To find out what stairs you can currently challenge someone in, first go to the Main Stairs Page, then click on "Show your stairs only" link. The ones in BOLD are ones you can make a challenge in.
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When a match is finished, a message is sent to both players stating the outcome of the match. An option is also available to send another game invitation to that player, optionally deleting the message.
In Stairs games, instead of "another game with the same player" could there be an option "challange another player in this Stair" or something similar? Maintaining the option to automatically delete the message, of course ;)
(hide) If you are waiting for your turn, click on "change" next to the "refresh" on the main page, then set refresh the page to 30 seconds to get your turn to move displayed faster. (Servant) (show all tips)