Thinking of building a cube intended to replicate a retail draft environment. (Original Ravnica block, 05-06, so I did the math accordingly below.) A bit more curation, but mostly in the rares which don't much matter for this question. Is there preexisting math for
how many copies of a C/U/R you "should" have in your population to feel like eight packs out of a retail booster box?
I did a lot of useless calculations, people who don't care can skip to the end:
Scryfall says there's 57 commons in Dissension.
A draft is 8 packs * 11 commons each (ignoring foils replacing one back then) => 88 commons from a pool of 57 => 88/57 = 1.54 copies per draft in expectation (if uniformly distributed, see justifcation below)
But, picking the easiest example to find in the format:
Takuya Osawa's PT Prague 2006 winning draft deck had 3
Aquastrand Spiders
plus
Big Oots's deck (does anyone else even
remember that was Rasmus Sibast's nickname?) had another.
If commons are uniformly distributed*
*and they should be, we know a maximum of 1 common is underprinted per set
**one can safely assume that you can start anywhere in the print run fragments contained within the pack whether it's an AB set or an ABC set or whatever (lethe.xyz does not have collation info for the original block)
Then this is a binomial distribution since we're selecting "with replacement" from an infinite pool, so we expect to see 4+ copies of "a given fixed common, so in this case
specifically Aquastrand Spider" just under 7% of the time.
But there's 57 commons so that's actually "0.93 chance to
not see 4 Aquastrand Spiders" and then there's 56 other commons...
But
but this is not actually indepdendent because of print runs - if we fail to see 4x Spider we also know that we have a noticeably decreased chance of seeing 4x of either of the 2+ commons next to Spider anywhere on the sheet...
And you can see why I'm asking! (It's because I'm dumb)
Is it just "X of every common of the small sets and Y of the large set, less for uncommons, shrug and ship it?"
Do people typically use more complicated distribution methods than shuffling together three sets and hoping it works out?
Any information much appreciated, I know this is a thing people have done before but I don't know if anyone actually cared enough to crunch numbers!
