Sharing a pepperoni pizza with your worst enemy

Believe it or not, this problem has been studied before (in the superficially different formulation of a pizza sliced into radial slices of unequal size). It turns out that the first player can only guarantee getting $4/9$ of the pizza: there are slicings of the pizza under which the second player can get $5/9$ of the pizza. See, for example, this arxiv preprint. If you have access to MathSciNet, this review of the same paper might also be a decent index into the history of the problem.

This problem reminds me of the first problem, "Coins in a Row", in Peter Winkler's Mathematical Puzzles: A Connoisseur's Collection.

There are quite a number of discussions of this problem online, for example here's a blog post that looks to maximize a linear version of this problem.

Curiously, with the linear version of the problem (where players can either pick the first or last "slice" in the line), an even number of "slices" guarantees that the first player can have more "pepperoni", but an odd number of "slices" often gives the second player an advantage.