1 Ishmael: Did you know Siobhan was such a board game nerd?
2 Elspeth: I had no idea she was a nerd at all.
3 Ishmael: I mean, it’s fine and all...
4 Ishmael: But I’d really like to not lose for once.
4 Siobhan: Ha! 14 military! Eat iron!
4 Martian 1: With Babylon, wow.

The game they're playing is 7 Wonders.

It's a board game in which each of up to 7 players is in charge of a classical-era civilisation, represented by the Seven Wonders of the Ancient World. Each player is randomly assigned one of the Wonders at the beginning of the game, represented by a small individual game board which you place in front of you. The board shows you the stages of building your particular Wonder, each stage of which is an action that you can take during the game.

The game is played with a set of cards which are dealt out to the players. Each turn, simultaneously each player secretly selects (or "drafts") a card from their hand to keep, and then passes the remainder of the hand to the next player around the table. All of the drafted cards are revealed simultaneously. This process is repeated until only one undrafted card is left in each hand, which is discarded. This completes a single Age of the game, and the process is repeated for a total of three Ages. The card set for each Age is predefined, and the cards become more powerful in later Ages.

Some of the cards are free - you can draft them at any time. Other cards require you to possess resources (e.g. wood, bricks, stone, cloth, glass, etc.). They have a cost indicated by resource icons on the card. You can only draft a card with a cost if you already have production facilities (e.g. a lumber yard, clay pool, stone pit, loom, or glassworks, respectively for the resources previously mentioned) that produce all of the required resources - or if you can make up the cost by buying resources from the players immediately neighbouring you on either side. Buying resources involves paying them a number of coins, allowing you to use resources from their production facilities to pay the cost of a card - the original owner of the production facility does not lose it. Some of the production facilities are free cards, so you can bootstrap yourself and build up to buying cards that cost several resources.

Other cards provide coins, or make buying resources cheaper for you, or give you various amounts of points. A subset of the cards are "science" cards, which notionally provide advances in technology. Collecting sets of these cards is worth an escalating amount of points. Another subset of cards are "military" cards. Collecting these allows you to score points by having more military might than your neighbours, at the end of each Age.

Finally, instead of drafting a card to add to your tableau, you can draft any card to build a stage of your Wonder. Each stage has a cost that must be paid in the same way as the cost of a card, and provides a different bonus once built. Some are simply worth a lot of points, while others allow you to do things such as rummage through the discard pile and build any card from there.

At the end of the third Age, whoever has the most points wins. Because there are many different ways to earn points, there are multiple different strategies that you can pursue for victory, and they are well balanced, so no one strategy dominates.

The game really shines with 7 players, but works decently for 3-6. It's a firm favourite with my group of gaming buddies, and we play it regularly. Many would consider it a better option for 7 players than the previously discussed Diplomacy.