Is the following a valid
set in Indian-Rummy when we're using three decks of cards? What about when we use two decks?
6♠️ - 6♠️ - joker
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That set is acceptable only in Indian Rummy's three deck variant. (I'll call Indian Rummy by its name Paplu here for some better clarity.)
Two-deck Paplu and regular Rummy only has sets (same card value, different suites) and runs (same suit, sequential card values) and that move isn't legal in this format.
Three-deck Paplu allows the set type you describe, called a tanala:
When three decks are used it is customary also to allow an additional type of combination consisting of three identical cards - such as ♣️10-♣️10-♣️10. This is known as a tanala, and is treated as equivalent to a straight run.
The joker is a wild card that can stand in for any other card at all, which means it's legitimate for completing the tanala.