The typo is most likely the extra /, in (x/y)/(x^2+y^2) instead of (xy)/(x^2+y^2).
`2^x & 2^y ...is the & a bitwise operator...???? That would produce a unique ID? That would be very interesting, is that provable?`
Yes, & is bitwise and. It's just treating your players as a bit vector. It's not so much provable as a tautology, it is exactly the property that players x and y are present. It's not _useful_ tho because the field size you'd need to hold the bit vector is enormous.
As for the problem...it sounds bloom-filter adjacent (a bloom filter of players in a hand would give a single id with a low probability of collision for a set of players; you'd use this to accelerate exact checks), but also like an indexed many-to-many table might have done the job, but all depends on what the actual queries you needed to run were, I'm just idly speculating.
`2^x & 2^y ...is the & a bitwise operator...???? That would produce a unique ID? That would be very interesting, is that provable?`
Yes, & is bitwise and. It's just treating your players as a bit vector. It's not so much provable as a tautology, it is exactly the property that players x and y are present. It's not _useful_ tho because the field size you'd need to hold the bit vector is enormous.
As for the problem...it sounds bloom-filter adjacent (a bloom filter of players in a hand would give a single id with a low probability of collision for a set of players; you'd use this to accelerate exact checks), but also like an indexed many-to-many table might have done the job, but all depends on what the actual queries you needed to run were, I'm just idly speculating.