1

According to the Comprehensive Rules,

103.4c In a multiplayer game and in any Brawl game, the first mulligan a player takes doesn’t count toward the number of cards that player will put on the bottom of their library or the number of mulligans that player may take. Subsequent mulligans are counted toward these numbers as normal.

Does this mean that the first mulligan in a multiplayer (3+ persons) game is "free" (that player keeps all 7 cards), the second mulligan forces that player to put one (not two) card to the bottom of their library, the third mulligan forces that player to put two cards to the bottom of their library, and so on?

4

Yes. It's referring to the emphasized part below of rule 103.4:

To take a mulligan, a player shuffles the cards in their hand back into their library, draws a new hand of cards equal to their starting hand size, then puts a number of those cards equal to the number of times that player has taken a mulligan on the bottom of their library in any order.

That number is simply reduced by one.

1

Yes, that's exactly what that means, you can mulligan once without a hand size reduction.

The logic behind this is in part because one-on-one matches are generally best-of-three, but multiplayer games are usually much longer and because of this matches are usually played best-of-one. When the entire match is decided by a single game, a bad starting hand hits a lot harder and hurts your chances even more than it would if there are still up to 2 other games to decide the match. A 'free' mulligan in multiplayer games helps give players a better starting hand, blunting the impact of the entire match being decided by single games.

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