Who is here
Pair the room
Tick everybody who has turned up and the board works out the tables. It looks for the games that teach the ladder the most: close ones, fresh ones, and the ones against a player whose own number is settled enough to be worth measuring against. Everybody present gets the best game the room can give them, not just the two who happen to match up best.
Who is here
Chases the best games it can find, while making sure nobody goes home having had a wasted evening. The setting for an ordinary night.
Next round remembers who has already played tonight, so the board stops offering the same two people to each other all evening. Nothing here is recorded. Report the games on the Score Card as usual.
Tick who is here and press Pair the room.
How the tables are chosen
Every rating on the ladder carries a deviation beside it, which is how sure the club is of that number. A game brings a deviation in, and some games bring it in further than others. Three things make an opponent worth more: a close match teaches more than a foregone one, a player whose own number is settled teaches more than one nobody has the measure of yet, and a first meeting teaches more than a tenth.
That last one is why the board keeps sending you at people you have not played. The fourth game against the same person counts about half as much towards certainty as the first, because by then the club is hearing the same thing again. Play a variety of people and your number comes in faster, and since the ladder seats you on your rating minus a deviation, it also moves you up.
Seating the room is not the same as ranking your opponents, which is why this page exists and the list on your profile is not enough. The settled players are very nearly everybody's first choice, so a room told to go and play their own best opponent would all converge on the same two people. The board solves the whole room at once instead, and the seating rule above decides whether it chases the best games it can find or makes sure nobody goes home with a wasted evening.
One caveat on the arrows. A deviation widens on its own while a player is away from the board, so the number each card starts from has some of that in it. Turning up and playing anybody at all takes that part back. The rest is the game, and that is the part the seating is choosing on.