Answer: He made the bet on a whim
Step-by-step explanation:
According to the information gotten from the question, the banker says that, on his part, the bet, was "the caprice of a pampered man. This simply means that the bet is a thoughtless bet to make.
When someone is said to "act with caprice", it means that such individual acts impulsively and unthinkingly. The bet is impulsive as it was made during the summer party when there was an ongoing conversation about death penalty.