I've set a line as to what kind of hands I want to keep with Tron. Never keep a hand that doesn't have two guaranteed Tron pieces (an Urza land plus a way to get another one). This is actually true for any linear Modern/Legacy deck, as most of them have established do's and don'ts, because they are always trying to assemble x pieces no matter what’s in front of them.
How has the new mulligan rule changed that? Not at all. In fact, you should mulligan even more aggressively.
What gets trickier is that all the other non-linear decks—mostly in Standard, Limited, and grindy Eternal decks such as Jund, Grixis, and Jeskai—look at disrupting their opponents and playing a long game instead of accomplishing one simple goal.
I’ve separated my explanations by format rather than strategy because it’s easy to generalize the hand an average deck in these formats should be mulligan. They are ranked from formats in which you should mulligan the most to formats in which you should mulligan the least.
Modern rewards proactive strategies. The card pool is so deep that reactive strategies are hard to build because you need the right answer for the right deck at all times, and that’s hard to accomplish when you face 10 different decks in a tournament.
Let’s examine this hand. Against an unknown opponent playing a creature strategy, this would be a great hand, but what if they are playing Ad Nauseam or another creatureless deck? You could lose the game instantly based on your mulligan decision. I’m not saying you should mulligan the hand above—in fact, you should never do that unless you have a reason to think your opponent is playing a creatureless strategy—that’s just my brief take on why I think reactive decks are bad in Modern. If you’re one of the brave souls who decides to play such a deck, I suggest you read the Standard and Limited sections coming next week.
Real Modern talk now. You should absolutely mulligan this hand, for two reasons:
There are so many broken cards in Modern that make a huge difference when they are in your opening hand, drastically improving your odds to win a game. Mox Opal is one of the them, and this hand doesn't have it.
The risk of going down to 6 cards is highly mitigated by the addition of the scry rule, especially in a format where card advantage is rarely the path to victory. You're looking to assemble combos or find specific cards, rather than play a 12-turn game and trade resources.
TL;DR: Play proactive strategies with broken cards, and mulligan aggressively to find said broken cards. Profit.
Legacy is pretty similar to Modern in terms of the number of decks played and broken cards available. But reactive decks are much better because Force of Will is a generic answer to anything. The games are more often decided by card advantage wars since the fair and grindy decks are more popular.
The land mix here could be anything, I’m not trying to represent a particular blue deck—I just want to show the power of Brainstorm. You should never mulligan this hand—the card selection is so good in Legacy that trying to mulligan hands to find a particular card isn't worth it. You should only mulligan when your hand doesn't allow you to play Magic, i.e., one without lands or spells. If you replace Brainstorm with another Ponder in the hand shown above, then I would need to know what blue deck you are playing because there’s a chance 4 lands is too many. Delver would mulligan that hand, Shardless BUG might not.
Some other decks, such as Lands and Dredge, instead act as Modern decks, aggressively mulliganing into their most broken cards (Exploration and Lion’s Eye Diamond) because they couldn't care less about card advantage—they just need to get their engines going.
TL;DR: Play Brainstorm and rarely take mulligans, or play broken cards and mulligan aggressively to find them.
What about my 6-card hand?
You should evaluate it entirely differently than what I explained above. In fact, you should start being greedy and keep 1-landers and such because not only does the scry help, but going down to 5 cards now has a huge cost. Even though your deck might not count card advantage at all, getting a functioning 5-card hand starts getting unlikely and it snowballs the more mulligans you take.
As a general idea, you should mulligan any 7-card hand that is mediocre to try and make it good. Keep any 6-card hand that is mediocre or has a chance to be good with your scry.
Standard and Limited
Part 2, including Standard and Limited, will be posted next week—this second part includes lots of "DON’T MULLIGAN THAT HAND!"