  A class of discrete Bidding Combinatorial Games that generalize alternating
normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major
questions concerning optimal outcomes were resolved. By generalizing standard
game comparison techniques from alternating normal play, we propose an
algorithmic play-solution to the problem of game comparison for bidding games.
We demonstrate some consequences of this result that generalize classical
results in alternating play (from Winning Ways 1982 and On Numbers and Games
1976). In particular, integers, dyadics and numbers have many nice properties,
such as group structures, but on the other hand the game * is non-invertible.
We state a couple of thrilling conjectures and open problems for readers to
dive into this promising path of bidding combinatorial games.
