Finchley Central is a mind game in which two players take turns naming stations in the London Underground. The first person to name Finchley Central is the winner. Of course, the first player could say "Finchley Central" straight away, but as maths professor Jonathan Partington notes,
An opening move of "Finchley Central" is too much of a cheat, and you might wish to start with, say, Liverpool Street, when, assuming that your opponent isn't rude enough to reply with Finchley Central, leaves you with a mate on your second move (though you probably would prefer to stall by playing, say, Bank, in the hopes of a more spectacular win later).
The game was first described by the mathematicians Anatole Beck and David Fowler in the Spring 1969 issue of Manifold magazine (A Pandora's Box of Non-games page 32). Beck and Fowler note,
It is clear that the ‘best’ time to say Finchley Central is exactly before your opponent does. Failing that it is good that he should be considering it. You could, of course, say ‘Finchley Central’ on your second turn. In that case, your opponent puffs on his cigarette and says, ‘Well…’ Shame on you.
Finchley Central became the basis for the game Mornington Crescent in the BBC Radio 4 series I'm Sorry I Haven't a Clue. It has also been suggested as a possible origin for The Game.