As I work on unblocking items in my Fridge, I have been thinking a bit about the chances of finding a specific item. I'm creating this thread partly for clarification, partly to satisfy my own obsession, and partly as public service. I did consider putting this in the Ask Questions thread, but the topic seems a bit intricate and would quickly get lost in the 200+ pages of material.
First off, for those who don't want to dig it up:
coeff. 1: 52.323% - about 1 in 2 items
coeff. 2: 34.085% - about 1 in 3
coeff. 3: 11.999% - about 1 in 8
coeff. 4: 01.542% - about 1 in 65
coeff. 5: 0.1400% - about 1 in 700
coeff. 6: 0.0045% - about 1 in 22,000
Now, my primary question is, do these numbers represent the chance of finding an item of the specific coefficient in a given level or the chance of an individual item in the level being that coefficient? I assume the latter, meaning there's about a 1 in 700 chance of your effect item being Coefficient 5 and a 1 in 700 chance of your point item being Coefficient 5. That gives closer to a 1 in 350 chance of finding any Coefficient 5 in any given level (an important statistic since so many of us keep track of how many total Coefficient 5s we have, regardless of which they are).
My second question is, do the percentages change as more families become available? For example, Good-looking Harry's delights includes five Coefficient 1 items and one Coefficient 2 item. After completing Divine Sweets, does your chance of seeing a Coefficient 1 become greater than it was before because there are more available? My hope would be that it doesn't, but I haven't tracked my collection of Coefficient 1 and 2 items so I can't be sure.
Now here's the fun part. Assuming the math is as stated in the quote above and assuming that math doesn't change as more items become available, the chance of finding a specific item would be the named percentage divided by the total number of items available. For example, if every item is available, the chance of finding Tuber's Bag would be .14% (chance of finding a Coefficient 5) divided by 8 (number of Coefficient 5 effect items), or .0175% (about 1 in 5715). For the Candy Cane, the chance would be 1.542% divided by 26, or .059% (about 1 in 1695). The chance of seeing a Wine Key would be 11.999% divided by 55, or .2181% (about 1 in 459).
At that rate, if you average 120 levels that have items per game, you'd see one of a specific Coefficient 3 every 4 games and unblock it in 40. A specific Coefficient 4 would be seen every 14 games. And a specific Coefficient 5 would show up once in every 47.5 games.
Obviously those numbers will be more or less depending on how the randomness is treating you(we all know you can see the same Coefficient 3 three times in one game and then not see another one for a couple months) but I think think the math is reasonable. Does this this sound right to you? Is there anything I'm overlooking?
