Are albinos actually statistically rarer than any other cat gene combination you're able to get from Nestor/business cards?

so... i'm not entirely sure what you mean by "cat gene combination", but my autistic brain (which interprets everything literally) saw an interesting question and i feel an infodump coming on in 3... 2... 1...


^{in a nutshell:}

if you have a specific gene configuration in mind - for example, [C] [NN] [SS] [BBFF4] [NNMS] [NN0C] [AA] [BB] (since that's the first example mentioned in this excellent guide, which i'm referencing heavily to put this post together) - the odds of receiving a cat with that exact genome string (assuming that all alleles are equally likely to appear and that allele order matters) are currently 1 in 4671406080, or 0.0000000214%


^{some disclaimers:}

• i have no idea whether the first assumption mentioned above ("all alleles are equally likely to appear") is true or not... and if your question was simply "is the 10 allele for White Level rarer than any of the other alleles?" then my answer is simply "i don't know"! xD
  
  
• the second assumption ("allele order matters") is much stronger than it needs to be (unless, for example, you really care whether your trade wind not-cat is NS or SN). with the exception of Color Group and Growth Rate (and possibly Mystery Gene), allele order has no effect on cat appearance or breeding outcomes.
  
  
• it's currently 3 AM where i am, and i'm very very eepy
  
  
• it's also been over 10 years since i last took a probability class (dear goodness i'm old /lh) so corrections are very welcome and appreciated! ^^
  
  
• even if i miraculously got all these numbers correct on the first try, they will become outdated in the future, as more alleles (e.g. the mercat species, unnatural color groups via alchemy, etc.) are added to the game. (exciting!!)

^{the math n stuff:}


now we multiply all the individual numbers of permutations (in the rightmost column of the table) together to get the number of permutations of the entire genome string:

1 * 9 * 4 * 4 * 4 * 4 * 4 * 16 * 4 * 11 * 5 * 9 * 16 = 4671406080

and then do a bit more wrangling to get that number into the form of a percent chance:

(1 / 4671406080) * 100 ≈ 2.1406831 * 10^-8 ≈ 0.0000000214

and there ya go! i'd say that's quite a bit rarer than an albino

@nuz Oh wow I need to be more careful about my wording LOL. I really just meant "is an albino any more or less rare than getting any other type of not-cat?" But this math is fascinating and genuinely cool to me, so thank you for explaining it!! I never would've guessed there were that many potential not-cat possibilities!

@Mercrow
Albinism is rarer than other genes! While the math above looks partially right, it operates under the assumption that every allele is weighted equally, which isn't the case. Some are much more rare than others.

ha… ha ha… laughing in maths and pain The Math Rambles of Last Year

Over 4 billion genetic possibilities, about 55000 visual possibilities




Anyway, yeah, albinos are statistically rarer to get from nestor and cards, there is at least one survey of sorts gathering info on cats nestor gives out, but it’s limited by the number of people responding.

To put it into a little perspective, I have over 200 cats, only about 5 of them are Nestor Albinos. Give or take about 20? from breeding and my starters, that’s like 5 out of 180 cats that were visible albinos. Then of course you flip that over and I’ve got 30 no-white cats from nestor, and 35 white level 1 and 2.

Essentially Everything is weighted differently, and albino is quite rare

@Nae @Darkfang8901 Makes sense to me. It does sound like I'll statistically get one in a few years simply by playing though, which is the outcome I was hoping for! I don't really wanna grind for one bajillion notes to prep for an albino bidding war lol, I would rather one simply fell into my village.