What's the cheapest fare from A to B? A new website called Faremap reckons it's got it cracked, with a fancy mapping interface that shows the price pockets and least expensive route.
Let's give it a spin with a common commuting corridor:
Clapham Junction -> Bank
There are many ways of completing this journey. The map doesn't suggest the quickest (many other sites do that), but instead displays different ticketing options. Here, the cheapest route is to use TfL-only services (e.g. Overground to Clapham High Street, then do an interchange to the Northern line). The perhaps more-common option of using national rail services to Waterloo, then taking the tube to Bank adds £1.60 to the fare. The most expensive option is to buy a paper ticket for any route, at £6.20.
Let's try another example, with a literal A to B.
Acton Central -> Brighton
According to the site, the cheapest you can do it (without any savings from pre-booking or special deals) is £17.10 — almost half the price of buying an 'any route' paper ticket, and about £7 cheaper than the usual tactic of going around rather than through central London. To make the saving, though, you have to use three separate tickets, known as split ticketing. This is perhaps too much of a faff for the typical traveller, but a handy tip if money's tight.
Faremap, a non-commercial, open-source platform, covers the whole of the UK and is a joy to play with. It does have shortcomings — for example, it's blind to bus routes, which can shave further money of a journey. But it's only just launched and could do with some constructive feedback. See what it suggests for your usual routes and let us know in the comments if you find any anomalies or pleasant surprises.