Draughts is a funky little café tucked into a railway arch in Islington, in north London. It has exposed brick walls, a bar stocked with trendy craft beers and a selection of comfy chairs. The toast is artisanal and the avocados are smashed. But the most striking thing is the shelves arrayed at the back of the café. They groan with board games – more than 700 of them, according to Russell Chapman, who works there. When it was founded in 2014, Draughts became London’s first dedicated board-game café.

All the old classics are there: Monopoly, Risk, Battleship, along with their memories of family arguments at Christmas. But the main draw for the patrons is a new generation of deeper, more involving – simply better – games that have been devised over the past couple of decades. At one table a group of people are playing Pandemic, a tricky, strategy game in which players are cast as doctors and scientists trying to save the world from four plagues. Their neighbours are engrossed in a game of Castle Panic, in which the defenders co-operate to defend a fortress from a horde of encroaching monsters.

A board-game café sounds like the sort of niche business that appeals only to hip millennials with a fondness for ironic nostalgia. But, on a Friday afternoon, the crowd is more diverse than that, with families and 50-somethings alongside the youngsters. Draughts is doing so well that its owners are now pondering opening another branch. It is just one beneficiary of a new golden age in board games.

The most popular games sell in their millions. Top of the list is Settlers of Catan, in which players compete to settle a fictional wilderness. It has shifted more than 20m copies since the first edition of 5,000 was released in Germany in 1995. Dominion, a medieval-flavoured card game, released in 2008, has sold 2.5m copies.

There are now competitions and a festival circuit for the most committed fans. In 2016 174,000 people streamed through the doors at International Spieltage, the industry’s flagship trade-show-cum-festival, held every year in the German city of Essen. GenCon, held in America, counted 208,000 people through the turnstiles in 2017. The UK Games Expo, held in Birmingham, has grown from 1,200 visitors in 2007 to 31,000 in 2017. The trend is global, but there are pockets of intense enthusiasm. One is Silicon Valley, where Settlers of Catan is an obsession among many. Reid Hoffman, LinkedIn’s founder and a board-game aficionado, says that Settlers of Catan is “the board game of entrepreneurship”. Earlier this year, Maybe Capital, a satirical game about the Valley, complete with discriminatory rewards for male and female players, was launched on Kickstarter, a crowd-funding site.

One reason for the tabletop-gaming boom is simply that the products have improved. The best modern games are sociable, engaging and easy to learn, but also cerebral, intriguing and difficult to master. The slow triumph of what used to be called “nerd culture” – think smartphone gaming and “Game of Thrones” on television – has given adults permission to engage openly in pastimes that were previously looked down on as juvenile. And the increasing ubiquity of screens has, paradoxically, fuelled a demand for in-person socialising. Board gaming is another example of an old-style, analogue pastime that, far from being killed by technology, has been reinvigorated by it.

The revival began in the 1990s, says Matt Leacock, an American game designer responsible for Pandemic, as the internet began spreading into people’s homes. Leacock was a programmer at Yahoo! at the time. Germany, he says, is the spiritual home of board-gaming. “For whatever reason there has always been a culture there of playing these things, of families sitting around the table at a weekend,” he says. The internet helped that culture spread: “I remember we used to rely on these little hobbyist websites that would do amateur translations into English of all the new German games that were coming out,” says Leacock. As with everything from Japanese cartoons to Jane Austen fandom, the internet helped bring together like-minded people all over the world.

Those early websites have blossomed into a thriving scene of podcasts and YouTube channels, discussing strategy, spreading rumours of new games and offering reviews of the latest games. (“TableTop”, one of the most popular YouTube programmes, is hosted by Wil Wheaton, whom dedicated fans may remember from “Star Trek: The Next Generation”.) Fans can talk directly to designers, who, in turn, can recruit fans to test early versions of their games. Crowd-funding sites allow designers, whether amateur or professional, to raise money for games that have not yet been made, drastically reducing the risks involved in sinking time into a project. Draughts itself began life on Kickstarter, rather than with the traditional loan from a bank.

At the same time, says Steve Buckmaster of Esdevium Games, a British importer of board games, the prevalence of screens has made people keener to connect in person. Board games offer the sort of social experience that no amount of FaceTime, Skype or Destiny can quite replace. “People are sitting in front of a computer all day at work,” he says. “Do they really want to do even more of that when they get home?” Chapman agrees. “I think, paradoxically, one of the things social media can end up doing is keeping you away from your friends,” he says.

The cultural changes wrought by technology have helped, too. “I think the popularity of video games is a factor,” says Leacock. Over the past few decades video-gaming has grown into a $90bn industry. The typical gamer is in their 30s, and almost as likely to be a woman as a man. “It gets rid of this silly idea that games are something only kids should enjoy.” The tactility of board games can be a pleasure in an increasingly virtual world. Many modern games have rich, lovingly crafted pieces. In Kanagawa, for instance, the players are apprentices of Katsushika Hokusai, the most famous Japanese classical artist, and must strive to produce the best paintings in order to win the favour of their master. The playing pieces include a set of miniature brushes, a bamboo mat and a series of beautifully drawn cards featuring images of stags, mountains and blossom leaves. The goal of the game is to assemble them into a larger, harmonious painting.

Finally, and perhaps most importantly, by bringing fans together and allowing them to trade wisdom and good ideas, technology has drastically improved the games themselves. One consequence of the board-gaming boom has been to help designers come up with a set of principles and rules-of-thumb that add up, more or less, to a theory of fun. One way to get a sense of it is to look at a well-known game that violates many of this theory’s tenets. Monopoly is, by most calculations, the bestselling board game of all time. Yet it languishes near the bottom of a list of games as reviewed by the users of BoardGameGeek, a popular website. In the eyes of a modern game designer, it does almost everything wrong. (One reason may be that Monopoly is a polemic disguised as a board game, designed to warn of the dangers of untrammelled capitalist power. It was not intended to be a jolly Christmas pastime.)

One of Monopoly’s big mistakes is positive feedback, designer-speak for a mechanism by which a small advantage early on snowballs into a big, insurmountable one later in the game, which makes things boring for the other players. Modern designers tend to prefer negative feedback, in which life gets harder for those doing well. Sometimes that is enforced by explicit penalties. Sometimes it emerges by itself, or through political dealing by other players. Conquering too many planets in a game of Twilight Imperium may make it hard to defend existing territory, for instance, especially if other players decide to gang up on the leader. That helps to keep things interesting for everyone.

Another problem is that Monopoly has a large element of luck (movement is controlled by rolling dice) and limited strategic depth. Some properties simply offer a better return on investment than others: buying them is always a good idea. Better to offer players less obvious, more thought-provoking choices: advantages that come with significant trade-offs, for instance, or whose usefulness varies depending on what is happening in the rest of the game. Hidden information opens up the potential for bluffing and misdirection. In Ticket to Ride, players compete to build railways across Europe. At the beginning, each player is given a set of secret objectives. If her opponents are to thwart them, they must first try to infer these from how she is playing. Introducing elements of politics, diplomacy or trading can give players things to do even when it is not their turn, helping to keep their interest from wandering.

And the new ideas are still coming. Pandemic, in which the players work together, fuelled a boom in co-operative games, uniting players to work together against the game itself. Computers are finding their way into board games directly: in X-Com (which is based on a bestselling video-game franchise) the players must work together to defend Earth from an alien invasion. The alien forces are marshalled by a smartphone app, which reacts to how the players are doing. By hiving the book-keeping off to a computer, designers are able to experiment with more complex sets of rules that would be fiddly and tedious for human players to administer.

The latest innovation is so-called “legacy” games, named for Risk: Legacy, a 2012 reboot of the classic game that founded the genre. As with modern TV series, the idea is to introduce an overarching narrative, which advances as you play the game multiple times. As an extra twist, the rules change between each playthrough. Depending on the results of a particular game, players could receive instructions to draw new features onto the board, rip up existing rules or be given new powers or obstacles. One such game, Pandemic: Legacy, is, according to the denizens of BoardGameGeek, the single best board game ever made.

Despite its new-found popularity, board-gaming remains a slightly nerdy pastime (there are a number of fans among Economist journalists). And although they are meant to be fun, squint and you can probably justify playing them on the grounds that it is good for you. Board-gaming will improve your mental arithmetic, give you a good grasp of probability and familiarise you with game theory.

The most hardcore games veer on simulation. Volko Ruhnke designs wargames based on real-world conflicts. A Distant Plain aims to recreate the Western invasion of Afghanistan in 2001, in all its political complexity. He is enthusiastic about games’ potential as a teaching tool. America’s spies, it seems, agree. One of Ruhnke’s sidelines is in designing wargames for the cia, which uses them to train analysts and operatives. “A wargame puts you into history in a way that no book can,” he says. “If I’m doing my job properly, the mechanics of the game will force you to consider the choices that real people had to make. That’s advanced. That’s grad-school history, not grade-school stuff.”