Many would say hiring and using a servant will make construction training go much faster. Let's look at the cost of using the servants to run noted logs to the sawmill.
The earliest servant to take noted logs is the cook, who will unnote and carry back 16 planks. She's available at level 30 construction, but for this we'll hire her at level 33, the level we can make oak larders. Her salary is 3,000 gp upon hiring and per every eight trips afterwards. In order to reach level 99, we need to make 27,118 oak larders (216,944 oak logs). If we take 24 oak planks with us for the first trip and have the cook convert the remaining oak logs into planks, we'll need 59,324,000 gp to cover the costs of her salary (5,088,000 gp) and oak log payments (54,236,000 gp).
A little over five million gold extra paid because we're too lazy to convert our own logs. Of course, this is sticking with the cook. How much would it cost if we upgraded to the butler and then to the demon butler at the appropriate levels?
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