Quick answer
On your own turn, after you draw or call and before you discard, you may take a joker from any exposed set, yours included, by giving the exact natural tile it stands for. The joker then joins your hand to use anywhere a joker is legal. Jokers in a hidden hand or the discard pile can never be taken.
The joker exchange lets you take a joker from any exposed set, yours included, by giving the real tile it stands for. Here is how it works, and the four ways it goes wrong.
What can be exchanged
Only a joker that is sitting in an exposed set on someone's rack, yours included, can be exchanged. Jokers in a player's hidden hand are untouchable. Jokers in the discard pile are dead and cannot be taken.
You exchange by giving the exact natural tile the joker is representing. If the exposure is a pung of six bams with a joker as the third six bam, only a six bam buys that joker.
A hand being declared dead does not take its jokers off the table. A joker in a dead player's exposure can still be exchanged, as long as that exposure was correct when it was made and is not what made the hand dead.
When you can do it
You can exchange only on your own turn, after you have drawn or called a tile and before you discard. You may make more than one exchange in a single turn if you hold more than one matching tile, but you cannot exchange instead of drawing.
If you called a discard, finish that exposure first. A joker you take in an exchange cannot be used to complete the set you just exposed with the called tile.
What happens to the joker
It goes into your hidden hand, and you can use it anywhere a joker is legal, such as a pung, kong, or quint in the hand you are building. You then discard as normal. Your tile count does not change, since you gave one tile and received one.
Exchanging is not calling a discard, so it never makes you expose anything. You can exchange for a joker even while you are playing a concealed hand.
Can you take an exchange back?
No. Once you have handed your natural tile to the other player, set it on their rack, or taken hold of their joker, you are committed to the exchange. You cannot take your tile back or put the joker back. The League's 2014 newsletter says the exchange is committed once it is made, even if the joker has not yet reached your own hand.
So decide before you reach. Check that your tile matches the set exactly and that you want the joker, then make the exchange.
Four ways it goes wrong
The first is offering a tile that does not exactly match the set. A six crak does not redeem a joker standing for a six bam. If nobody catches the mistake before the exchanger discards, the wrong tile stays in that exposure, and the dead hand is the one whose rack holds that exposure, not the exchanger's. So check any tile that goes into your own sets.
The second is reaching for a joker in a pair. A joker can never be part of a pair, so there is never one there to take.
The third is exchanging at the wrong moment. Exchanging on another player's turn, or on your own turn before you have drawn or called a tile, makes the exchanger's hand dead. The League published that ruling in its 2020 newsletter.
The fourth is naming the natural tile, or letting it touch the table, before you ask. Hold the tile out to the player whose rack has the joker, and ask for the joker. Under the League's tournament rules, a tile counts as discarded once you have said its name, even part of it, or once it has touched the table, and a discarded tile can no longer be exchanged.
Why it matters strategically
Every exposed joker is a loan you can lose. Any player holding the matching natural tile may exchange it for your joker on their own turn. So exposing a set that contains a joker is a bigger decision than exposing one made of naturals, and the later you can leave it, the safer it is.
When an exchange helps an opponent
It can. Under League rules a hand with no joker in it when mah jongg is declared is paid double. Take the last joker out of an opponent's exposures and their hand may now be jokerless, so if they go on to win and declare it jokerless, every payment to them doubles.
Put it into practice
New to the game? Start the course at Lesson 1, Meet the Tiles. The first three lessons are free and need no account.
Already play? Have the coach read a real dealt hand for you, free. It names the direction the hand goes for, what to keep, what to pass, and the reasoning behind each call.
Whether to expose a set with a joker in it depends on where your whole hand is going. Our AI coach reads a dealt hand and says which direction it points, free, with the reasoning.