A round-robin Zoom breakout room organizer for breaking into groups of twos over multiple rounds with unique pairings. This extension is only valid with "Paid"/"Licensed" Zoom accounts, as the breakout room feature is only available to users with these accounts. The extension is similar to Zoom's "Automatically" split participants into rooms feature. However, this feature randomly assigns participants to rooms, and thus over multiple rounds users will often be paired many times with some other users and no times with other users. The extension addresses this issue by consistently pairing users over multiple breakout sessions. The extension thus allows a host to have round-robin pairings over multiple rounds of breakout sessions while ensuring that participants have a one-on-one breakout session with every other user in the meeting before being paired twice with any other participant. A number of feature requests have been made to Zoom regarding addition of this feature via their development channel (round-robin tournament style pairings for breakout rooms), but for the time being the feature is not supported. Other details:

The extension is run by the meeting host only. Participants may be using the browser or desktop versions of the Zoom client, as typical. Participants do not need to install or run the extension.
Zoom includes a browser version of their video chat. The browser version of the Zoom video chat is available by navigating to the following web address: (https://web.zoom.us/wc/<Zoom Room ID>/start to start a meeting and https://web.zoom.us/wc/<Zoom Room ID>/join to join a meeting). The web client links occasionally appear when opening a meeting in the browser. The host must be running the browser version of Zoom client in order for the extension to work. The host can optionally also be running the desktop client.
The extension adds a "Zoomie" button to the breakout rooms dialogue box, which may then be used to manage automating breakout rooms of two people over multiple rounds.
A future feature to support is the ability to control the number of participants added to a breakout room, as Zoom allows an indefinite number of users per breakout room. For the time being this is limited to two participants per room.
During the course of the meeting, the host should not navigate away from the Zoom meeting. Doing so will reset the round-robin pairings saved in the extension. A future feature to support is saving pairings in a cache such that the host can leave the room and return and the previous round-robin pairings and round-number will still be accessible (browsing away currently resets both the pairings and the round-number ).
Two videos are available on Youtube detailing the extension's expected usage: https://www.youtube.com/watch?v=l-t-FtH0GW8 (short); https://www.youtube.com/watch?v=vkE3dhM6Hs0 (long). The extension was originally made for Google Chrome but works equally well without modification in Firefox.
The host is never added to the round-robin pairings, as by default Zoom does not include the host in the list of users available to add to a breakout room.
The host can use the extension to specify a singular "co-host" for the meeting. The "co-host" participant will be added to the round-robin pairings only if there is an odd-number of participants in the meeting (excluding the co-host user and host user). Optionally, the host may also specify to always exclude the co-host user from round-robin pairings regardless of the number of other participants (odd/even) in the meeting.
If there are an odd number of users in the meeting (excluding co-host and host), then the extension will perform a leave-one-out assignment of users to breakout rooms. That is, over the course of a full round of pairings, each user will be left out one time. The host should alert this user that they will be remaining in the main room, and/or alert users to this behavior beforehand.
The host may choose to ignore any user from being put into a breakout room. In this case, the extension will exclude the user when calculating round-robin pairings.
The host should wait for all users to return to the room before using the "Zoomie" button to assign users to rooms. Failing to wait for users to join back will result in the round-robin pairings being regenerated (previous pairings reset).
On each round, the host should click the "Zoomie" button and confirm the round's pairings and other settings. Clicking the "Okay" button in the "Zoomie" dialog will then assign users to rooms according to the current round and round-robin pairing. The host then should click the "Open all rooms" button to move users to their respective rooms.
(Optional) "Auto-close rooms after (seconds)". Allows for fine-grained closing of breakout rooms. Presently, Zoom only allows a minutes timer for auto-closing rooms (e.g., 1 minute, 2 minutes, 3 minutes). The extension "clicks" the "Close all rooms" button after this specified time. Example: 30 seconds.

The extension was created by David Shumway, a PhD student at University of Illinois at Chicago. The extension is open-source and may be used by any group or individual. Questions, concerns, and feedback may be mailed to dshumw2@uic.edu.

Developer response