It would be possible to show the choices for sure, but this would actually nerf the card. From seeing what your opponent's illusion cards were, YOU now know that YOUR OPPONENT now knows that you DON'T have these cards in your deck.
Sure, this is no big deal most of the time, but can impact the game in some scenarios. For instance, when it comes to secret shenanigans. Imagine playing hunter against a priest who plays Cuirous Glimmerroot, and one of the illusions is Explosive Trap. So your opponent knows that you are definitely not running that card.
As it is: You don't know about that, and you might play your Snake Trap while your opponent has a bunch of 2 health minions, basically bluffing an Explosive Trap. The priest knows that it is a bluff, and can go face (well, unlikely as priest, but whatever. There are better examples for sure).
If you instead knew what your opponent's illusions have been, you'd know that the bluff won't have any chance to succeed and probably would play something else.
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We understand completely what you're saying, but it's just not correct.
This post I made a few minutes ago points to a public data set that makes absolutely clear that across thousands of players the matchmaking is random with respect to what is in your deck.
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In my post above, I offered you a source of a huge amount of publicly available data that says you're not right about this. Have you looked at it yet?
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They have stated that they try to match newer players against each other, but other than that the third on your list is certainly not the case. How do I know? Easy. If you visit HSReplay's Meta Matchups tab, you can mouse over each archetype matchup in their entire database and see both popularity percentages and raw numbers of times those matchups have occurred in their entire data set.
I'll cut to the chase so you don't have to: The percentage matchups for each archetype closely track the popularity of each opponent archetype. Or, to put it another way, they are not manipulating your opponents based on what is in your deck.
It's unlikely there's a more comprehensive data set out there for looking at these numbers. Fortunately, HSReplay.net has put it all out there for anyone to see who cares enough to look.
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I sympathize with your frustration with the confirmation bias people bring to these threads, but matchmaking systems are a particularly interesting game design problem that companies like Blizzard tend to talk about very sparingly (probably to avoid people trying to game their systems.)
It's a legitimate topic for discussion, though I'd love to get away from the use of loaded terms like "rigged."
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If the different methodology is to exclude mobile revenue, sure.
Regardless, Hearthstone is a tremendous moneymaker for Blizzard at any of these revenue levels. The team is small, the game is technically simple, and the art costs are relatively quite low compared to any other Blizzard game.
However, I do know a lot of people who used to play on PC who have migrated to playing entirely on mobile because their mobile implementation is so good and the short game length works well with how people play mobile games.
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People just complain that it's "autopilot" because it can be very frustrating to lose to a well-played combo deck. They don't get to see the hours of awful games that led up to that point for their priest opponent. :)
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This is the deck I have been running with. I have not been feeling weak against aggro in general, though there are some games that I just straight-up lose. Trick is to mulligan heavily for early AOE and card draw vs. paladin, rogue, druid (just in case), and, to a lesser extent, warlock. Key cards for this are Spirit Lash, Duskbreaker, Dragonfire Potion, Kazakus (which can give you both AOE and card draw), Netherspite Historian (to fish for Duskbreaker), Primordial Drake, and Psychic Scream.
Sometimes aggro decks just walk all over me, but just as often, it feels like I can come up with an answer for everything they do and they just get nowhere while I chip away at them.
Edit: Pint-Size Potion and Shadow Word: Horror are a great combo, but I find it's easier just to run some heavier AOE that doesn't require having both cards, particularly since Pint-Size Potion doesn't seem that handy on its own. But, I haven't spent a lot of time working out how best to use them.
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The single best thing you can do to accelerate your climb to legend is start playing very carefully. Work on improving the little mistakes you make.
Beyond that, play a relatively fast deck so you can play a lot of games quickly.
Finally, if the idea going around is correct that matchmaking takes either your class or deck into account to match you against opponents who are predicted to average a 50% win rate against you (and this is far from proven), you might find it helpful to pick a deck with an unusually high skill cap and master it, since such a matchmaking system would best reward people who far exceed average performance with their decks.