Competition for the New York City affordable-housing lottery is stiff: On average, there are 450 applications received for each rental unit.urfinguss/Getty Images/iStockphotoFor some New Yorkers, winning the NYC housing lottery is the only way they can afford to stay in the city.But competition is tough: There are about 3.5 million applications each year.Those who have won say it often took multiple applications and months of waiting before they heard back.Louis Ciprian, 29, moved around New York City a lot when he was younger.His father died when he was 11, and Ciprian and his mother fell on hard times.