Invoice first. Ask questions later.

On the flip side, often I will just buy the keg, throw the party myself, charge $5 at the door, and keep the profits.

Agree with the point though... expecting people to "even up" later is a joke.

More often than not, you're better off taking on responsibility for the whole venture, or staying out of it.

I agree. I've never had any luck getting people to share the expenses when they're not even willing to share the workload, and social structures are the worst, because nobody wanted to rudely spell it out, so afterwards people just quietly ... ignore it.

In business, though, it's nice and clear cut. Payment is due upon approval of the final deliverable. Approval must be given within ten days of the receipt of the project, or it is assumed approved and payment is due immediately.

It's nice to spell out those contingencies, because in my experience the hardest feelings occur when your client thinks you should be more understanding of "shit happening" and you think the client should review what the words "due immediately" mean.