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Can't give you an example, as generally power is also a form of wealth, I guess.

Wealth can buy almost anything, including hard power. But in some cases is not enough. Imagine, for example, that you have a considerable amount of fiat money, let's say, 20M. It'll bring inevitably some people to your side (employees, "friends", politicians and so on). On the other side, it can bring some enemies too.

Then, the ability to balance the number of tolerable "friends" and enemies will ultimately determine you power. If you have a lot of money and assets but no allies, you're doomed.

You can have billions, but if someone has just a few millions and a small army, you're doomed as well. Just notice how militia and cartel grows so fast, they certainly must be helped by other people with enough "soft" power (bureaucrats and scum).

I don't know anyone rich enough that hasn't a certain amount of power, or the contrary. Perhaps gurus and sect leaders, some of them have a little influence on a particular sphere, but not broadly.

You're very wealthy but you're in a coma

Wealth != health

The Treasure of the Sierra Madre (John Huston, 1948) Fred C. Dobbs and Bob Curtin, both down-on-his-luck in Tampico, Mexico, in 1925, encounter a gray-haired gold prospector named Howard and decide to join him in search of gold in the wilds of central Mexico. Through enormous hardships, they finally manage to strike gold, but bandits, elements, and most of all, greed threaten to turn their success into disaster. https://archive.org/details/the-treasure-of-the-sierra-madre-1948-1080p

Owning 49% of a blue chip stock

People that got wealth in from selling a business soon realize that the power thier millions or billions brings them is nothing compared to the power wielded by politicians proximal the money printer or the power of the inflexibility of government policy whether by incompetence or design.

A national example of this could be Vivek Ramaswamy, but where I really see this is at the state or local level where a wealthy guy that is used to being able to pay people to do just about anything runs headlong into a deadlock of local government bureaucracy that prevents him from getting something he wants and it makes him so mad he decides to run for office. Usually these guys spend a ton of money and rarely are elected.

wealth < health

Elon musk