The "bias" in this case or the predicted exploitable property would be the assumption (or prediction) that the hurst exponent will be < 0.5 all the time. The grid would be a mean reversion strategy and the anti-grid with wider grid spacing would compensate the (smaller) trending component. The lot size of the anti-grid should be exactly
lot_antigrid = lot_grid * (spacing_antigrid / spacing_grid)
This way price could move in any direction as far as it wants (and even stay there forever), the anti-grid floating profit would always exactly compensate the total floating loss of the grid.
The grid is profitable if H<0.5 and I have temporary unlimited sources of capital. The capital when needed would not be supplied by me, it would be supplied on the fly by the anti-grid, therefore it would not have to be mentioned in my books. In a scenario where for example the antigrid has two times the spacing of the grid (and two times the lot size) the floating losses could never ever exceed three (1 + 2) grid steps times lot_grid (and the open positions would never exceed 2 * lot_grid). The balance (realized profits) would steadily go up.
I had a strategy that had some fatal assumptions built-in, what worries me is that the details you are giving here sound awfully familar...
Where the train came off the track for me was when rollover fees started accumulating (asymetric consumption of capital as floating losses were not a conserved quantity dictated by price alone) and the fact you don't have access to unlimited capital because your leverage is finite (margin requirements) and spread volatility can make free margin problematic at the very time you need to be able to rely on your hedges.
When did I say i want to nedge?
If for example the grid has 0.02 lots short and my anti-grid wants to open 0.02 lots long then i do not hedge them! Instead of buying 0.02 lots i just close 0.02 of the sell positions. This way i wont ever have more than 0.02 lots open.
[...] would be the assumption (or prediction) that the hurst exponent will be < 0.5 all the time. [...]
I see. I feel intuitively that we are missing something and this should not work, but I can't put my finger on it at the moment, need some time to think (and to be honest, my knowledge isn't all that deep in these subjects - need some time to read too).
The next step is to try to incorporate this into your current analysis and find mathematical justification to your idea. Beware of trying to find that justification via Testing/Optimization... You might fall into the 'curve fitting' trap.