The protagonist is Paul, the little boy. He is striving to, through the riding of his rocking-horse, win the affections of his cold and distant mother. We can't help but relate to that plight, and our hearts go out to him in his quest. The antagonist would have to be his mother, her aloof nature, and her incessant quest for more money that, in the end, takes the life of her son. She is painted as shallow and vapid, unwilling to work hard or manage her money well, and as uncaring and cold. She is the "bad guy." Another possibility for the antagonist is greed itself; it is the evil demon that drives this family to tragedy and ruin.
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In the short story "The Rocking Horse Winner" Paul is a young boy who has been seeking his mother's love and attention. The boy hears his mother always referring to his father as a loser because he ahs never made it economically. She considers it being unlucky. Paul is the protagonist. He strives to gain money and success through luck, but in truth it is hard work.
Paul finds a way to ride his rocking horse until it beats real race horses in a race. He begins betting on the horses and puts away some money. He continues to race but each race drains him p[physically. In an effort to gain his mother's love and care for his mother, he continues to ride.
His mother is happy with Paul's situation. She is the antagonist. She is greedy as is his father. No matter how much more Paul earns it is not enough. The more money he wins the greater the demands of his parents as they increase the financial level of their lifestyle but still do not have enough money to make ends meet.
Paul continues to try and meet his mother's financial needs and wants until it kills him.