Wizards of the Coast have implemented a brand new change to the mulligan rules today for Magic: The Gathering that will go across all forms gameplay. The news broke this morning as part of the new Core Set 2020 as they're introducing it to all competitive formats. They originally tested this at the Mythic Championship II in London as well as on Magic Online. Here is the new rule, per WotC.
103.4. Each player draws a number of cards equal to their starting hand size, which is normally seven. (Some effects can modify a player's starting hand size.) A player who is dissatisfied with their initial hand may take a mulligan. First, the starting player declares whether they will take a mulligan. Then each other player in turn order does the same. Once each player has made a declaration, all players who decided to take mulligans do so at the same time. 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. Once a player chooses not to take a mulligan, the remaining cards become that player's opening hand, and that player may not take any further mulligans. This process is then repeated until no player takes a mulligan. A player can take mulligans until their opening hand would be zero cards.
The rule sounds simple enough, right? It's a simple change with the slight variation that you get to pick which cards you don't want from your mulligan go to the bottom of the deck rather than just drawing six cards if you take a mulligan. Some would argue it gives you the advantage to throw out useless cards you don't need right away, but you're still at a disadvantage of not starting with seven. We'll see how the rule plays out in the tournaments to come.