Taken from the esimates in this thread: Assume this generous estimation is correct and assuming there're nothing shady and all items use the same probability distribution, let's say I really want legendary L. Right now there are 219 non-treasure legendaries in the game, so the chance for one to show up in any one particular slots in the shop is 7.5%/219 or 0.0342465753424658%, accurate up to 15 numbers after the decimal. There are 30 item slots in the shop, thus the chance of it not showing up in any of them is (100% - 0.0327510917030568%)^30 = 98.9776882716909%. Meaning I need log(50%,99.0221189755656%) = ~67.45 weeks or around 1 year, 3 months and 2 weeks to have a 50% chance of being graced with any particular legendary's presence. THAT'S FAR TOO LONG!! The median MMO age nowadays is like 2 years, meaning there's a good chance the game will close even before I get to see the fruit of all the farming. Thus I suggest to increase the amount of items in the rarity shop. To be more precise, to 30*67.45/26 = ~78 items for roughly 1 year wait or, better yet, 30*67.45/13 = ~156 items! for a roughly 6 months wait. The 26 and 13 used here are the rough week counts for 6 and 3 months respectively. Would this affect the pizza hut frequent? Well, not really. Here's why: Let's say I'm an avid pay-to-win-save-time player. I flip burgers 8 hours a day, 7 days a week for $8/h and spend half of that on real life pizza and the other half on virtual pizza. That's $32/day to blue manchu's bank account. Ka-ching. I spend wisely, and only buy the 3800 pizza pack for $99 each. That's around 1228.3 pizzas a day. I then convert the pizza to power epic chests. An epic chest drop 5 items with 2 guaranteed epics. Each normal slot has a 0.2% chance to be legendary and each epic slot has a 30% chance of being legendary according to Munak's math. Thus the chance of the chest not spewing out the legendary I want is: (1-0.2/219)^3*(1-0.3/219)^2 = 99.4532419850567%, accurate up to 15 digits after the decimal. This means I have to buy log(50%,99.4532419850567%) ~= 126.4 chests to have a 50% chance of getting it. This is equivalent to 18960 pizza. Now since I sacrifice 1228.3/day to the pizza god, that's 18960/1228.3 ~= 15.4 days for a first class citizen to get a 50% chance of obtaining the item, or around a 31 days wait. 6 times faster then just waiting for the rare shop to spawn it with my suggestion!! I would have an extra 5 months of noob-pwning!! Woo-hoo!! EDIT: fixed some numbers cause epic chest dont spawn treasures.
Ten of those legendaries are treasures, and treasures never appear in purchased chests (or shops), so your formulas need to use "219".
