How does the "shuffle back" mechanic work?

Every turn you can "shuffle back" (or mulligan) up to 2 cards from your hands to your deck and draw another card for each. Actually, it put them aside, which means you won't see it again, before every other card is seen.

Since in Steamworld quest you've got a party of 3 with 8 cards each, I was wondering if the shuffle count only the character who is shuffling (1 in 8 you won't see for a while) or all the team (1 in 24).

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