I love it when people apply operations research technologies to silly things like video games.

One thing I'm missing in this article is a discussion of how useful the ILP techniques really were compared to dumber heuristics. Take the first optimal build as an example:

- We know we will need some items that give us a large boost to our stats thanks to the six-item limit.

- Nashor's tooth seems like an "obvious" choice for the above, given that it supplies 130 units of desirable stats at only 100 gold per unit.

- Once we have that, the Amplifying Tome is really only there to fill out the remaining units of one of the stats.

I guess what I'm saying is the optimal item selection has surprisingly few interactions. That seems like a solution we could get close to with far simpler methods!