William Perkins, Cases of Conscience in Works, Vol. 2, pp. 141-142 (modernized type):
Games of hazard are those in which hazard only bears the sway, and orders the game, and not wit; wherein also there is (as we say) chance, yea, mere chance in regard of us. Of this kind is Dicing, and sundry games at the Tables and Cards. Now games that are of mere hazard, by the consent of godly Divines are unlawful. The reasons are these.
First, games of mere hazard are indeed lots; and the use of a lot is an act of religion, in which we refer unto God the determination of things of moment, that can no other way be determined. For in the use of a lot there be four things. The first is, a causal act done by us, as the casting of the Die. The second is, the applying of this act to the determination of some particular controversy, the ending whereof maintain peace, order and love among men. The third is confession, that God is a sovereign Judge, to end and determine things that can no other way be determined. The fourth is supplication, that God would by the disposition of the lot when it is cast, determine the event. And these actions are enfolded in the use of a lot, and they are expressed, Act. 1. v. 24, 25, 26. Now then, seeing the use of a lot is a solemn act of religion, it may not be applied to sporting, as I have showed in the first conclusion. Secondly, such games are not recreations, but rather matter of stirring up troublesome passions, as fear, sorrow, &c. and so they distemper the body and mind. Thirdly, covetousness is commonly the ground of them all. Whereupon it is, that men usually play for money. And for these causes, such plays by the consent of learned Divines, are unlawful.
The third kind of plays are mixed, which stand partly of hazard, and partly of wit, and in which hazard begins the game, and skill gets the victory: and that which defective by reason of hazard, is corrected by wit.
To this kind are referred some games at the cards and tables. Now the common opinion of learned Divines is, that as they are not to be commended, so they are not simply to be condemned, and if they be used, they must be used very sparingly. Yet there be others that hold these mixed games to be unlawful, and judge the very dealing of the cards to be a lot, because it is a mere causal action. But (as I take it) the bare dealing of the cards is no more a lot, than the dealing of an alms, when the Princes Almner puts his hand into his pocket, and gives, for example, to one man six pence, to another twelve pence, to another two pence, what comes forth without any choice. Now this causal distribution is not a lot, but only a causal action. And in a lot there must be two things. The first is, a causal act: the second, the applying of the foresaid act, to the determination of some particular and uncertain event. Now the dealing of the cards is a causal act; but the determination of the uncertain victory is not from the dealing of the cards in mixed games, but from the wit and skill, at least from the will of the players. But in things that are of the nature of a lot, the wit and will and a man hath no stroke at all. Nevertheless, though the dealing of the cards and mixed games be no lots; yet it is far safer and better to abstain from them, than to use them, and where they are abolished, they are not to be restored again, because in common experience, many abuses and inconveniences attend upon them: and things unnecessary, when they are much abuses, because they are abused, they must not be used, but rather removed, as the brazen serpent was, 2 King. 18. 4.
In seventeen-century old England and new England, one card game in particular stood out as an acceptable recreation, and it was called Whist. It's predecessor was Ruff and Honours, and its successor in popularity is Bridge. Whist is wist not (unknown, pardon the grammatical awkwardness as well as the feeble attempt at humor) by many today, but it gained widespread acceptance even in Puritan circles back in the day.
Francis J. Bremer and Tom Webster, eds., Puritans and Puritanism in Europe and America, p. 554:
Card games, which took England by storm in the sixteenth and seventeenth centuries, did pose a dilemma to Puritans. They associated cards with the Italians and French, both of whom they assumed were usually depraved in their pursuit of amusements. Additionally, cards lent themselves easily to gambling and indolence. On the other hand, card games were cheap, easily accessed, great fun, and could teach arithmetic skills. In general, most Puritan moralists never explicitly condemned card games but remained uneasy about them. In New England, however, during the late seventeenth century, whist became an extremely popular card game and enjoyed widespread acceptability. Whist parties became commonplace and often had more than a dozen participating couples.
Bruce C. Daniels, Puritans at Play, p. 179:
Whist was the most frequently played game in old and New England. Particularly popular with the upper classes in England, whist was so ubiquitous among the gentry and clergy that it becamse a staple of satirical literature used to lampoon them: "to cheat the thirsty moments, whist awhile," one wit advised a minister fighting boredom. People believed that whist required quiet concentration to devise strategy; hence its name: "whist" meant "silence." [This is disputed by some since the game was originally called "whisk" which was morphed into "whist."] No one knows its origins for certain, but in England whist was first widely played in the 1640s. Its appeal to the elite rested somewhat on its snob appeal as a game reputedly for refined and intelligent players.
Whist applead to the same constituency in New England as it did in England. Ministers, merchants, college students, and professionals embraced it as their game of choice. Women seldom played cards -- the competition was thought to be inimicable to their nature -- but elite women did often play whist, which seemed to be the exception to the rule.
In almost all ways whist was the ideal game for Puritan society: quiet, contemplative, and companionable, it required skills of logic and arithmetic; it could not be readily played in a rowdy atmosphere or under the influence of alcohol; and, unlike many games, whist needed no betting to make the competition exciting. In fact players seldom gambled on whist. Not likely to lead to other vices, whist met all the criteria for useful recreation.