There are a lot of wrong statements in your post. A lot of wealthy people worked hard for that wealth, and no luck was involved. They deserve to live a comfortable life. A lot of poor people are not poor because they were unlucky, some are just lazy.
A typical example of this was when the Berlin Wall was broken down. Some of the people who was living in East Germany was simply not used to working hard and they were lazy too. So when the Wall came down, a lot of them went into poverty, because they were too lazy to work or they were not used to the concept of hard work = higher income, like in the west.
The Communist system in East Germany made them lazy and some of them could not handle the change. So, Capitalism is not all bad, people are encouraged to work harder for a chance of a better life.
I give more than 10% of my income to charities that are helping poor people find jobs and a way to sustain them until they reach that goal. Teach them how to Fish!