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Can a trade happen “in between” the bid and ask price?
All the time. For high volume stocks, it may be tough to see exactly what's going on, e.g. the bid/ask may be moving faster than your connection to the broker can show you.  What I've observed is with options. The volume on some options is measured in the 10's or 100's of contracts in a day. I'll see a case where it's $1.80/$2.00 bid/ask, and by offering $1.90 will often see a fill at that price. Since I may be the only trade on that option in the 15 minute period and note that the stock wasn't moving more than a penny during that time, I know that it was my order that managed to fill between the bid/ask.