D&D.Sci II: The Sorceror's Personal Shopper

Blue Pendant of Hope, Blue Hammer of Capability, Yellow Plough of Plenty, Yellow Warhammer of Justice +1, gaining 124+ mana for 145gp.

Do not gamble with green items or the red pendant of truth; the value of a good, lucrative client with a somewhat useful sensing device and your own credibility is worth much more than some gold pieces today.

Regularities found:

• blue items register +/- 1 on the thaugister, except jewelry gets a +22
• weapon mana is at least 10x the bonus and no more than 10(x+1) the bonus
• (axes and hammers are tools, not weapons)
• yellow items yield 18-21 mana
• green items are capped at 40 mana and their thauyard readings seem very uncorrelated
• actually all jewelry gets a +22 to its thaudout
• jewelry-adjusted blue-adjusted thaulues are at most 60
• red mana is always some product of 2s, 3s, and 5s
• green items always yield an even amount of mana
• non-blue items have thauras whose only prime factors are 2, 3, 5, or 7
• green items yield mana whose prime factorization's non-2 exponents sum to at most 2, and only if exactly 1 from bases greater than 5
• some identical red and green items have wildly different mana/thauata

200gp, 120m? We can get that with Blue Pendant of Hope, Blue Hammer of Capability, Yellow Plough of Plenty, Yellow Warhammer of Justice +1, gaining 124+ mana for 145gp. Definitely take the job, and try to figure out on the road what's up with the Red Pendant of Truth and all the Green items. A good Green item saves ~30gp, but if we can know the Red Pendant of Truth is great we could save even more.

Crucially, no probabilistic choices should be made, for three reasons:

• You have no guarantee about the distribution of item stats presented. They are very likely not uniform random. In fact meta-you suspects that there was once a list of 1000 items and 164 got filtered out.
• You have a good client who is handing you 55gp for a day's work. This is an excellent situation. It is far better to keep this client than to try to eke out additional gold for this particular job.
• Further, you have valuable information. You know what the client's thaudget does with jewelry and items with a blue glow, and you know how weapon mana and bonuses are related, and you know the yield of items with a yellow glow, and you know the maximum yield of items with a green glow. You can use this information in future deals with the client, or, if you can arrange a more profitable deal for the information itself, perhaps land a major score. But this second possibility is far, far less likely if you accidentally damage your credibility by supplying less than 120 mana.

 WH o Ju, Pl o Pl, Ha o Ca, Pe o Ho. I expect a little under 130 mana, for a cost of 144gp.

 Yellow-glowing things get 18-21 mana; I haven't found patterns beyond that. Green-glowing things get 2-40 mana, always an even number; I haven't found patterns beyond that. Red-glowing things get 2^a 3^b 5^c mana; other than the fact that somehow we never get >96 even though we separately get 64, 27, 5, I haven't found patterns beyond that. Blue-glowing things get highly variable mana, also favouring small prime factors though 7 occurs; for these (and only these) the thaumometer gives plainly useful information, yielding the true mana gain +-1 except that items you wear yield a number too high by 22. So the two cheaper yellow items are pretty good value, as are the highest-thaumperature blue ones even though one of them is overrated. We should get at least 18+18 for the yellow ones and at least 34+54 for the blue ones.

I suspect there may be more going on than I yet understand with the red and green items, for which at present I don't think I know anything useful. And maybe the finer details of the yellow and blue ones are predictable too.

X-Y chart of mana vs thaumometer looked interesting, splitting it into separate charts for each colour returned useful results for blue:

• blue gives 2 diagonal lines, one for tools/weapons, one for jewelry - for tools/weapons it's pretty accurate, +-1, but optimistic by 21 or 23 for jewelry

and... that's basically it, the thaumometer seems relatively useless for the other colours.

But: 

green gives an even number of mana that looks uniformish in the range of 2-40

yellow always gives mana in the range of 18-21

red gives mana that can be really high, up to 96, but is not uniform, median 18

easy strategy: 

pendant of hope (blue, 77 thaumometer reading -> 54 or 56 mana expected), 34 gp

hammer of capability (blue, 35 thaumometer reading -> 34 or 36 mana expected), 35 gp

Plough of Plenty (yellow, 18-21 mana expected), 35 gp

Warhammer of Justice +1 (yellow, 18-21 mana expected), 41 gp

For a total of at least 124 mana at the cost of 145 gp, leaving 55 gp left over

Now, if I was doing this at the time, I would likely investigate further to check if, say, high red or green values can be predicted.

But, I admit I have some meta knowledge here - it was stated in discussion of difficulty of a recent problem, if I recall correctly, that this was one of the easier ones. So, I'm guessing there isn't a hidden decipherable pattern to predict mana values for the reds and greens.

// Plotting a graph of reading v colour reveals the following.
//- Blue somewhat erratic but definite trend of increasing mana with increasing reading
//  The erratic part is in the 22 - 63 range, before and after steady increase/decrease.
//- Green  seems to fluctuate in the 2- 40 range regardless or reading
//- red erratic all over the place, no consistent pattern
//- yellow seems to fluctuate in the 18 - 21 range regardless of reading
//
// Green has an average mana of 21, red 25 , though green seems to have fewer with really low values.
//
// There is no obvious correlation based on the items name.
// Eliminating obviously uneconomic items suggest the following are realistic:
//Pendant of Hope         54 mana      34 gold    BLUE
//Ring of Joy             10-30 mana   32 gold    BLUE
//Hammer of Capability    15-35 mana   35 gold    BLUE
//Warhammer of Justice +1 18-21 mana   41 gold    YELLOW
//Plough of Plenty        18-21 mana   35 gold    YELLOW
//Saw of Capability +1    avg 21 mana  35 gold    GREEN
//Amulet of Wounding +2   avg 21 mana  35 gold    GREEN
//Pendant of Truth        avg 25 mana  38 gold    RED
//
// Pendant of Hope is obviously the best. Could reach target with near 100 percent certainty with top 5 items
// leaving me with 23 gold.
//
// Pendant of Hope + Saw of Capabilty + amulet of Wounding + Pendant of Truth would leave me with 58 gold
// if it worked, but would probably fail just under 50 percent of the time. This could be reduce significantly
// by paying 32 gold, but that would only leave me with 3 gold more, and still looks less certain.
//
// As avoiding being in debt by 200 gold is probably much more important to me than gaining 25 gold I will go
// for what looks to be the safe option of:
// Pendant of Hope
// Ring of Joy
// Hammer of Capability
// Warhammer of Justice + 1
// Plough of Plenty
// And hopefully 23 gold.
 

Though I didn't participate in this exercise, I enjoyed reading about it and looking over the answers below. It put me in mind of a particular meta-point, which is that predictability turned out to be the key. The most profitable answers all hinged on noticing which categories the thaumatometer gave accurate readings for, and using those to minimize uncertainty.