Here we totally disagree. If you inherit a fortune from your parents, it's your parents skin in the game the one you end up holding. If you waste your inherited fortune you waste their life of savings, not yours. It did cost you nothing to get that fortune. This is why most people who are winning a lottery end up losing everything. It does cost them nothing to get the fortune - to buy a lottery ticket is not really a cost, nor a merit - and the "skin-in-the-game" value of that fortune is zero. When the skin-in-the-game value of something you are holding is zero your pain in losing it is infinitely lower than the pain of losing something where's a lot of YOUR skin-in-the-game. If you make a mistake which leads you to lose all the savings of all your life you are much more inclined to commit suicide than if you make a mistake which leads you to lose the saving of someone's elses life, which happened to be in your possession just by the way of luck because you have won it or inherited it.
In my Ivory Tower post I'm mentioning also modern politicians ruling without skin in the game. Of course if they make mistakes they have something to lose - their power, but they don't really have to pay the whole price of their mistakes, like it would happen in a distant past. The same applies to top bankers. It's not THEIR skin-in-the-game at stake. All those aspects have been widely and well described by Nassim Nicholas Taleb in his book "Skin in The Game". Understanding the meaning of skin-in-the-game is not limited to the concept of "having something to lose", but it deals with the true subjective value of what you have to lose in a game.
So, when does the easily acquired wealth convert into a "skin in the game"? Do you have skin in the game if you buy a ASIC miners with that money or is it still "skin in the game" of the parents?
Does it convert into "skin in the game" after you have hodled it for 8 years? I mean, that's how we have Bitcoin millionaires today, some have been rewarded for not selling.
Do you have skin in a game when you have done physical or mental work in order to get those coins? What if you got paid in alts that were created from air and then converted to Bitcoin?
Or do you only have skin in the game if you invest into cryptocurrencies or its hardware with the work you got paid in fiat currencies?
Because it is a subjective quantity you cannot define it with an equation, and there are obviously gradations in how much skin-in-the-game one can have in any situation. Impossible to reduce this to a formula like the Metcalfe's law. How do you measure the pain of risking or losing your assets? How do you measure someone attachment to what they have? Totally subjective. The fact that a principle exists and it has an influence in a system doesn't imply that we have the instruments to measure its strenght and its effects. Nevertheless, we shouldn't ignore it's existence, and we whould try to understand as much as possible of its mechanisms and make our plans accordingly.
Actually i didn't read Taleb's book yet, these are just my own thoughts, perhaps after I will have read Taleb I will have better answers.