as a polite equivalent) are classified as their own words, they are actually just combinations of だ
, or です
, and が
is usually used as a formal way of saying ‘but’, or ‘nevertheless’. Due to this, we can see that だ
is being used to ‘determine’ that a statement is true, while が
simply shows that there is other important information to follow.
In this way, だが
is very similar to the expression ‘that may be, but…’ in English. だが
may be used at the beginning of any phrase, or between sentences.
He is a lawyer, but he is not very smart… How odd.
I bought 100 lottery tickets. However, I didn’t win.
When using ですが
, it will automatically mean that the rest of the sentence should also use 丁寧語（ていねいご） (polite speech).
I went to the hair salon, but since it was expensive, I came home.
To make だが
sound a little bit softer, sometimes ね
is added. However, this is not so common in modern-day Japanese, and is more limited to the older generation.
I have heard that you are a good person. However, I can't trust you yet.
Due to だが and ですが using が (the formal equivalent of けど), this phrase can sound quite stiff. Therefore, it is far more common to hear でも at the beginning of a sentence in casual speech.