How many perfect pandora seeds exist?

I've been looking at Gamerpuppy's Pandora's Box seeds. This user generated, using a program that quickly tries the output of Java's random number generator with a given 64-bit seed, and tries to find one that has the most repetitions of a given number (modulo the number of cards) in the output, as well as an initial roll of pandora's box for Neow (1/22).

In slay the spire, the characters start with the following number of strikes and defends, and have this number of cards available:

ironclad:   9    72
silent:    10    71
defect:     8    71
watcher:    8    71

I'm interested in what the probability would be of there existing a 'perfect' pandora seed: one where every generated card is the same. Knowing exactly would mean brute-forcing the whole space, which seems computationally unfeasible without a collaborative effort. So instead, to simplify; you may assume the generation is perfectly random instead of only a PRNG.