Wintersday Math

During Wintersday finale you can participate in a game of chance similar to Nine Rings.



Source

Number of rounds per event: 3
Number of games per round: 5
Number of games total: 15

Thus, you need 15 Candy Cane Shards to play in all games per event and 9 * 15 = 135 to participate in all games of all nine events. However, the minimal initial amount you need is less because you have to take into account the shards you win in the process. What would be the minimal initial amount of Candy Cane Shards needed to play all rounds in all nine events?

- Assume you are standing at the center ring
- Probability of receiving any shards is 5/9 = around 0.55 (center ring + four orthogonal rings)