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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playBunny: I don't think colors are randomly assigned. It looks to me like the challenger always makes the first move.
But random color assignment would be a decent system. Even if a game is tilted heavily in favor of one color (Maharajah chess, anyone?), the combined procedure of first randomly assigning colors to the players and then playing the game is fair.
playBunny: I have to agree with BIG BAD WOLF (and not only because sharp teeth are more persuasive than floppy ears). With the match types currently available on BrainKing, it's not possible (except in backgammon and its variants) to create a match that is fair to both players and has no possibility of a draw. For my part, I prefer fairness over drawlessness, and I hope the existing stairs will remain as they are.
Having said that, I would have no objection to the creation of additional stairs with single games or 2-win matches or whatever. And maybe you'll have more success than I've had in my attempts to get a set of Fischer-clock stairs with longer time controls.
Another possibility would be the implementation of a new type of match, similar to the n-win matches, but with pairs of games (rather than single games) as the basic building block. Thus after the first two games, if one player has reached some predetermined victory condition, then he wins the match; otherwise they play two more games, etc.
Why are there no Standard Fischer's Stairs? Maybe I don't have time to make a move every three hours, but it would still be nice to know that a game will eventually have an end.