We have to be very careful about our terminology when we talk about profitability of trading days. I have not inspected Virtu's trades, pnl statements, or legal documents related to them, so this is less about them specifically than about trade pnl generally.

When most firms talk about profitability of trading day, they are talking about the the profitability of just their trades. That is, if they bought for 1 million dollars and sold for 1 million and 1 dollars. That is technically a profitable trading day. If the cost of entering and exiting that trade cost them 2 billion dollars they will still mark that as a "profitable" trading day, even though it clearly isn't.

That is to say, it is trivial under this accounting scheme to come up with a strategy that has no losses. Just don't trade.

I apologize for not going into more depth about why I think Lewis is wrong. I've explained it a lot in my comments on HN lately and can't be bothered to do it again. That said, if the linked article was more professionally presented and didn't have the weird racial language the points are basically what I would argue against Lewis' premise.