Does the board need to be mathematically balanced?

> Question remains: Does the board need to be mathematically balanced?

For most games, you want all systems -- including the board -- mathematically balanced.

But this does *not* imply symmetry or equality within each system.

Consider the board for Settlers of Catan. The tiles aren't symmetric, but the designer imposes balance through order of placement in the starting settlements. Players go clockwise around the table when placing their first settlement. Then, starting with the last person to place, proceed counter-clockwise placing the second settlement.

In your case, you could have fewer, larger treasures in one area (with correspondingly tougher monsters), and "below average" treasures and monsters in another, leaving the third area as you have them, now. This is just an example. I don't know enough about your game to suggest actual changes. Hopefully, it demonstrates two important points:

1) You can balance a group of systems without requiring each system to balance individually.
2) Balance is not the same as symmetry.

Good luck!

According to Christopher Alexander's theory:

"Local symmetry" is good but not complete symmetry. Some games elements needs to be symmetric but not the complete game.

The property he calls "Roughness" explains that imperfection is better than perfection. In board games, this is generally the case for special abilities or unit stats where you know it is not perfectly balanced for sure.

Take a look at my article "playing with numbers" that explains how to use number sequence to make a game look better designed:

http://bgd.lariennalibrary.com/index.php?n=DesignArticle.Article-Playing...