When I decide to throw away my hand and use a mulligan, should I simply draw a new hand from the library or shuffle my thrown hand into the library before redrawing? I'm mostly interested in magic-the-gathering mulligan rules, but I believe a "mulligan" isn't system-specific; I'd accept a well-sourced system-agnostic answer as well.
In Magic you always shuffle your hand into your library then draw a new hand.
103.4. [...] To take a mulligan, a player shuffles his or her hand back into his or her library, then draws a new hand of one fewer cards than he or she had before. [...]