I agree in that I also prefer playing with Zombies.
However, I can't fully agree that they are imbalanced as I haven't found definitive proof of that. The fact that I got destroyed by 4 different plant players in a row playing with different plant avatars against the zombie deck that I've been very successfully playing for diamond and taco league tells me that plants can most certainly counter a good zombie deck when properly played.
Something I could agree with is that zombies are easier to play due to the fact that they play tricks last. With plants there is more need to know what kind of things the zombie player is capable of doing and in having a deck built with the tools to play around them effectively.
For example, that weed spray trick. If you know the zombie player might have that trick, then you avoid over-committing to the board and build your plant deck to assume that you might play a zombie player with that card (and the chickening). That means looking to add buffs to your deck and using them when you see that the zombie player could potentially play it.
By the way, every single card game has cards like this and situations where it feels like "they played this card and there was nothing I could do about it". What this usually means is that you need to play differently so that you don't get into a state where that card destroys your game. There is also the rock/paper/scissors effect where you can build a deck that is specialized to be strong in certain popular matchups but you assume that if you go against a deck with a specific card your deck is just not equipped to deal with it and you just accept the loss. If you see that zombies are using that card a lot, then you build your own deck to avoid being wrecked by it.
Anyway, my recommendation is to play zombies as much as you can, since you obviously feel they are superior. If you continue winning then that is great for you, but at some point you will reach higher level players that will start to beat you and that's the easiest way to learn the weaknesses of zombies and the strengths of plants.
As for Arm wrestler, I consider it a very solid card. It could definitely be nerfed to a 1/2 as GrinningRuiner suggested but I'm not sure it's actually necessary. Time will tell.
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Zombies have the Hot Dog Imp which is strikethrough, Team Up is easily countered by FRENZY and cards like the chicken stampede and Weed Spray, splash seems good but splash plants like the Lightning Reed are super rare. Freezing is good, but even Brain Freeze can do that. The only special thing plants have is Team Up. But even if you are using Wall-Nuts and defensive plants, the zombies also have the Deadly power to ignore all of it.
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In this paragraph you make it sound like all zombie decks have access to these cards all the time and that's just not true. Yes, there will be matchups where the zombie player has exactly the right counter to the play you made but that's how all card games work and that works out exactly for plants too. You can have the counter to their cards just like them. They played the hot dog imp? you can move it, buff your plants, do a bonus attack, set its stength to 0, freeze it, destroy it, etc.. and there is nothing the zombie player can do about any of those (except the buff perhaps). One of the best plays against a deadly zombie is to set their attack to 0, and actually, one of the best strategies is to just leave the zombies with lanes full of 0 strength zombies. A lot of players don't realize at first just how disruptive it is because you can't replace characters and it is far more problematic for zombies because they don't have team up.
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I don't have an iceberg lettuce and even if I did, I would have to draw THAT, AND Snowdrop to stop the Arm Wrestler??? Two cards for one??
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This is actually a combo that gets you a 3/4 and destroys one of their creatures. It's 2 for 2 (you play and keep the flower 1 for 1, then you play the .letucce on their creature and it is killed by the flower without taking damage, 1 for 1). While it's not card advantage, having a 3/4 on turn 2 is very powerful and will most likely turn into card advantage or get in for a lot of damage unless they have something similarly powerful to counter it with.