Whist - wist

Whist and wist form one of the sets of homophones listed by the then Poet Laureate Robert Bridges.
(For more, see Bridges homophones). AWE has a category listing our articles on each of these.

• Whist is a card game. It is like Bridge, which developed from it, a trick-taking game between four players, who form two partnerships.

Whist, being a word little needed in academic writing, is usually a typographical error when seen in a student's work. 
If you have written 'whist', you probably meant whilst. 

Whilst is  essentially a variant spelling of the conjunction while.

• Whist can also be a form of whisht or wheesht, a variant of shush or, most simply, Sh!, an attempt to represent in writing the sound that parents make to young children to remind them to be silent. (This noise is also used by many older groups to younger groups to ask for silence.) This word developed in Ireland and Scotland, and has been less used in England

• OED lists three words written wist, one adjective, one noun and one verb. All are archaic, but may be met with in some forms of academic study.
  • The adjective wist meant 'attentive', 'intent'. It led to the current adjective wistful, which originally meant the same; it is now closer to 'yearning'. 'intent on acquiring [something unobtainable, either because it is past; or for an object of unreciprocated desire]'. OED (1928) defined it as "Expectantly or yearningly eager, watchful, or intent; mournfully expectant or longing."
  • The noun 'a wist' meant a measurement of Land, used in Sussex. (Its precise modern equivalent is unclear.)
  • When used verbally, wist was originally (in Old and Middle English) the past form of the irregular verb 'to wit'. By the Early Modern period, it was often being used erron[eously] (OED) as a present tense meaning 'to know'. The modern use of wist is also contaminated by the errors surrounding i-wis.