Yes, you can discard a Joker in Mahjong Island. But once a Joker lands in the Discards, it is dead. Nobody can take it, not even to Win.
What is a Joker?
A Joker is a wild tile. It stands in for a tile in a Set, Quad, Quint, or Sextet. A Set is three matching tiles, and a Quad is four.
A Joker can never fill a Single (one tile) or a Pair (two identical tiles).
How does discarding a Joker work?
It works like any other discard. On your turn you draw a tile from the Draw Pile, then discard 1 tile. That tile can be a Joker.
Most discards can be claimed. Another player may Take Tile to Win or to make an Open Group, which is 3 to 6 identical tiles placed face up. A Joker is different: nobody can take it.
Should you discard a Joker?
A Joker can stand in for a tile in any Set, Quad, Quint, or Sextet, so it is often useful. Each Joker kind has its own Mult bonus, a multiplier on your score, when it is in your winning hand.
Still, a Joker only helps a hand that needs a Set, Quad, Quint, or Sextet. If the hand you chose has no place for it, you may let it go.
For the full picture, read the Mahjong Island Jokers guide or the complete Mahjong Island rules.
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