If you have a seriously, utterly wealthy NPC, say, the king of a huge merchant kingdom, who should have truly astounding access to money, how should you deal with that in game? Not necessarily for fighting the PCs, you know, more like finding out his general capabilities, for things like information gathering, defenses against prying eyes, and the like? The most simple solution seems to be to increase the CR, but at some point that is not going to be enough.
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You only have to worry about CR if the players are going to fight him. Otherwise, don't worry about it. He's an NPC, so he doesn't have to follow the rules. Just give him access to what you need to tell the story, the rest doesn't matter
You don't change his CR. He probably doesn't have that many magical items on him. Though he might be decked on like a PC.
No, he has spellcasters that he pays to do things for him. Armies of people at his command. His individual CR really shouldn't change, but the cadre of people you will be forced to deal with on the way to him are going to be a challenge of their own.
He might also have things like Adamantine Golems. Or trained magicbane bandersnatches.
Ultimately, don't worry about CR or things like that. He is a king, basically he can do whatever he wants for the most part. Basically, unless the PCs take action to prevent the king from scrying or unless they catch that they're being followed the king knows everything he can.
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If the NPC is tactically well-prepared for the PCs due to their information-gathering resources, give them a +1 or +2 CR boost due to favorable circumstances.
If the NPC is using their resources to throw obstacles at the PCs from a distance, treat those obstacles as separate encounters with their own CR. Same deal with indirect defenses the PCs need to carve through (guards, wards, traps, etc).
If the NPC isn't fighting the PCs or throwing obstacles at them their CR is irrelevant.
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Personally I'm a fan of the Authority=Asskicking theorem in RPGs.
In the real world a president might be physically feeble, but PF is not like the real world. High-level individuals can do stuff that stumps large groups of somewhat trained people. I have no problem with a PF king that fights demons himself. It's because he's such a badass that he's the king; you don't want a low-level-low-Will-save chump as king.
That's certainly true in the Land of Linnorm Kings. They all had to kill a Linnorm themselves, and survive the death curse, to become kings.
But the king's wealth and his fighting ability and his CR needn't be related.
Ignore the chart.
Give him what a king needs.
Be careful what you let the players get away with.
Equip the king as a PC. It's what they did for King Irovetti of Pitax and one or two other BBEGs in Kingmaker and Rise of the Runelords. Authority can come from both natural and temporal power, and any king with his salt has elite guards, assasins, wizards, the heads of churches, etc to call upon.
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Giving a king combat gear equal to PC wealth is certainly appropriate and would result in a +1 increase to CR. However their ability to call on elite guards, assassins, wizards, etc is best represented by taking the CR of those servitors into account.
I'd say authority correlates with asskicking.
High-level people are more likely to gain political power whether by earning titles, marrying into royalty, or simply taking over a country they like and are also more likely to defend their country & claim. Also, people with wealth & political power are more likely to provide their heirs with opportunities to develop great personal skill (in a hereditary meritocracy). But it's also possible that a personally weak leader may be defended by someone or something strong (explains why kings like marrying their daughters to dragon-slayers!). If the crown acts as a Headband of Mental Perfection +6 that also provides immunity against mental control, and the king has are a quartet of loyal 16th level characters as bodyguards/advisors, it doesn't really matter that the king himself is only a 3rd level aristocrat.
Except that the king might well be chump sniped to death by any high-level character in the mood for a little regicide, of course. Still, that is what resurrection is for.
Thank you for the suggestions. Truth be told, I was designing a near-divine character to act as a political, spiritual and "moral" center for an empire of wicked winged elves, a la the theory that the ways the ruler acts are reflected in how the society works. Doing this rather massive statblock, I found that for example ioun stones are quite impressive in the right situation. However, they cost money. Now, if the emperor uses them, it is likely to become some kind of fad among the elves, leading to such stones being marks of status, objects of trade, and good things to create. It also freed up the cloak slot from ye olde cloak of resistance, something winged elves would appreciate. Much like the stat block for Baba Yaga, it is not someone you're supposed to fight. Still, the main point here is: there are no reasonable limits to that wealth, so I agree fully that the WBL chart misses the mark.
Contingency spells are your best friend. Drop a dispel magic vs any dimensional anchor bolts/javelins/snuck in magic items and a second contingency that allows the king to transport himself (refuge is a good spell for this) to another location. A modified amulet of proof vs detection and location, keyed to one or two people that the king trusts to allow his or her spellcasters to scry on him or her.
As for your suggestion on ioun stone usage, you might want to check the Thassilon book. It has rules for implanting ioun stones in your body ala the Runelords of old, and could work nicely for support with your winged elves.
You can also have a western star ioun stone to give you disguise self at will... and make all the ioun stones you wear invisible. =)
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*looks at WBL and CR charts*
*dutifully folds them, with exceptional care to the creases*
*lights them on fire*
The thing's a guideline not a law.
That being said, its unlikely the king's going to be sitting around wearing all his magical hoo-doo because maybe he doesn't want to, maybe its ceremonial, maybe its for functions.
This ties back to a bugaboo that usually comes up for me. The +1 padded armor of sleeping.
PCs are odd folks because they live, eat and sleep (if possible) in their armor. They don't take it off. They don't go to the outhouse without their +2 dagger.
Don't worry about 'CR' and xp budgets. Thats for when you're having trouble putting encounters together properly. Look at capabilities.
If your party's AC is around say a 25, and the king (even with magical hoodoo) is managing a +7 to hit. He's still not that much of a threat.
If the magical hoodoo he gets actually makes a genuine difference in how the encounter goes down? Then it might be time to worry about 'CRs.'
The merchant/king/etc. isn't the character.
Their empire is.
I would approach it that way?
WBL and CR are merely tools for the GM. Ignore them for stuff like this.
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Well, most of us seem to be in agreement that CR is a guideline.
That being said, my inner contrarian feels obliged to help out a bit here with what the OP might be asking about, which is balance issues.
Examine your party and its capabilities, and what they're capable of.
Take that into account and take into account what you want the king here to represent.
A lot of premade NPCs or 'premade encounters' don't seem to take this into account. To the point that after a certain point, an NPC either can't hit the enemy at all, or is constantly whalloping them.
CR has trouble accounting also for the 'nickle and dime' combat. 2 dozen first level sorcerers is barely a CR 6 but the amount of magic missile hurt they can lay out means that even a high level character routinely running into these guys can see his hp worn down.
Similarly, a melee NPC at AC 30 (like the 20th level NPC 'Infernal Champion') might as well be fighting nude for all the good his AC's going to do him against other melee types at level 20 (or hell, level 16 or, hell, level 14!).
If the guy is meant to be 'super tanky king' then make him hard to hit, and equip him for it. If you just want to show off his loot, then do that.
There are two economies in pathfinder that have nothing at all to do with each other:
One is the everyday, normal economy, where craftspeople craft, farmers farm traders trade and so on. In this economy, one's wealth is measured by one's social status and it will most likely never change very much over one's life.
The other one consists of objects of personal empowerment won by killing things and taking their objects of personal empowerment with a little dash of crafting your own objects of personal empowerment or buying them from some source of OPEs. Every single magic spell is part of this economy. In this economy, one's wealth (appearing as OPEs) is not really economical value but just one aspect of the strange property called level. And as one's level changes (it only ever rises and it typically rises very fast, it can go from 1 to 20 in a year or so) one's wealth changes geometrically.
Do not succumb to the illusion fostered by both kinds of wealth being measured in "gold pieces". These two economies must never be allowed to interact! Even small, seemingly inconspicuous interactions can cause disaster if anyone should make the mistake of applying logic and reasoning to it.
A kings vast fortune is part of the first economy. He is rich in normal things, objects or art and the service of able people. He is not rich in OPE because he is not of high level.
I consider the wealth by level chart to be a guideline for what the NPC has on hand right now for 'adventuring purposes' -- the castle and what not doesn't help if you can't use it for adventuring so I don't track it against the (N)PC.
Just like if the party is awash with 25 +1 large falchions I don't count it against their WBL until it can be turned into something they can actually use (unless they are a party of 25 large creatures and then since they can use it the items count).
A party of level 3 wizards with 5 suits of +1 full plate might might have all the actual wealth by level they should have, but that doesn't mean it's actually useful gear.
As to the actual interaction of the rules, economy and NPCs, I have this thread were I do an indepth look into such.