The goal of Ticket to Ride is to build train routes crisscrossing North America. It’s one of the most addictive multiplayer games on Xbox Live.

Playful Entertainment

I’m a sucker for big, juicy games with flashy graphics, block-rockin’ audio and tons of things to do. This summer has been unusually rich in such ambitious productions, with high-profile releases like Metal Gear Solid 4, Ninja Gaiden II and Grid.

But smaller games can be just as satisfying. Sometimes you just want to play for 15 minutes or so, and that’s where casual games become an important part of your diet. They’re fast, they’re easy to learn and, perhaps most important, they’re inexpensive.

Microsoft’s Xbox Live Arcade has become an invaluable resource for high-quality casual games. If you haven’t connected your Xbox 360 to the Internet, you’re missing out on a great deal of what the system has to offer. Here are some of the finer games that have appeared on Arcade this summer.

Braid (Microsoft, for the Xbox 360, $15): Created by independent developer Jonathan Blow, Braid looks and sounds unlike any other video game. Its gorgeous watercolor art and soothing music give it a dreamlike feeling — although you probably won’t feel so relaxed after wrestling with some of its innovative, devious puzzles.

The story is your standard rescue-the-kidnapped-princess narrative, though it’s laced with a sense of melancholy and regret that hints at a deeper interpretation. On each level you have to navigate a series of pits and platforms to retrieve pieces of a jigsaw puzzle, but you can rewind time at any point to correct a mistake.

That time-bending ability is the key to most of the puzzles in Braid. On some levels, time moves forward when you go right and reverses when you go left. On others, you can drop a ring that slows down time in a small area of the landscape. I stared at some of the puzzles for hours, only to walk away and have the solution come to me while I was doing something else. It’s an unusually satisfying experience, marred only by its relatively brief length.

Ticket to Ride (Playful Entertainment, for the Xbox 360, $10): Board-game designer Alan R. Moon has developed a worldwide following for his elegant inventions, and his award-winning Ticket to Ride is his first game to go electronic. A new studio, Playful Entertainment, has done an exemplary translation, turning Ticket to Ride into one of the most addictive multiplayer games on Xbox Live.

A map of North America is crisscrossed by multicolored train routes, and your goal is to connect cities by placing your train cars on those routes. To claim a route, you need the correct number of cards that match its color; for example, it takes six red cards to get from New Orleans to Miami. Destination cards tell you which pairs of cities you need to connect, and you score more points for connecting distant locales (say, Seattle to New York over Kansas City to Houston).

The endgame usually boils down to a frantic race to finish a route before someone runs out of train cars. Win or lose, you’ll usually find yourself wanting to play just one more game. Playful has already released a $7.50 European expansion, which adds ferries and tunnels, and more maps are on the way. Geometry Wars: Retro Evolved 2 (Activision, for the Xbox 360, $10): Geometry Wars was one of the first big hits on Xbox Live Arcade, reviving the old-fashioned 2D shoot-’em-up with its unique double-joystick controls. It’s essentially a jazzed-up version of Asteroids: You fly a ship around and shoot everything that moves, setting off the occasional bomb when things get too hectic.

The major enhancement to GW2 is the addition of geoms, which appear whenever you destroy an enemy; each geom you grab increases your score multiplier. The sequel also adds five new game modes. In King, for example, you have to zip between shrinking safe zones, which are the only areas you can shoot from. In Pacifism, you can’t use your weapons at all and have to lure your enemies through rotating gates.

The new gimmicks add some refreshing variety to a solid game formula, and will force GW veterans to develop new strategies. It’s mystifying, though, that the series’ developers still haven’t embraced online competition.