Morning!
I think the aspect of drawing good Hands can be broke down to 4 major factors.
1. Don´t get blinded while Deck construction. Cards may be awesome. Boi. Cherrybomb almost always trades 2 for 1 and oftentimes even 3 for 1! Better include 4! Nah. Cards may be awesome and yes, you might want to play them and yes they are obviously good for the previously stated reason. But if you draw poor starthands it is often a reason of poor Deckbuilding. "Poor" might be a harsh word but almost every Deck has a ways to get "better".
2. Don´t get blinded while re-drawing/taking mulligan. Your Deck is obviously awesome (of course it is! you build it :D!) so your cards must be too. But not every Card is awesome in the first 6 Turns. And not every card is equally good against every opponent. Prepare your hand against certain foes by discarding everything that MIGHT be bad against that guy (along with the cards that are to expensive to be useful any time soon) and success will follow. Now this requires practise and experience but trying to be critical with your own decisions will help you a LOT
3. Now this one might be a bit less "Obvious" and maybe even a bit confusing; Do not overcommit/panic and "suggest" perfection and control; I can asure you that ultimate league players do not have secret buffs on luck. First of all you can not know if its "perfect", "good" or "just enough" to beat you. It is just your assumption.
Now the more complex part of decision making that "suggests" perfection is to never ever overcommit if its not absolutely needed. "I have to remove that NOW because it will kill me because he has the perfect hand"/"just to make sure ill double tap this gus to death". Nah. your opponent might be able to pull up a nice trick from his sleeve to safe his dude if you don´t but then again he wasted a card on it. Card advantage is crucial so if he gets his guy to survive a trade somehow your can usually still double tap him next round without much of a loss. You took the risk to loose a trade and did because he used a trick. Then you used your trick to kill the guy in the next round. The card advantage is the same but if you had won the "risky" trade it would have been better. Taking calculated risks and when to take them is important to improve your own game.
4. Get lucky and don´t be afraid to try. Now this might sound stupid. But actually it is part of the "calculated" risks part. Just be confidant you will draw "better" when you mulligan a card. "okay" is just not "good". If you have one good card for your early game in hand you can always try to get better on the rest. If you build your deck properly its unlikely you will draw poorly so take the risk to aim for perfection.
In General just practise redrawing. It is foolish to assume a hand can´t get better and you usually can find some improvement if you think hard enough and consider your opponents hero. Be confidant in your decision making, do not assume your opponent to be super lucky (and play accordingly), do not be afraid of taking risks. On average this should help you a lot.
(of COURSE you might LOOSE a few games because you where a little TOO "on point" with taking risks and assumptions but on average this will probably help you)
Stay sunny
