Front running is illegal. However, making a better price prediction than the rest of the market and trading on it is not the same thing as front running.

[1] https://www.investopedia.com/terms/f/frontrunning.asp#:~:tex....

Hmm, I don't think that answers the question. See https://www.nyujlb.org/single-post/2017/11/27/high-frequency... (which is EU-specific). I think https://www.cnbc.com/2014/04/03/high-frequency-traders-cant-... is suggesting that this is similarly legal in the US.

Again, not an expert.

Generally, illegal trading resolves around the idea of trading on non-public information. And front running falls under that category (access to order data that other participants do not).

However, HFT's do not trade on non-public information. Every participant has access to the same market data. I could start my own "HFT firm" tomorrow; I would just be incredibly unsuccessful at it because I don't have the finances or computing resources to execute.

Right. I think we're saying the same thing?

I think I'm missing the connection between how HFT's trade and how it takes money away from regular people.

This is a pretty widely discussed question, and while I think the empirical evidence is so far unclear, there are some obvious theoretical models where costs for large institutional investors (like pension funds) go up. E.g. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2238516.

Pinging (https://www.finra.org/investors/insights/getting-speed-high-...) would be an example such strategy.