[areyousure]

Sadly, firms abuse odd lot rules to give people terrible prices: https://academiccommons.columbia.edu/doi/10.7916/2y01-1s13/d...

In example 3, the NBBO for stock ABC is 495--500, but there is also an odd lot offer for 497 on exchange. If a Robinhood customer sends a market buy order, then Citadel is allowed to fill it for 499.999 even though it's better to send to the exchange. (And if they then pick up the odd lot themselves, it's easy arbitrage.)

By the way, while you're correct about some of your claims, odd lot executions definitely have to occur within the NBBO. (How could it be otherwise?) Otherwise, in the example above, Citadel would give an even worse price!

[atomicnumber3]

I mostly mean scenarios where your limit order might not be marketable, end up resting on the book, and then get traded "through". I'm speaking from the perspective of an actual direct market participant, where you're not using a market order but are trying to enter a position while adding liquidity/collecting a rebate. (Most exchanges reward participants who have some % of their trades as liquidity-added, with rebate tiers).

Round lots are excluded from the NBBO so that the NBBO can't be as easily influenced by quantities of shares that don't represent any material price signal. 1 share of practically anything but BRK class A represents ~nothing. Less than a round lot on a price level is basically no liquidity available at that level.