You might want to restrict this somewhat in time and perhaps social class.

If we just look at the Anglican gentry of Regency England (i.e., the milieu of Jane Austen and her novels), we really don't see any sex-based distinctions on play of card and board games. They were a common social activity for mixed-sex parties. In Austen's own writings we find quite a selection of card games including whist, casino, commerce, lanterloo, vingt-un, lottery tickets, piquet, quadrille, brag, and cribbage. (You can look up all these games: basically they run the gamut from skill-intensive trick taking games like whist, the quintessential thinker's game of the period, to pure luck games like lottery tickets. Commerce and brag are rather like poker, a game that did not yet exist.)

These games were usually, perhaps nearly always, played for small stakes, pennies or shillings. This would probably seem like gambling to us, but it was quite acceptable. The priggish clergyman Mr. Collins boasts in Pride & Prejudice that he can afford to lose five shillings at whist, apparently without any threat to his moral standing. In the same novel, Elizabeth Bennet decides to skip a game of lanterloo at Netherfield Park because she suspects the much wealthier hosts and guests are "playing high" and she will not be able to afford the stakes. So Elizabeth starts reading a book instead, establishing her reputation for bookishness with this set. One of Jane Austen's letters about her actual life relates that she held back from playing much commerce at a party because she could not afford to lose the three-shilling stake twice. Gambling becomes a problem when it leads to debts that cannot be paid: thus, when the cad Wickham's debts are revealed, he is immediately identified as a "gamester" and not to be trusted in any manner.

Board games are not as much seen in Austen's novels. In Emma the title character plays backgammon with her father.

So at least in this social milieu, I don't think we see much if any distinction between men's and women's games.