Upon each opening, the probability for obtaining Rare Prize will be increased. Obtaining Rare Prize will reset the probability. 15 times is the maximum, which will guarantee Rare Prize.
When certain items have not been included in the prize pool or hit the maximum times of obtaining, their probability will be distributed proportionally to other items.
"Probability" mentioned here are statistical results from a large sample size(a lot of players) and could produce differences with the small set of testing data from certain individual player.