In the case of equities timing, imo the house is not the shareholders, it's the investment bankers, hedge funds, and other major traders.
Right. My ability to trade as a small investor is after all of the quants and algorithms take their cut trading the noise of the market. Meanwhile I have an account I can look at a few times a day at most. And then I have most of my assets 401(k) that can trade once a day, at most, at a time chosen by the company the next day in funds chosen by the company.
In a casino, it's the impetus of the establishment to make money. In the stock market, it's the impetus of the shareholders to make money. If the house always wins[1], shareholders are the house.
1. This is a tenuous metaphor for the stock market--true in the US over long periods of time, but perpetual growth is not guaranteed.