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Scroll of proficiency detail

The scroll of proficiency requires a Construction level of 60 and a Dungeoneering level of 60. Reading the scroll of proficiency permanently unlocks the ability: when constructing a piece of furniture that requires three planks or more, there is a chance of that you will retain one plank. The chances are:

It is not possible to obtain multiple scrolls or to buy a scroll if the player has previously unlocked the scroll's ability.

When read, you get the message: The secret is yours! You unlock the ability to save planks when constructing. and when you save a plank you get the message: Your proficient construction ability means you retain [amount] plank[s].

Analysis[]

The scroll of proficiency rolls to save a plank for every third plank used in an item. This means it can save up to 1 plank in items that use 3-5 planks, 2 planks in items that use 6-8, and 3 in items using 9-11.

The chances and average savings are as such:

Plank 3-5 plank items 6-8 plank items 9-11 plank items
Save: 0 1 Avg 0 1 2 Avg 0 1 2 3 Avg
Normal 50% 50% 0.5 25% 50% 25% 1 12.5% 37.5% 37.5% 12.5% 1.5
Oak 75% 25% 0.25 56.25% 37.5% 6.25% 0.5 42.19% 42.19% 14.06% 1.56% 0.75
Teak 80% 20% 0.2 64% 32% 4% 0.4 51.2% 38.4% 9.6% 0.8% 0.6
Mahogany 90% 10% 0.1 81% 18% 1% 0.2 72.9% 24.3% 2.7% 0.1% 0.3
Protean 95% 5% 0.05 90.25% 9.5% 0.25% 0.1 85.74% 13.54% 0.71% 0.01% 0.15

Because the scroll rolls with equal chance for every third plank, it increases efficiency the most when constructing items that use 3, 6, or 9 planks. Constructing items with different numbers of planks adds planks without adding an extra chance to save, resulting in decreased efficiency, as shown below.

The expected percentages of planks saved are as follows:

Plank Number of planks
1 2 3 4 5 6 7 8 9 10 11
Normal 0% 0% 16.67% 12.5% 10% 16.67% 14.29% 12.5% 16.67% 15% 13.64%
Oak 0% 0% 8.33% 6.25% 5% 8.33% 7.14% 6.25% 8.33% 7.5% 6.82%
Teak 0% 0% 6.67% 5% 4% 6.67% 5.71% 5% 6.67% 6% 5.45%
Mahogany 0% 0% 3.33% 2.5% 2% 3.33% 2.86% 2.5% 3.33% 3% 2.73%
Protean 0% 0% 1.67% 1.25% 1% 1.67% 1.4% 1.25% 1.67% 1.5% 1.36%

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