Poker is a five-card vying game played with standard playing-cards.

A five-card vying game is one where, no matter how many cards may be dealt to each player, the only valid combinations are those of five cards. In orthodox Poker these are, from highest to lowest.
The birth of Poker has been convincingly dated to the first or second decade of the 19th century. It appeared in former French territory centred on New Orleans which was ceded to the infant United States by the Louisiana Purchase of 1803.

For the sake of clarity, they may be grouped according to the number of cards dealt and listed as follows.

Three-card games include Belle, Flux & Trente-un (French, 17th - 18th centuries, known as Dreisatz in Germany), Post & Pair (English and American, 17th - 18th centuries) and its derivative Brag (18th century to present), Brelan (French, 17th - 18th centuries) and its derivative Bouillotte (late 18th - 19th centuries, French and American). Of these, Bouillotte and Brag are most relevant to the genesis of Poker.

Four-card games include Primiera (Italian, 16th century - present) and its English equivalent Primero (16th - 17th centuries), Gilet (under various spellings, French, 16th - 18th centuries), Mus (Spanish, specifically Basque, current, of unknown age), Ambigu (French, 18th century). None of these have much bearing, if any, on Poker.
Five-card games include the German Pochen or Pochspiel, which may be equated with a 15th-century game recorded as Bocken, and was played in France first under the name Glic and subsequently as Poque. Of all early European gambling games this one is most obviously germane to the genesis of Poker to the extent of having ultimately furnished its name. Pochen is a verb meaning to primarily to hit, strike, or knock on the table, and secondarily ‘(I) play’ or ‘bet’ or ‘raise’. Thus Pochspiel is the game (Spiel) of poching, i.e. knocking or betting. In its earliest form it appears as boeckels, bocken, bogel, bockspiel and suchlike.