It's true, people might not often change their choice.

One way to put your mind at ease would be to, client-side, randomly choose above or below behind the scenes, in addition to the main screen one; I might implement that, shouldn't take more than five minutes.

This method of provably fair however (even with the modification above) makes a lot more sense to the average player, than having them input a seed, and not really knowing how to verify that they aren't being cheated.