I wonder if the ideal compound would be one that can shelter thousands of people and a massive soup kitchen. When the bombs drop, you're the only person bothering to help others and so you amass followers that you can now use to raid other billionaires that instead spent their money on pools or saunas.
Every litre of water you put into a pool is a litre of water you could be using to supply a soldier to steal some other guy's pool to hydrate more soldiers within a drought-stricken wasteland. Every 500k you spent on a luxury bulletproof SUV is enough to buy 10x the Toyota Hiluxes that can outflank the SUV and pin it in. And the 6x6 luxury SUV is a prime target since anyone riding in one of those has a lot of stuff to steal.
If the rule of law disappears and society collapses, I doubt anybody is going to maintain a pre-war standard of living because the competitive pressures are going to push people to spend a lot more on weapons/violence. The best you can hope for is to become a charismatic warlord, but now you personally have to spend your wealth on providing protection and welfare for the people, plus you have to win against every other person with the same idea.
It'd be cheaper to just pool your wealth together with everyone else in a given area to create a government that enforces certain basic rules, provides for certain basic needs, and allows everyone to stop worrying about killing each other.