Looking back at the original Puzzle Quest, it worked the same way a lot of games with a luck element did - Magic: The Gathering, for example. Basically, the player was able to minimize the effects of luck on their overall win/loss rate through:
Skill
Abilities
Progression
Skill is basically making good matches and using abilities wisely.
Abilities let you deal damage (giving bad luck less time to take hold) and manipulate events in your favor (board shake, etc.)
Progression gave you more resources (health, damage, starting mana, etc.) so that you could get better, go back, and beat a fight youi couldn’t before, as in other RPG’s.
This is all obvious stuff, but when you look at Marvel Puzzle Quest, especially in the state it is now, the advantages of progression have been seriously reduced by scaling. In PvP, you really only get the progression advantage once you complete a star transition with at least half a dozen key characters maxed, and even then, throughout the climb, you’re rarely so much better than your opponents that you have a distinct advantage. When you throw into the mix the whole “AI on defense” system and the fact that victory + how much damage you take during that victory has an important value in the metagame, progression helps to mitigate luck, but only in broad strokes and not as much as you’d expect from the “RPG” genre.
And then there’s abilities. Unfortunately, a LOT of the ability nerfs throughout MPQ’s history have been to the very things that mitigate the luck factor the most. Infinite loop combos, abilities that generate AP to fuel other abilities, board manipulation, and to a lesser extent, board shake. All of these things cut way back on the effect of luck, and there’s been a conscious effort to push back on that by the designers over the game’s two year history, in the name of maintaining challenge and making difficulty calibration easier. Or, as cynics call it, selling more health packs.
MPQ also has boosts, which again help mitigate the effects of luck by speeding up match damage or AP generation, and those got cut back too, in the same way as abilities and for the same reasons.
And on top of it all, this is a freemium game, and there’s ample evidence that luck and purchases go hand in hand. The classic example is when they removed guaranteed cover rarities from token packs and token sales went up, not down. Gambling sinks hooks into the human brain.
So there’s lots of stuff they could do - lots of stuff other games have done - but it seems that, consciously or subconsiously, the design goal is to push the luck factor of the game as far as they can without completely alienating an admittedly already addicted playerbase. 4* DDQ? Luck plus progression, and with token pulls, progression in this case also has some luck to it. Galactus? A lot of luck in rounds 5-6, although from what I read, two abiliities (Prof X and Hulk) made luck less of an issue in rounds 7-8.