An average item yields about 20 mana, so six average items would be needed to yield 120 mana. An average item costs about 40gp, so six average items costs about 240gp. Since I only have 200gp I would need to be pretty confident of my choices to expect to make a profit from this. The expected profit for any combination of items is 200*P(success) - cost, so for a purchase to be profitable, it is necessary that P(success) > cost/200.
I estimated the optimism of the Thaumometer for each item by averaging the optimism scores of each trait (average of ln of reading/actual for items with that trait). I used this optimism estimate to calculate a corrected reading for each item. I also calculated a separate mana score for each item by averaging the mana scores of each trait. Finally, I averaged the corrected Thaumometer score with the mana score for each item to get a final guess for its mana yield.
I sorted the list of available items by efficiency (final guess divided by price). [10, 11, 3, 12, 4, 7, 6, 5, 9, 8, 1, 2]
The profit-maximizing strategy should be some number of the most efficient items with at least 120 total expected mana that cost no more than 200gp. As it turns out, there is only one such number of items (5). This combination yields an expected 128 mana and costs 181gp for a profit of 19gp. However, for any purchase to be profitable, the probability of success has to be greater than (purchase price)/(budget). In this case that is 181⁄200 or 90.5%. Given that the expected mana yield is only barely above the threshold, I think I’m only about 65% confident of success—nowhere near 90%.
My choice, therefore, is to decline the offer and return the 200gp.
I feel silly now after looking at gjm’s answer. I had actually sorted the list by type, attribute and modifier already without finding obvious patterns, and I had planned to do color as well, but then I took a break and when I came back I forgot to look at the colors.
An average item yields about 20 mana, so six average items would be needed to yield 120 mana. An average item costs about 40gp, so six average items costs about 240gp. Since I only have 200gp I would need to be pretty confident of my choices to expect to make a profit from this. The expected profit for any combination of items is 200*P(success) - cost, so for a purchase to be profitable, it is necessary that P(success) > cost/200.
I estimated the optimism of the Thaumometer for each item by averaging the optimism scores of each trait (average of ln of reading/actual for items with that trait). I used this optimism estimate to calculate a corrected reading for each item. I also calculated a separate mana score for each item by averaging the mana scores of each trait. Finally, I averaged the corrected Thaumometer score with the mana score for each item to get a final guess for its mana yield.
I sorted the list of available items by efficiency (final guess divided by price). [10, 11, 3, 12, 4, 7, 6, 5, 9, 8, 1, 2]
The profit-maximizing strategy should be some number of the most efficient items with at least 120 total expected mana that cost no more than 200gp. As it turns out, there is only one such number of items (5). This combination yields an expected 128 mana and costs 181gp for a profit of 19gp. However, for any purchase to be profitable, the probability of success has to be greater than (purchase price)/(budget). In this case that is 181⁄200 or 90.5%. Given that the expected mana yield is only barely above the threshold, I think I’m only about 65% confident of success—nowhere near 90%.
My choice, therefore, is to decline the offer and return the 200gp.
I feel silly now after looking at gjm’s answer. I had actually sorted the list by type, attribute and modifier already without finding obvious patterns, and I had planned to do color as well, but then I took a break and when I came back I forgot to look at the colors.