It's not clear to me that the added complexity aka risk of bugs is worth it in your case for any reasonable game design.
In the chess example, knowing it's possible to lose from X positions is almost meaningless most of the time. The issue is search space sizes are either to large to be useful or small enough for brute force.
You can always use it things that are not critical for the game to work; and a good coder would make it in a separate class/container so most possible bugs are isolated as well.
In the chess example the most importan thing its not for the machine to win (or lose); is so the user feels its not the same game they already played; or -dare I say- think that the enemy is "learning"
Even cellphones can run chess programs powerful enough to beat any human. The normal way to tone them down is to make them more random which prevents games from repeating in the first place. Making this a non issue.
Even ignoring that and assuming you wanted to do a lookup vs all games played with someone that's a tiny dataset so looking it up has no real downside.
