Wizard's Hat
Wizard's Hat Megabonk – Explained
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 (tome level caps at 109)
- 2nd hat: +9 (tome level caps at 118)
- 3rd hat: +8 (tome level caps at 126)
- 4th hat: +7 (tome level caps at 133)
- 5th hat: +6 (tome level caps at 139)
- 6th hat: +5 (tome level caps at 144)
- 7th hat: +4 (tome level caps at 148)
- 8th hat: +3 (tome level caps at 151)
- 9th hat: +2 (tome level caps at 153)
- 10th+ hat: +2 each
If your tomes are already at their current max level and you microwave away a hat, you can level them further than before.
Example:
1. You have 2x hats and your tome levels are maxed up to level 118
2. You microwave away a hat, and you now have 1x hat in total
3. You can now level up your tomes to level 128
This also works with more hats: for example, if you had 4 hats and microwave one away (dropping to 3), you can then level your tomes up by +8 levels again, matching the bonus the 3rd hat normally gives.
There may also be some conditions where you can get even more levels from microwaving away a hat (some players have reported this), but it’s unclear exactly what needs to happen for that to occur.
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 (tome level caps at 109)
- 2nd hat: +9 (tome level caps at 118)
- 3rd hat: +8 (tome level caps at 126)
- 4th hat: +7 (tome level caps at 133)
- 5th hat: +6 (tome level caps at 139)
- 6th hat: +5 (tome level caps at 144)
- 7th hat: +4 (tome level caps at 148)
- 8th hat: +3 (tome level caps at 151)
- 9th hat: +2 (tome level caps at 153)
- 10th+ hat: +2 each
Microwave bug
If your tomes are already at their current max level and you microwave away a hat, you can level them further than before.
Example:
1. You have 2x hats and your tome levels are maxed up to level 118
2. You microwave away a hat, and you now have 1x hat in total
3. You can now level up your tomes to level 128
This also works with more hats: for example, if you had 4 hats and microwave one away (dropping to 3), you can then level your tomes up by +8 levels again, matching the bonus the 3rd hat normally gives.
There may also be some conditions where you can get even more levels from microwaving away a hat (some players have reported this), but it’s unclear exactly what needs to happen for that to occur.
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