In my first part on how to mulligan, I covered Eternal formats, where I supported aggressive mulligans, mainly because decks are more streamlined and powerful, and games center less around card advantage.
I emphasized that Standard and Limited mulligan philosophy should be thought of differently, because the two are in totally different worlds.
Games of Standard usually don’t end quickly—some cards are powerful, but they either take over later in the game or can be answered by almost any deck. This leads to much more grindy games where every single card counts and it’s common that someone finishes the game using their last card in hand. The latter makes your mulligan decisions much more significant, because the one card you are giving up could end up costing you the entire game.
There are many things that can go wrong with this hand, especially if you face an aggressive start or if you are on the draw. Either way, you should keep it against an unknown opponent. There are more unstable 6-card hands than scenarios where you lose with this hand, because your deck has way too many cards that are only good in certain scenarios. Gideon, Secure the Wastes, Languish and your mediocre mana base can easily make for unplayable hands, so you should keep lands, spells, and anything that can curve reasonably—you don’t have the luxury to find specific cards.
The less linear your deck is, the more you should keep hands like that. A simple rule is that 2-4 lands and spells on curve (early interaction or threats) are snap-keeps. When you aren't linear and trying to play long games won by card advantage, being down one card can lose you the game, especially in a deck full of answers where you might draw too many copies of the wrong kind.
This could be any mix of three spells in this spot and you would have to mulligan. Every land you draw from this point on is technically dead, because you’ll never get to use it—even the fourth is a stretch since all you get for 4 mana is Gryff’s Boon’s graveyard ability.
White Weenie is the most linear deck in Standard, so you should mulligan with it a little bit like Modern linear decks, except you can’t really afford to find your broken cards like Thalia’s Lieutenant. What you can afford to do is curve and make sure not to flood. You can do that because the requirement for a hand to function is any 2 lands (because you are one color and don’t have colorless lands), and the rest of the cards can be anything, since they can all fit into your curve and can all be cast off of 2 or 3 lands.
Draft and Sealed are treated the same here—more often than not, Draft decks are more streamlined than Sealed ones, but the difference isn’t big enough that it should be treated like a Constructed deck by any means.
A Limited deck’s goal is almost always to grind your opponent down to their last card. Decks trying to accomplish something different, such as getting their opponent to zero as fast as possible without interacting, are in the minority.
You should always acknowledge how greedy your deck is before starting to play with it. If you are playing a deck with a 7-drop and are splashing for 2 cards, and your opening hand contains a 3-drop, 4-mana draw spell and 5 lands (including all your colors), you should keep it. Just like the WB Control example above, there are too many scenarios where you can get cards in the wrong order or where you’re missing a color. You should appreciate having access to all your colors and having the mana you need for your 7-drop in your opening hand. Now, all that can go wrong if your opponent has too aggressive a draw.
If the same deck has this kind of opening hand: 2-drop, 2-drop, 2-drop, land, land, 7-drop, and splashed card, there’s a high chance it’s going to be awful, mostly because this deck isn't designed to be aggressive, so having your three 2-drops in hand isn't going to get you very far—you’re nowhere close to casting this 7-drop and you can’t even cast your splashed card.
One argument might be, "look, this hand is kind of like a mulligan to 5, since your 7-drop and splashed card don't do anything in that hand." While this can be true, you should be careful using that logic, since it isn't always. The first hand with 5 lands, even though it can’t actually cast the 7-drop, is much closer and so you shouldn't ignore the card.
Now what if you are playing a deck looking to ignore long-term card advantage and instead get your opponent’s life total to zero? The first step is to be aware of how long of a game your deck can play—how much removal does it have, and do you have big creatures or not? This will tell you how much you can afford to try to interact with the other player, or if you should abandon that plan and curve them out recklessly.
Shadows over Innistrad’s red aggressive decks can be that way between Uncaged Fury, Rush of Adrenaline, and Magmatic Chasm, you should not want to play a long game. Instead, you should push through as much damage as possible so that you can finish them with a bunch of pump spells. Any hand that can’t deal early damage should be sent back—a luxury that requires good deck building. Make sure you've included enough early creatures that you don't have to mulligan too much to find them.
I hope these baselines help you make better decisions in the future. Comment with your hard mulligan decisions you’ve been struggling with—it’d be a pleasure to answer them to the best of my knowledge!