Depends on what I believe about the person criticizing me. On average you'd probably win the bet, but there are exceptions.

Depending on what it is that the other person disapproves of about me, I might feel annoyed or offended. But so what if I do? If I'm cooperating with a person to achieve something that's important to me, learning that he thinks one of my beliefs is stupid (for example) isn't going to change anything about my resolve to cooperate. Feeling otherwise would be foolish.

As it turns out, I have been called 'dogmatic' and 'fundamentalist' and various other charming adjectives because of my belief that an essential part of fostering the growth of a rational society consists of creating a social climate in which irrationality is seen in a bad light, and the best way to do that is conversational intolerance of unreason. I can't say I enjoyed being called dogmatic, but it hasn't affected my desire to cooperate with those I see as mostly rational enablers of foolishness. If I can get over my hurt feelings, why can't they?