> So your best bet is to own the market through a broad index fund that has almost no cost.

There's also the fact that index funds have de facto become pension funds in most of the Western world, so Western politicians are trying to do their damn best to keep the stock exchanges afloat (i.e. always going up) in order to keep those aged 45-50 and older on their side when it comes to voting. We've last had a market crash in 2008-2009 (the covid thing was just a blip), I don't see today's politicians allowing a crash like that to happen if they can help it.

So in fact putting one's money into index funds is betting on the current political system continuing doing its thing, no need to involve any advanced maths.