Gemstone Caverns — ruling 1

If multiple Gemstone Caverns are put onto the battlefield under a single player's control before the game begins, the "legend rule" won't put the extras into that player's graveyard until just before the starting player gets priority during the game's first upkeep step. There's no opportunity to tap the extras for mana.

Gemstone Caverns — ruling 2

A player's "opening hand" is the hand of cards the player has after all players have taken mulligans. If players have any cards in hand that allow actions to be taken with them from a player's opening hand, the starting player takes all such actions first in any order, followed by each other player in turn order. Then the first turn begins.

Gemstone Caverns : règles, fonctionnement et interactions (MTG)

Gemstone Caverns is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

If this card is in your opening hand and you're not the starting player, you may begin the game with Gemstone Caverns on the battlefield with a luck counter on it. If you do, exile a card from your hand. : Add . If Gemstone Caverns has a luck counter on it, instead add one mana of any color.

How it works : Gemstone Caverns

Original English text — Wizards of the Coast / Scryfall

#1March 19, 2021· Wizards of the Coast
If multiple Gemstone Caverns are put onto the battlefield under a single player's control before the game begins, the "legend rule" won't put the extras into that player's graveyard until just before the starting player gets priority during the game's first upkeep step. There's no opportunity to tap the extras for mana.
No other card is named in this ruling.
#2March 19, 2021· Wizards of the Coast
A player's "opening hand" is the hand of cards the player has after all players have taken mulligans. If players have any cards in hand that allow actions to be taken with them from a player's opening hand, the starting player takes all such actions first in any order, followed by each other player in turn order. Then the first turn begins.
No other card is named in this ruling.