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THREE-PLAYER MAH JONGG (Article 188)
When there are fewer than four players, the National Mah Jongg League official rule is to omit the Charleston to avoid complications and ensure fair play.
The Charleston aims to allow players to transform their dealt hand in a series of 3-tile passes between opponents. Some players pass defensively, and some do not. Risky passes can be very useful to the receiving player. In a 3-player game, passes from the missing player are simulated by taking random tiles from the wall, and those random tiles could have useful tiles (e.g., jokers, flowers, pairs, like tiles). Also, when players pass to the missing player, they can include useful tiles in their pass with no risk.
In a 3-player game with the Charleston, the player sitting across from the missing player has a disadvantage. The two situations that create unfairness are 1) the player to the left of the missing player could get two passes in a row with tiles that would likely not be passed by a human (e.g., flower, joker, like numbers, pairs), and 2) the player to the right of the missing player can do two risky passes in a row (e.g., flower, like numbers, pairs). Both situations can give these players critical mass in hand development.
Some groups enjoy the Charleston so much that they have figured out ways to include it, but the league considers them house rules. If your group decides to do the Charleston anyway, you are playing by a house rule, and your group must define logistics and the rules. Here is a video demonstration of three ways to do it: https://youtu.be/uYUja7aZ3bE
From the NMJL: Four walls are built. The three players draw tiles from the wall, four at a time, until everyone has twelve tiles. Wall without a player does not draw any tiles. Each player then picks one tile in turn, for a total of 13 tiles, with East then picking a 14th tile from the wall. The Charleston is omitted, and East starts the game by discarding the first tile.
Source: Mah Jongg Made Easy (2024 page 26)