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. .
KotDB: Lol. You do agree with me. -- it's not possible (except in backgammon and its variants)
Given that I was prompted to make my posts as a result of getting nowhere on the Ludo 2-games Stairs, and that I otherwise only play Backgammon and its variants, it's nice that you do agree with me. ;-) BBW's objection on behalf of the starter-has-the-advantage games is no problem for me and I agree that 2-wins isn't a flawless solution to the problem there. But in fact I have no idea whether there is a problem perceived by the climbers of those Stairs, so I won't make any claims on their behalf. ;-)
But on the other solutions put forward, I don't see much difference between a single game and a 2-wins match. The starter in a single game has the advantage. More so than in a 2-wins match, surely? I like your paired-games idea. 2-wins of paired games. It could make for a lot of games, though, lol, but at least it would have a winner.
I don't particularly mind what solution was be used, just so that in games where draws are most likely there be some way of playing only for a win. Restricting it to game types where there's some small difference between the who-starts-wins percentages (say 5%) does makes sense although, in the long term, players wouldn't benefit from the advantage given that starting colours are randomly assigned in the Stairs.
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