Not very much. If you are big, you want big fills. You need market makers for that - i.e., you need what HFT's are selling and would be worse off without them.
Of course if you are time insensitive, you can certainly play games. This basically means running your own HFT strategy, but biased in the direction of the trade you want. You'll also opportunistically take liquidity if the fill you want is in the book.
Of course if you are time insensitive, you can certainly play games. This basically means running your own HFT strategy, but biased in the direction of the trade you want. You'll also opportunistically take liquidity if the fill you want is in the book.