Why do you think you would get double reward then? at the same time you would be just long one of both...
Because instead of 1 BTC on A and 1 BTC on B I would get 2 BTC on A/B.
I think if you have 1 BTC before, then you will later have 1 one A or B, not 1 on both? As you have to decide what chain you will use.