Wizard's Hat
LegendaryExpand magical knowlegde. +10 max levels for all tomes. Gives one less max level per stack, for a minimum of 2 at 9 stacks
Scaling Type:
Decreasing linear scaling (diminishing returns) per additional copy, with a minimum of +2 max tome levels per copy (from 9+ stacks)
Detailed Explanation
Wizard's Hat increases the maximum level cap for all tomes.
No hidden mechanics:
- The 1st Wizard's Hat gives +10 max tome levels.
- Each additional hat gives 1 less max tome level than the previous hat.
- This falloff continues until a minimum of +2 max tome levels per hat (reached at 9 stacks and beyond).
So it’s a "diminishing returns" max-level increase that only affects tomes (not weapons).
No hidden mechanics:
- The 1st Wizard's Hat gives +10 max tome levels.
- Each additional hat gives 1 less max tome level than the previous hat.
- This falloff continues until a minimum of +2 max tome levels per hat (reached at 9 stacks and beyond).
So it’s a "diminishing returns" max-level increase that only affects tomes (not weapons).
How it Stacks
Let $n$ be the number of Wizard's Hats.
So the first few hats give:
- 1st hat: +10
- 2nd hat: +9
- 3rd hat: +8
- 4th hat: +7
- 5th hat: +6
- 6th hat: +5
- 7th hat: +4
- 8th hat: +3
- 9th hat: +2
- 10th+ hat: +2 each
Max tome levels gained per hat (diminishing)
The amount added by the $k$-th hat is:$$\Delta(k)=\max(2,\ 11-k)$$
So the first few hats give:
- 1st hat: +10
- 2nd hat: +9
- 3rd hat: +8
- 4th hat: +7
- 5th hat: +6
- 6th hat: +5
- 7th hat: +4
- 8th hat: +3
- 9th hat: +2
- 10th+ hat: +2 each