to take any longer than using the District Line to Richmond but it
isn't listed at all, so I have no idea what fare would be charged.
Not only that I don't know how to find out.

That would be charged at 3.90/2.80 as well.

Peter Smyth