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A contact who recently retired after a long career within the rail industry was telling me today about triangular tickets.   

If you were travelling from A to B, then from B to C and back to A, where B was not between A and C (I know that's a hard concept given the letters I have chosen) and neither is C between A and B, the ticket office could use the fare manual to work out a price that was somewhat below the cost of 3 singles.

Let's try an example. I'm headed from Melksham to Manchester on Saturday, on to Cambridge on Sunday night then back to Melksham off peak - middle of the day - Wednesday.

Single fares - £89.00 + £54.10 + £69.20 = £212.30

Return fares - £90.00 + £86.50 + £70.20 = £246.70

Triangle calculations - I don't know how they work(ed)
.. simply half return totals = £123.35
.. half of outward and return leg returns, plus single from Manchester to Cambridge = £134.20

Do these fares still exist?

I recall they were called "compilation fares" and for the example given by you, were the sum of the return fares divided by 2.

They were abolished in the BR era, I think, before computer whizzery was available to make calculation easy.

Melksham - Manchester - Cambridge - Melksham.

Can be done with the following:

Westbury - Manchester Stns Off Peak Return (not via London) £94.10.

Excess the return portion to (+via London) for £10.10 ((£114.30 -  £94.10)/2).

Return from Manchester via Sheffield and Leicester. Break the return journey at Leicester (for up to 1 month) and then buy:

Leicester - Cambridge Off Peak Return £54.20

Resume return journey from Leicester after your few days in Cambridge.

Total: £94.10+£10.10+£54.20 = £158.40

I remember them being described as "Circular Savers", but there were probably some ordinary ones as well.

And somewhere in my archives I have a fine example of the genre:

    Worcester - Llandudno Junction
    Route: Out Direct
    Return via Newcastle-upon-Tyne and Hull

We won't have the re-introduction of triangular/circular tickets while there is ORCATS. The revenue allocation will be deemed to difficult by TOCs and the Rail Delivery Group.

So, we'd need ORCATS to disappear. And for that we'd need renationalisation.

I suspect your use of the word "deemed" is highly significant.  It's a simple share of the revenue between the three journeys in proportions to the amount of money spent on each journey - a trivial algorithm to code.  But the much lower fare for the total triangle than three singles would be seen as a loss of revenue, with the user group for his type of ticket not being characterised by either getting lots of social brownie points for the TOCs, nor having huge political support, nor filling trains that otherwise carry fresh air.  So a request to provide such fares would lead to the question "and why would we want to?"

Much appreciate the answers, and the suggestions for the detailed Melksham - Manchester - Cambridge case.  I suspect that the fare quoted would require me to travel back via Leicester, which would hit time constraints. Noting the Westbury start - yep, that's a good one (used it before) as a Westbury to Manchester may be valid via London where a Melksham to Manchester is not. Got to love the fare system!

Yes, you would have to travel back via Leicester. I was looking at price ahead of time constraints. You'd have to leave Cambridge by midday to avoid the start of the Paddington peak. Or later to connect with the 1845 off Paddington, for the 2006 from Swindon to Melksham.  

Surely the simplest solution is to make singles half (or close to half) the price of the return.   It would fit the flexible travel patterns of the modern traveller (bus into town, train back; train to work, get a lift home; train to airport, pick up a hire car on the way back;  sleeper to Inverness, fly back to London) and also the last minute nature of many people's travel decisions which are not catered for with triangular fares.   

At present, the difference between single and return fares is very variable.  On two of the three legs of my original triangle, return was just £1 more than single - i.e. return fares are 101.1% and 101.4% that of the single ... and on the third leg the figure was 159.8%.    FGW used to be around that 102% too for many tickets, but changed it a few years back - Melksham to Paddington anytime standard return now 174.3% of a single and as I recall the change involved a drop in the single fare rather than just a hike in the return.  Credit due to FGW as they were called.

175% strikes me a reasonable and sensible.  There is something to be said for not making them closer to 200% - encourage people to buy returns rather than have zero benefit and have two separate ticket issuing transactions.  And keeping return fares widely in place also helps on revenue protection - I have heard an argument for the £1 more being "well - if w don't catch 'em on the way out, we get 'em on the way back and we've only lost a quid".

I wasn't going to suggest abolishing returns just pricing them at twice the price of a single.  The revenue protection angle has something going for it, but I suspect was more relevant in the days of ungated stations.  Not so long ago even decent size stations (I am thinking Bath, Chippenham, Temple Meads, Manchester Picc,  Durham) would have lacked barriers. 

Not with the majority of Singles currently being just £1 less than the Return. That would almost double the cost of most Returns based on the current pricing model.

I think you meant to say that Singles should be half the price of Returns. Maybe plus a small percentage supplement for the Single. Say, £100 Return, £55 single.