Adding a nonce, as I propose, would make the system remain provably fair even in that case.
I agree with Dooglus that adding a nonce doesn't seem to make it any harder for a malicious actor find collisions. The key to being resilient against collisions is choosing a good hash algorithm like SHA2.
Alternatively, let us assume a game scaled-down to only 12 cards: it is reasonable to expect that you could repeat a previously seen permutation and be abused by a malicious player. Adding a nonce would prevent cheating also in that case.
We protect ourselves from this scenario by adding a random server_seed to the Secret component. So, even for a game with a small deck of cards, the Secret will always be different because we'll choose a different server_seed for every shuffle.