The Collaborative International Dictionary of English v.0.48:

Finesse \Fi*nesse"\, v. i. [imp. & p. p. Finessed; p. pr. &
   vb. n. Finessing.]
   1. To use artifice or stratagem. --Goldsmith.
      [1913 Webster]

   2. (Whist Playing) To attempt, when second or third player,
      to make a lower card answer the purpose of a higher, when
      an intermediate card is out, risking the chance of its
      being held by the opponent yet to play.
      [1913 Webster]