It would be helpful to define terms first. Capitalism is the system of private ownership of scarce objects. People are scarce, land is scarce, resources are scarce. Even if energy becomes plentiful, the means of production of that energy will remain scarce (solar panels and other capital goods). Even if you can 3D print any object, the resources used as inputs are still scarce.
In short, scarcity will not go away, although it will continue to get significantly better, as more valuable and useful things can be produced with less (less labor, less energy, less resources, etc). Therefore private ownership and voluntary association, aka capitalism, will remain.
There is a difference between P(“Heads came up”) and P(“Heads came up” given that “I was just woken up”). Since you will be woken up (memory-less) multiple times if tails came up, the fact that you are just getting woken up gives you information and increases the probability that tails came up.
Let’s consider P(H | JustWoken) = P(H and Monday | JustWoken) + P(H and Tuesday | JustWoken) Because I have no information about the scientist’s behavior (when he chooses to ask the question), I have to assign equal probabilities (one third) to P(H and Monday | JustWoken), P(T and Monday | JustWoken) and P(T and Tuesday | JustWoken). And it’s impossible to be woken up on Tuesday if Heads came up, so P(H and Tuesday | JustWoken) = 0. In result, P(H | JustWoken) = 1⁄3.
If anyone doubts that, we could set up a computer simulation (you write the scientist and coin code and I write code for the beauty answering the question) and we bet. But I would require an experimental condition, stating that the scientist will ask the beauty the question every time she wakes up. Under those conditions, a beauty which always bets that “tails came up” any time she gets woken up will win 2⁄3 of the time. If we could not agree to those conditions (getting interviewed by the scientist on every occasion), the bet would be broken because you know what answer I will give and you have information that I don’t have (strategy for when to interview).