The check proves one narrow thing: the result came from seeds committed before the round. That is real, and it is not enough.
Done properly, the scheme shows the site picked its seed before you played, sealed it with a hash, and could not change it after seeing your stake. Re-running the formula reproduces your result. For that round, the dice were not swapped after the throw. That is a genuine improvement on blind trust.
Nothing in the scheme touches the terms. It does not prove withdrawals are paid, that the house is solvent, that bonuses are honest, or that rounds cannot be voided after the click. It does not tell you who the operator is or whether the same desk runs forty other skins. A verified result from a desk that never pays out is still a loss.
It checks the dice, not the desk.
So use provably fair as the first gate, not the last. A site that fails the seed check fails everything. A site that passes has earned exactly one thing: the right to be checked on the rest.
If you would like to learn more about the technical workings of provably fair algorithms, you can download the whitepaper.