Theoretically speaking, a noble's wealth exists to contribute to society, practicing charity through making the citizen's world a better place. I say theoretically, because if you ever wanted to see a more selfish and pompous noble in all of Canterlot, you don't need to look much further than Princess celestia's niece, Prince Blueblood.
The concept of sharing seems to be the absolute last thing on his mind: last year, he spent a large proportion of Equestria's taxes on securing a solid gold bathtub for himself, and most recently he has earned the nickname amongst Canterlot's common citizens as the Prince of Anti-Fun, as his crusade on nightclubs and other "more seedy nonsense" needed to be done away with. He has tried several petitions to his aunt, with no success. He is also incredibly rude, condescending, has no sense of chivalry, and can basically be described in scientific terms as "an absolute jerk-face".
No, there's little that is tolerable about him, and as soon as you meet the stallion personally, you suddenly appreciate why Rarity, an old friend of yours from Ponyville, would have rather overly violent fantasies about the guy. Nonetheless, the Royal Dispute Settler's Oath prevents you from turning away anypony in need of assistance, and so you agree to give him a chance...while keeping a mental note to yourself to double your standard fee for this jerk afterwards.
Much to your relief, this ISN'T about the whole nightclub thing. As it turns out, there is to be a special charity auction to be held at Canterlot Castle tomorrow, and according to his intel, there is to be a special exclusive portrait of Star-swirl the Bearded, after a recent foray into Tutti-Fruity Sugar Punch, listed as one of the items for sale. It is a very obscure painting, largely due to how it depicts the ancient wizard during his less flattering moments (mooning a rather embarrassed Princess Luna), and Blueblood estimates it could be worth quite a pretty bit...and it would look positively fabulous in his private chambers, because of course you'd never display a portrait of Star-swirl showing his flank at Princess Luna PUBLICLY. He informs you that about there will be twenty-nine other nobles attending the auction, and including himself, that makes thirty ponies total vying for Star-swirl's buttocks in a frame.
When you question him about how much he values the painting, he replies that he would never give away how much out of fear of any eavesdroppers in the room, while giving the stink-eye to the royal Guards stationed right by the doors of your chambers, before finally admitting that he prices it anywhere between zero and one million bits. So far, nothing suggests that you need to do anything special, as per the golden rule: whoever has the gold makes the rules, and surely Prince Blueblood can easily afford it, except you soon learn that the auction is going to have a degree of randomness thrown in the mix.
The auction works by having everypony who wants to bid on the painting write down how much they're willing to spend, along with their name, and then sealing their bid away in an envelope, which will then be handed to the auctioneer. Afterwards, the envelopes are opened, and whoever bid the most money wins the painting, and must pay whatever was written on that paper.
However, as much as Prince Blueblood wants that painting, bidding any amount of cash would involve dipping into his funds necessary to exterminate all the nightclubs across Equestria, and so he asks that you suggest a way to minimise any losses he could incur while still offering decent odds of getting the painting. And so, he concludes, this is the task that has been given to you. How much should you tell Prince Blueblood to bid on the painting to minimise his losses? And don't go suggesting the highest amount just to drain his money pool just because he's a jerk-face: your oath is to help all ponies to the best of your ability, and frankly, getting sued by this guy would be a bit more trouble than it's worth. So how should he play this?