I have the feeling that I have to reattach almost every transaction I do. What is the probability that a transaction is being confirmed directly? And does this probability change with a second or third reattachment?
The probability after reattaching a transaction shouldn't change, assuming that the node you use is not overloaded and has good neighbours. However, the cumulative probability does increase of course. Please don't spam reattachs through, just wait 30 minutes. With the new wallet update, you can promote your transactions, which is often more efficient than reattaching.
Taking a look at my transaction history, almost half of my transactions went through without having to reattach. A single reattach fixed this in all cases except for one.
There are some numbers on this page, don't know how accurate they are through http://analytics.iotaledger.net/stresstest.table
The probability for a transaction to be confirmed without reattach is 66% in theory