Why do Major Barbara and Undershaft shake hands?

Question

In George Bernard Shaw's Major Barbara, I came across the following conversation which culminates with Barbara and her father Colonel Undershaft shaking hands:

BARBARA. No. Will you let me try?

UNDERSHAFT. Well, I will make a bargain with you. If I go to see you to-morrow in your Salvation Shelter, will you come the day after to see me in my cannon works?

BARBARA. Take care. It may end in your giving up the cannons for the sake of the Salvation Army.

UNDERSHAFT. Are you sure it will not end in your giving up the Salvation Army for the sake of the cannons?

BARBARA. I will take my chance of that.

UNDERSHAFT. And I will take my chance of the other. [They shake hands on it]. Where is your shelter?

Does Barbara make a bet with Undershaft? If yes, does she ultimately win or lose?

Answer 1

They shook hands to seal the bargain they'd made a few lines earlier, she to visit his cannon works and he to come to her shelter.

I will make a bargain with you. If I go to see you to-morrow in your Salvation Shelter, will you come the day after to see me in my cannon works?

Shaking hands is a semi-formal way of making the compact a little more real. They've both committed their honour to the agreement and although it's not legally binding in any real sense, it shows the audience that both have made serious plans to follow through with this. It's not just idle chatter.