Are there any gaming console platforms that have casual games available?

I'm probably going to get booed out of here, but I don't know where else to ask. I'm a fan of casual games, like the kind you can find at Big Fish - hidden object, adventure, but most of all fairly quick. I'm not looking to spend $50 on a game that takes me weeks to finish; I'd rather spend $50 on 5 games that each take 6 or 7 hours.

I've never played with a console system before; strictly PC. But I just switched to Linux and there's a lack of available games on that platform, so I'm willing to spend some money on a console if there are casual games available. (Yes, I have a virtual machine running, and WINE, but there are hardware limitations that prevent most Windows games from running under either.)