> Turns out that an even easier way is just to assign 128 bits of randomness
52! is roughly 2^226.
You cannot address all 2^226 positions with a 2^128 address generated from 2^64 seed.
52! is roughly 2^226.
You cannot address all 2^226 positions with a 2^128 address generated from 2^64 seed.
Or you could have a lazily calculated infinite precision random number per card and use more like 6 bits per card on expectation. Other than using more (and annoyingly variable) memory, this may well be faster than a properly unbiased Fisher-Yates.
Or you could assign a few bits per card, sort, and then recurse on each group of cards that sorted into the same bucket.
In summary, there are lots of genuinely unbiased solutions (assuming a perfect binary RNG), and they all boil down to something roughly equivalent to rejection sampling.
We're not interested in sorting all possible decks, just all possible cards (52) into 1 unique randomized deck. The more bits we assign to these, the more any error or bias in the source goes to nil. (In contrast, consider the use of only 4 bits.)
Since everyone's bashing my use of ChatGPT, I don't think ChatGPT5 would have made that categorical error.
CSPRNG AES256 with 2^256 random seed is safe.
CSPRNG AES128 with 2^128 (or less) random seed is not safe.
That's theoretically true by a counting argument, but for a CSPRNG the only way to compute that next shuffle costs about as much computationally as brute force. 128 bits is enough to make that infeasible, though 256 may be preferable for the usual abundance of caution.
The number of permutations doesn't matter here, since an attack becomes computationally infeasible before it becomes counting infeasible. It's also possible for a practical attack to exist even when the output can't be predicted exactly, since statistical information is still valuable.