You are correct, the higest router id should serve as tie-breaker if the priorities are all the same. However, once the DR election is over if another router comes online with a higher priority/ID it wouldn't become the DR until the already elected DR/BDR fails. I assume you must have configured/powered on R3 after R1 & R2. Clear the ip ospf process on all 3 devices quickly and you should see the DR election resulting the expected outcome.
This is a fairly common issue to run into as you are learning OSPF. The explanations of OSPF election of DR/BDR focus on the relationship of loopback address/physical address as the RID and election based on the RID. The aspect that they typically do not discuss is the issue of timing. When the first router boots up it looks for neighbors and if it finds neighbors then there is an election as commonly described. But if there is no neighbor present, the router waits a short time to see if one will appear and if not then the router conducts the election for DR and that router is the only candidate.
So based on your description I believe that router 2 booted first and was the only router present for a little time, and conducted the election. Then router 3 booted up and was elected as BDR. If you want to test this, I suggest that you power down the routers, and then power up the routers as nearly simultaneously as you can and see what happens.
For a production environment, is it customary for a priority to be set for the preferred DR router and a lower priority to be set for the preferred BDR and the other routers set with a priority of zero?
In my experience most people do not bother with setting priority, especially in LAN environments. There are a few situations, especially multipoint Frame Relay, where it may be imoprtant to set priority, but I believe that mostly people use the default priority.
If you have a situation where you think it does matter, then you should plan carefully what router(s) get the highest priority, what router(s) get other priority, and what router(s) get zero priority. Also if you have a situation where you have assigned priority to manage which router is DR, then you should have a plan about monitoring to verify if that router continues to be DR. Because there could be a situation where that router (or that interface) went out of service temporarily, and then the router is no longer the DR.
If you are trying to learn about the protocol (and especially if you are studying for some certification) it is important to understand how features like this work. But many of these features are not widely used in production networks. They are used where they are needed.
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