This is purely for my fun (and also practice!), but is there any place online where I can play simultaneous chess against many opponents?
This would be against human players, of course, not against computers.
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You could do that on FICS, here's how:
Simuls "Simuls" = simultaneous chess matches; playing more than one opponent at a time. It is possible to play more than one opponent simultaneously on the chess server. Below are sections for Starting a Simul and for Joining a Simul. Users using an interface that only supports a single board (that is if two games are being observed a move from the second game will cause the position of the first game to disappear (such as Winboard and Xboard)) should issue "iset singleboard 1" before starting a simul. This will ensure that when simul participants move, only the board the simul holder is at will update. STARTING A SIMUL In order to play more than one chess match simultaneously you need to do the following: 1. Start the simul with the "simstart" command. Announce your simul conditions on shout and cshout enough to get the word out, but not so much as to annoy users. 2. Other users must then challenge you with "simmatch". 3. Accept or reject the challenges as they come in. The first game will be colored as is if was an ordinary match. The next game will be the opposite color, the next the opposite to that and so on. 4. When you are satisfied that you have started the number of games that you can handle, turn off your open flag with "set open 0". You can see your games with "simgames". 5. You can then start making moves on the board. The "simnext" command moves you to the next board; "simprev" moves you to the previous board. You will focus on one game at a time, going in a particular order. If you wish to skip to a board of particular interest "goboard <player>" or "goboard <game number>" will take you to that board. 6. If you are bothered by how long a player is taking to make the next move, or they are being disruptive you can abort that game with "simabort". You can also force an adjournment with "simadjourn". Only games adjourned during the simul can be resumed. After the simul any outstanding simul games may be resumed as normal matches. Should there be a need to terminate the simul "simallabort" and "simalladjourn" will abort or adjourn all games respectively. Both commands will also terminate the simul. 7. When you are finished type "simend". This will return you to normal playing mode and inform you of your statistics for the simul. Various commands you can use while running a simul include: goboard, simabort, simadjourn, simallabort, simalladjourn, simnext, simprev and simend. JOINING A SIMUL In order to play against a user who is open for playing simultaneous matches, here is what you do: 1. Using the "simmatch" command, challenge the person you will be playing. 2. You will be informed when the simul player is coming to your board. You should be prepared to move either before or shortly after that player arrives at your board. If you do not move within a reasonable time period, your game could be aborted. 3. It is impolite to offer a draw unless that player is at your board. It could very easily confuse the simul player if offers come in from different users at once. OBSERVING A SIMUL You can observe all games in a simul once they have started by typing "simobserve simul_player". All of the simul_player's simul games will be added to your observation list. As the simul_player moves from board to board, so will you. When the last game has ended, you will see the final results from the simul games. You can also use the "follow" command for this purpose. Using the "observe" command, however, is not reliable for this purpose.
I don't know if it affects your rating, never tried it. Be careful what you wish for :)
There's also RedHotPawn, it says that it offers that, maybe a member can verify that, I signed up there a year ago never used that site. But it's the second most popular online chess website after Chess.com I believe.
PlayChess server offers that as well but it's not free, but it's well known server, best of the best.
On Chess.com, you could play live chess and duplicate tabs, and you'll end up playing more than games at once, not the same window though.
There's also gameknot.com, I have never heard of it, but they claim it is possible to play such games on their site.
lichess is a good place for simuls: https://lichess.org/simul
As of 29 April 2020, Chess.com supports playing online simuls (simultaneous exhibitions) against human opponents.
To enable, users must select the setting "Play Multiple Games at a Time" at chess.com/settings/live.
Enabling the "Auto Switch Game" setting, "Chess.com will automatically take the simulgiver to the game in which they have the least time remaining as soon as they make a move."
A player can manually shuffle between their ongoing simul games using the specially designed interface.