Quick answer
The first Charleston is mandatory. Any one player can stop the second before it starts. The courtesy pass is still available either way. Here is how and when to use it.
Somebody at the table says 'stop' and half the players are not sure whether they were allowed to. Here is the rule, the timing, the strategy behind stopping or not stopping, and the two disputes it causes most often.
The rule
The first Charleston, three passes of three tiles (right, across, left), is mandatory and cannot be stopped by anyone. The second Charleston (left, across, right) is optional, and any single player may stop it. It does not need a vote, and nobody has to give a reason.
The optional courtesy pass, an exchange of one to three tiles with the player across from you, is available after the Charleston whether or not the second round was played. Both players must agree on the number, and either can decline it.
When to say it
The decision belongs to the moment between the end of the first Charleston and the start of the second. Say 'stop' or 'no second Charleston' out loud before anyone has passed a tile of the second round. Once the first pass of the second Charleston is under way, it runs to the end.
Say it clearly and once. At tables that play fast, a mumbled stop is the beginning of an argument, and the fair ruling when tiles have already moved is that the second Charleston stands.
Why a player stops
Because their hand is settled. After the first Charleston a player who already has two or three sets and a pair prospect has little to gain from passing three more tiles three more times and quite a lot to lose, since every pass forces them to give up something.
Because a full second Charleston would tell the table too much. Passing is information, and a player who keeps passing only jokers' neighbours and lone winds is showing everybody what they are not building.
Why you should usually let it run
If your hand is not settled, the second Charleston is six more tiles of chances at the pair or the joker you need, and the tiles you pass away are ones you were not using. Most beginners stop too early, out of fear of passing something useful, and end up with a deal that never moved.
The second Charleston also gives you information about everyone else. Watch what comes across and what goes left, and you learn which directions the table has abandoned, which is exactly what you need to know before the first discard.
What happens after a stop
Play proceeds to the courtesy pass, if the two players across from each other want one, and then to East's first discard. Nothing else changes: no penalty, no extra draw, no reshuffle.
A stop is not a tell in itself. Strong players stop with a bad hand sometimes, precisely so that a stop does not always mean a made hand. Read it together with everything else, not on its own.
The two disputes and how to settle them
First: a player says stop after the first tiles of the second Charleston have been passed. Too late; the round continues. Second: a player tries to stop the first Charleston, or to skip one pass of it. Not allowed; the first Charleston is played in full at every table that follows the League's rules.
If your group plays a house rule (some allow stopping the second Charleston mid-round if everyone agrees), agree it before the first deal, and treat it as a table rule rather than the game's rule when you sit at a new table.
Put it into practice
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Whether to stop the Charleston is the same question as whether your hand is settled. Mei, our AI coach, reads your tiles and says which direction leads, what the backup is, and whether the hand has committed yet.