In "The Bet," the banker says, "On my part it was the caprice of a pampered man, and on his part simple greed for money." Please explain to me why...

"Caprice" means sudden or impulsive.  Stores always put things like candy in the checkout lane, because they want customers to impulse buy.  They are trying to get customers to act capriciously.  

The banker believes that his making the bet was a capricious action, because the bet won't actually answer the question of whether or not the death penalty is better than life in prison.  He made the bet and wagered that much money, because...

"Caprice" means sudden or impulsive.  Stores always put things like candy in the checkout lane, because they want customers to impulse buy.  They are trying to get customers to act capriciously.  

The banker believes that his making the bet was a capricious action, because the bet won't actually answer the question of whether or not the death penalty is better than life in prison.  He made the bet and wagered that much money, because at the time, the money was a trivial amount.  

"To me two millions are a trifle, . . ."

Unfortunately, by the time the banker is telling his readers about his impulsive bet, he has come to regret it.  The reason for that is because the banker realizes that he is about to lose the bet.  Over the last fifteen years, he has lost most of his fortune, and now the two million rubles is all that he has left.  Losing his impulsive bet will now complete his financial ruin.  

"By our agreement I ought to pay him two millions. If I do pay him, it is all over with me: I shall be utterly ruined."