I'm wondering why a debut author would want a multi-book deal. It seems to me that the only thing the author gains is a guaranteed* amount of money. But they lose the ability to get paid more for the second book if the first book does better than expected. That effectively means they're betting against their own first book. If it does poorly, then yay, they get their guaranteed advance for book two. If it does amazingly well, then boo, they get their guaranteed advance for book two. Why isn't it always in the interests of the author (and agent) to negotiate a deal for the second book after the first one is published?
* for certain definitions of guaranteed.
You are misunderstanding how book contracts work. The amount of money an author is paid upfront is an advance against royalties. In other words, that money is recouped to the publisher before the author gets paid more.
So, if Book #1 does really well, the publisher recoups the advance, and then pays royalties to the author.
If Book #1 tanks, the publisher does NOT recoup the advance (the author does not need to repay it) but there probably aren't going to be any royalties.
Notice, this has nothing to do with Book #2.
Your premise is that if Book #1 goes stratospheric, the author would be in a better position to get more money. That's not true.
The author might get a larger advance, but that money must be recouped to the publisher before the author sees another Susan B. Anthony dollar.
In other words, it only affects when you get paid more that's different;upfront or via paid royalties.
But, let's shine the cold cruel light of day in here.
Most second books do appreciably worse than first books.
And most first books don't earn out.
Thus, you can see the attraction of a two or three book deal. It means my guy gets paid even if the book doesn't earn what we hope.