suppose the bid ask now is 20.01X20.05. I submit a buy order to buy 50 shares at 20.02. since my share is less than 100, the NBBO (bid and ask) does not change. suppose the NBBO bid occurs on ISLAND, but my odd share order is sitting on ARCA. when someone tries to hit the bid at NBBO, who has the priority to be filled? the NBBO bidder at ISLAND, or my better priced bid order at ARCA?
It is my understanding that Reg NMS only protects visible orders so odd lots have no standing. It is possible that some ECNs bulk odd lots and then show them if they reach 100 shares. There is no time order priority between ECNs.
I agree with Robert, odd lots are just there at the exchange waiting to be hit at that particular exchange. I can give an example (not an actual one, but similar things happened). NBBO is 20.01x20.05. I enter a buy order 50@20.02 routed to Island I enter another order 50@20.03 routed to ARCA. Someone sells 100@20.01 through Island. I get hit on my 20.02 on Island but the 20.03 still sit at ARCA. I can also agree with Robert that in my opinion and experience at least some exchanges aggregate bulk odd lots and they will appear in the NBBO once the total volume at a given price is >100.