They make money NOW either direction; this doesn't mean they will always make money. If a competitor suddenly starts being faster, they are going to start losing money no matter which direction the market goes.

Note that I'm not saying that market maker profit is correlated to the performance of the wider stock market, just pointing out that market maker performance can and will be affected by market-related factors that can cause all their market bets to go wrong at the same time, so the actual risk of losing money will always be much greater than what just naively applying the LLN says.

Here's a couple of plausible factors:

1. A flash crash is just a huge coin flip -- even if your market making firm has circuit breakers that stop it from making more trades (and successfully kept its position small), if the exchange ends up ripping up trades en masse you may suddenly have a large position that loses you a lot of money

2. Someone screws up an algo [1] and you burn through more than your entire market cap in half an hour

[1] https://www.bloomberg.com/news/articles/2012-08-02/knight-sh...

Not sure I understand why we can assume that its all trades are entirely "independent" here.

Agree with you that HFT performance is not correlated with market direction. But given the volume of trades it would imply that many of the trades are occurring on a smaller pool of equity instruments. I'd think that given liquidity constraints and competition that there's a sweet spot in terms of number of stocks that a given strategy is actually efficient on.

So not entirely sure why we consider every trade to be iid - rapid shocks (flash crash), equity specific news etc would affect a number of trades at once changing the 51% probability?

Also does anyone know if the profitability numbers include payments to be a market-maker?

Market makers typically have a requirement to be in the market a certain (high) percentage of the time. In return, they get rebates (which can be a significant source of revenue) and protections from the exchange against overfilling. This can help them for certain shock events.

Most likely, though, their profitability % is tuned by edge and risk parameters. They can adjust size, widen out, or tighten up the spread to tune trade frequency and profitability. They are finding a sweet spot between # of trades and profitability.

Those number absolutely include payments. It's rare (in my experience) for an equity market making strategy to be positive in gross terms (prior to the maker-taker rebate). These numbers you hear from Virtu/KCG should be net of exchange trading costs/rebates.

My friend at a different hit firm says they tend to make MORE profit in high volatility regimes

That's exactly what SEJeff is saying (profit is positively correlated with both trading volume and price volatility).

Correct sir! And I've spent the past 9 years of my career as a Linux monkey in electronic trading / HFT / whatever the hip term for it is today.