Yes. So seller A wants to sell for $1.00 and buyer B is willing to buy at $1.06, an algorithm will calculate the presence of this potential (or actually have knowledge from other systems that this a certainty) and purchase seller A's stock with a margin of overhead of $1.03 and sell to buyer B for $1.06 netting $0.03.

The algorithm is essentially a parasitic entity.

What you are describing is market making, and has existed pretty much as long as there are markets. Before computers rendered guys in the pits extinct, the spreads were much wider and those guys were known to literally front run you on occasion. You had legions of brokers and floor traders all taking home fat six figure paychecks each year and your trading costs were in the tens of dollars, not pennies. Those legions of traders have been replaced by a much smaller number of programmers who take home comfortable six figure paychecks.

They take on obligations as market makers to always buy and sell no matter what the market is doing.

How that worked was that he got a phone call saying "buy me 50k IBM" from a broker. Guy on the floor thinking smart money is behind this, or even not thinking there is smart money behind this, he just knows an order like that is going to move the market- will place his own order ahead of it and likely exit the trade immediately after. The advent of electronic trading, even when people were still on the floor, made this much harder to do since it became easier to slice and dice that order up to a bunch of different people, and there were now much better paper and electronic trails of the activity. Now its all computers talking to one another and this is not possible.

Right, gotcha: the market needs intermediaries to function properly.

This isn't really what market makers like JS do. While they do make profit from the spread between prices they buy and sell at, the key difference is that they will buy from seller A and sell to buyer B at different times. For the duration between the two trades, they either own a positive or negative amount of whatever the good is, so they are at risk of losing money if the price changes. The spread pays them for taking on the risk and providing liquidity (allowing people to buy and sell any time even if there's no matching counterparty).

JS and their ilk replace the market-makers, you're saying.

Can you explain to me very carefully why the orders of seller A and buyer B weren't able to match before Mr. Evil HFT came along?

Moreover, given that buyer and seller weren't able to match without Mr. E. HFT's help, hasn't he in fact rendered a valuable service (for which he should, of course, be paid)?

So that's the missing part you say? The Internet has been the biggest catalyst of disintermediation in history. But this is not disintermediatable without HFT?

My question is pure nuts and bolts.

A and B wake up one morning and want to trade MSFT. Both submit orders to "the market." You claim HFT somehow inserted itself into the middle of the transaction.

I'm asking if you can fill in the blanks on how this is possible.

I thought that was clear: prior to HFT, the seller would have made the deal with the buyer without the intermediary HFT because if the latency. HFT exists because of speed. Very hard to say "High Frequency Trading" without saying "High Frequency".

The HFT needs latency low enough to win a race against B.

If HFT and B are racing for the same order, they evidently have a very similar trading objective. In which case it's bizarre to ascribe some uniquely negative social value to HFT winning that race.

The HFT doesn’t want a position, it’s only trading because it anticipates what B is doing right now and adding cost to the process without improving the result.

Thanks, that's what I thought.

Your example makes no sense. If both those orders were on the books then the exchange would have to immediately execute that trade at $1.00 (Assuming A is before B).

This is flat out wrong, the market would cross in this case.