Available players that want to play list, jumps too much

[asd123321]

and game lists after it. If you only updated the overall slot positions every 10 seconds, it would be more stable.
Leave some spots open for a little while when one leaves and have a bunch at the end vacant that can be used until you run out. Don't adjust the length of the list for each single change.

[in8nirvana]

This impacts the ability to suggest games and change tables. Often, between putting mouse on a person/table and clicking, the target person/table has changed.

Making the player list a fixed size and scrollable would work.

[Willie333b]

Agree.