Yes, Virginia, there is a Big Lebowski convention:

Achievers pay $1 a chance (proceeds going to Big Brothers/Big Sisters) to try their hand at Lebowski-inspired games such as the Marmot Toss, the Malibu Sheriff Mug Toss and the Ringer Toss. In the latter, contestants sit in an approximation of the Dude's big, battered, rusty green car and try to toss the ringer (a bag full of dirty undies) at a make-shift target. (In the movie the Dude and Walter are supposed to toss a bag with $1 million to the kidnappers, but they toss the ringer, instead.) The prize is either a whoopee cushion or a cheeseburger yo-yo. I take the yo-yo.

Thanks to She Who Must Be Obeyed for the link.