Snow's Game
To President Snow, it's never about a hunting game; it's about the games being hunted.
Technically, the Hunger Games is a game with 24 players, but in reality, it's a one-to-one game, Snow against the games. Needless to say, Snow always wins.
He seems to enjoy it very much, although originally, it was just a policy to suppress the rebels. The people of the 12 districts have to bear with the pain of seeing their children being sent to the path of death helplessly, as to remind them their mistake for not obeying the strong.
Weakness itself is a sin, a deadly sin, to Snow.
Seeing the games hunting each other is the greatest pleasures of Snow's. Human beings return to their main purpose to survive, under the harsh condition, just like any other animals, simply to survive.
In the arena, the nature of every game is aroused. In order to survive, they are willing to do anything. At the end, only the fastest, strongest, bravest and smartest stand a chance to survive, like the order of nature.
When they are crowned, to receive the honour which isn't honourable at all, they would still be able to be smile, to be proud, to receive compliments, despite the lives they've taken. The people in their district will be cheerfully welcome them home and praise them for winning, forgetting. or rather, ignoring the fact that there's no winner for the game, no other than Snow.
Weak, foolish people...
That's probably why he's willing to die when Katniss Everdeen points her bow to him. He's been defeated, meaning he's weaker than this teenaged girl, and being weak itself is a deadly sin.
But Katniss shot Coin instead, making Snow smiles.
There's indeed a deadlier sin, namely selfish.