Hand #1: Booster Draft on the Play
Hands missing a color of mana are always risky, but I don’t mind this one because you can operate if you draw a Mountain but no Swamp. Three lands is better than two in a speculative hand because you won’t be as far behind if you draw your Swamp on turn 4 or 5.
If you draw a Swamp in your first two draw steps, this is an above-average hand. So long as you find any land in your first three draw steps, it will be functional and Brazen Buccaneers will help smooth your draw.
Hand #2: Booster Draft on the Draw
This is a bit slow. It’s bad to have only two lands with three expensive cards and no cheap creature. But you have one cheap card—Walk the Plank—that can help protect you. And Treasure Map, while slow, can help you hit your land drops and offers a plan for winning the game. You may lose to your opponent’s best draws, but this hand has a realistic plan for winning the game, and you should keep.
Hand #3: Booster Draft on the Draw
Keeping a 7-card, 1-land hand in Limited is an advanced move. If you mulliganed these every time, you’d only be making a mistake a small percentage of the time. But this hand has everything you look for in a keep. It has two spells that you can cast for 1 mana—Skittering Heartstopper and Skulduggery. It also has multiple above-par 2-drops in Wanted Scoundrels and Bloodcrazed Paladin. Importantly, it has little risk of color problems (even if it is a 2-color deck).
Hand #4: Sealed Deck on the Play
One flaw with this hand is that you have two expensive spells with only two lands. Even with only two lands, I would keep if I had both my colors of mana. But being unable to deploy my 2-drops before finding a Forest is a deal-breaker.
The funny thing is that this is a real opening hand that I had recently, and I did decide to keep it. My deck was mostly green with 11 Forests, so if I did find a land it was overwhelmingly likely to be a source of green mana. Even there, the hand is borderline. In a normal deck with 9 Forests and 8 Mountains, for example, you should mulligan for sure.
Hand #5: Sealed Deck on the Draw
You’ve put Pillar of Origins in your deck to name Pirate. Assume that you have at least 13 Pirates, and that many of them are expensive or have demanding color requirements.
If you’ve chosen to put Pillar of Origins in your deck, hopefully it’s a fairly good card to play on turn 2. This is a weak hand, but it’s one where all of the pieces are in place. You can spend your mana adding to the board in the early turns, and you have a powerful removal spell for the late game. (I say late game because you’ll have to draw a Swamp before you can cast it).
I could envision mulliganing this hand if I had a hyper-aggressive deck, but the presence of Pillar of Origins and the fact that it’s Sealed Deck rather than Booster Draft indicate that that’s not the case. I recommend a keep to avoid the resource disadvantage.