Game Mechanics Probabilities Break Getting the Christmas Paintings

DoofusNugget

Skeletron
So, in Terraria 1.4 the game now has a new feature where if you get to the max wave of the Pumpkin Moon or Frost Moon, then the Halloween/Christmas event will be active for one day depending on which Moon event you complete. You get the Halloween one from the Pumpkin Moon and the Christmas one from the Frost Moon.

Now, I'm happy with this addition it beats waiting for it in real time, or being cheeky with your clock. But, there's many main issues that result with this and all because of the reward only being one day long. I'm going to talk only about the biggest issue first, and hopefully the other issues I have with this in another post. The biggest dilemma being the pesky Traveling Merchant and his Christmas paintings. During Christmas time he sells 5 new paintings, but he can only sell one at a time and it's still up to chance whether you'll get it at all in his inventory.

On the Terraria Wiki here: Traveling Merchant
it says that the Traveling Merchant has a 22.12% chance of spawning each day after the proper criteria is met. Let's make that 20% to simplify things. This means your'll likely need to beat on average 5 Frost Moons at wave 20 to get him to show up.

But we can this a step further! On the Terraria Wiki it says there's 34 items in his "rare" category, 5 of them are the Christmas paintings we want. If these probabilities are all evenly distributed, then each item will have about a 2.9% chance of appearing instead of another rare category item. This means if the Traveling Merchant shows up with the 20% chance he has, he'll have a 14.5% chance of selling 1 of the 5 paintings at one time. So let's multiply the probabilities, 20% times 14.5% or (0.2*0.145 = 0.029, about 3% chance).

What does this 3% mean? Well, if you beat one Frost Moon at wave 20 that's the chance you'll have at getting the Traveling Merchant to spawn and him having 1 of the 5 Christmas paintings. You would have to fight 33 Frost Moons, get to wave 20 on ALL of them, then your percentage will have a "fair" 99% chance of getting at least 1 Christmas painting. Disclaimer: RNG can be mean or nice too, so it could be more or less Frost Moons.

What about getting all the paintings then? Every time you get a new Christmas painting then the percentage 14.5% will drop 11.6%, because you already got one painting that was a 2.9% chance by itself, and you don't want it again so we subtract it. This means, to get 1 of the 4 paintings you don't have will take a 2.3% chance or about 2% (the equation now being: 0.2*0.116 = 0.023). Again you'd need to fight lots of Frost Moons, about 50 of them to have a little over 100% chance of getting 1 of the 4 paintings. Note: this is after you fight the first 33 Frost Moons to wave 20, so the total amount so far would be on average 80 Frost Moons just for 2 Christmas paintings.

I'm sure everyone gets the point so I'll fast forward thus process to the end result. (Computations were rounded for easier calculation):

Getting 1 of the 5 paintings you need: about 3% chance after each Frost Moon ends, average = 33 Frost Moons
Getting 1 of the 4 Paintings you need: about 2% chance after each Frost Moon ends, average = 50 Frost Moons
Getting 1 of the 3 paintings you need: about 1.7% chance after each Frost Moon ends, average = 59 Frost Moons
Getting 1 of the 2 paintings you need: about 1% chance after each Frost Moon ends, average = 100 Frost Moons
Getting 1 of the 1 paintings you need: about 0.5% chance after each Frost Moon ends, average = 200 Frost Moons

Total Frost Moons at wave 20 to get all the Christmas paintings, 442 Frost Moons or:

8,840 Silk (61,880 Cobwebs, about 62 full stacks of Cobwebs)
2,210 Ectoplasm (about 22.4 full stacks of Ectopalsm, or on average 1,105 dungeon spirits killed)
2,210 Souls of Fright (about 2.3 full stacks of Souls of Fright, or on average 74 Skeletron Prime fights)

Clearly this reward needs to be adjusted. Note: all computations were made with classic mode in mind. Also, I really apologize if I got my math wrong and blew the probabilities out of proportion.
 
Back
Top Bottom