Well, if you're going to compare two scenarios using a numerical example, I think the assumption that the total pool of opportunity would decrease is a rather strong one!
>In the argument from justice, you think it's a moral mandate to take money away from people because other people have less money?
Well, not because other people have less money.
My politics are roughly "people should do whatever they want, but they should have to pay the price of the externalities of their actions", sprinkled with "reducing overall human misery is virtuous".
More like, because in order for the massively wealthy to exist there's a strong argument that there has to be a massive underclass to go along with it. In this light, being rich creates the externality of forcing people to be poor, and as a result it's perfectly moral to redistribute some of that wealth.
Another argument goes, we have a more vibrant and stable society if we ensure that a) everyone is healthy and gets a good education and b) no one person or group in particular can amass so much power as to be capable of destabilizing society as a whole.
There are a few other argument, but at the time of writing I think those two are the strongest. We can talk about right wrongs from the historical record, we can talk about the duty to minimize misery, we can talk about private property is a state-regulated right and thus it's legitimate to argue over it, we can talk about theological underpinnings, etc etc.
You may disagree, of course.