The lottery system which the Capitol uses to select competitors for the Hunger Games is constructed to directly impact the poor more than the wealthy. Katniss explains in the first chapter that when children turn twelve, their names are entered into the lottery once. At thirteen, their names are entered twice. Thus, each year of age results in an additional entry.
However, many families are so poor that they cannot feed themselves. The government is willing to provide tesserae, which is additional grain and oil for one person, in exchange for an additional entry into the lottery. Children can accept tesserae on behalf of their family members as well, accepting that they must have their names entered into the Hunger Games lottery once for each additional tessera ration.
Katniss explains that when she was twelve, she had her name entered into the lottery not once but four times. This means that she took tesserae for herself, Prim, and her mother in addition to the entry she was given for her age. The entries are cumulative, so at age sixteen, Katniss has her name entered twenty times. Her friend Gale is in a similar situation and at age eighteen has his name entered forty-two times.
Katniss has always protected her younger sister, Prim, from having her name entered additional times in the lottery. This is Prim's first year having to participate, so she mathematically has much better odds of not being selected compared to Katniss. This is part of the reason that Katniss is stunned when Prim's name is selected for the Hunger Games competition.
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