The earliest reference to the game of Noddy in the Oxford English Dictionary dates from 1589. The basic term noddy, means a fool or simpleton, but in the gaming sense, it is just the name given to the Knave of the suit turned up at the start of play. A very interesting description of the game can be found in Randle Holme's The Academy of Armory, written in 1688, which displays previously unrecorded scoring features and terminology.
Cribbage without the Crib
Noddy can be thought of as the "small Cribbage without the Crib". But it would seem that the game of Noddy was played for counters, and that it was fifteen or twenty-one up, as quoted by Shirley. In a play of Middleton's, Christmas, speaking of the sports of that time as children, says that the game was played for thirty one. And in Salton's Tales the game was depicted as being played for twenty one. It is probable, however, that it was played all the three ways, as 15, 21 and 31 points at the choice of the players. Edmund Gayton speaks of noddy boards, but Robert Nares in A Glossary: or Collection of words, phrases, names and allusions to customs, proverbs, &c says that Noddy was not played with a board, which seems to be plausible due to the natural evolution of card games.
Gameplay
Noddy is a game for two or four players - the latter presumably partners - receiving each 3 cards from a 52-card pack ranking from Ace to King. The object of the game is to peg points for making combinations both in the hand and in the play up to 31 over as many deals as it takes. A23 is a valid sequence, but AKQ isn't. Whoever cuts the lower card deals first.
*Three or more cards of the same suit: 1 per card.
Terminology
In the game, certain cards have peculiar names and scores, like "Flatback" 6, "Countenance" 4, "Roger" 5, and "Knave Noddy" - name applied to the Knave of the suit turned up at the start of the play - scores 2 to the dealer. The earliest reference to the game in the Oxford English Dictionary, dates from 1589. It is now presumed extinct, although recent reports suggests it is still played in parts of Lancashire.
Literature
Festivous notes on the History and adventures of the renowned Don Quixote by - 1768