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!
> I love it when people apply operations research technologies to silly things like video games
To be fair, video games can also be big money. And even if not, some take them very seriously.
> this is a useful result theoretically, but it's not very practical in game
Yeah, it's an unfortunate combination - the game itself is too complicated for the analysis to be useful (counters, full builds, game state), and the item space is too simple to need it.
I remember a story about Richard Feynman, where he said he had a dozen or so (?) mathematical "tricks" that he applied to every problem he encountered. When one worked, he looked like a genius. When it didn't...
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!