October 2016
Professor Brainstorm can have brainy and crazy zombies and has access to plenty of scientific zombies so it's easy to create a deck that takes advantage of their synergy. The deck below is one I built out of my limited collection. It is by no means optimized, though if some veterans care to make suggestions they would be greatly appreciated.
Tricks
4x Bungee Plumber
3x Beam Me Up
3x Lurch for Lunch
2x Rocket Science
3x Zombot's Wrath
3x The Chickening
Zombies
2x Chimney Sweep
4x Paparazzi Zombie
4x Zombot Drone Engineer
3x Brain Vendor
2x Electrician
1x Gentleman Zombie
2x Kite Flyer
2x Gadget Scientist
1x Portal Tecnician
Legends
1x Barrel of Deadbeards
1x Trickster
The strategy is simple. Use a combination of your zombies and tricks to gather card and board advantage as the game goes. Usually it's best to leave some brains free to play tricks rather than try to populate the board quickly.
November 2016
If you really want a good trick deck, use Immorticia instead. She is AMAZING. Her beastly typing contributes a lot more than the Crazy typing, although i still miss the Chickening a bit.
November 2016
Brainstorm is tons of fun and very powerful!
I'm rank 29, winning 75% of my games at least. I have one Trickster, but no other legendaries for the build. My suggestions are:
get rid of the Paparazzi. They just never amount to much, there are better cards
add a 4th Lurch for Lunch. You can never have too many bonus attacks
remove the Brain Vendors. They are not science zombies, and the stats are low enough that the card isn't that great overall.
(4) consider using fewer Drone Engineers. I use two. Admittedly, very good cards, not 100% sure that 2 is better than 3 or 4.
(5) consider adding one Fun Dead Raiser. There are times when Brainstorm does not have enough cards, and its death. Sometimes it sits in my hand, but I usually get around to using it.
craft a Gentleman Zombie if you don't have one. Rare, so crafting is affordable. Very handy, and much more useful than a Brain Vendor because the bonus brains are EVERY trick phase
(7) if you have a Mad Chemist, use it. Super rare, so too costly to craft.
(8) if you have a Valkyrie, use it. Another super rare, but possibly worth crafting. Valk + bonus attacks wins games
(9) other cards to consider to fill a slot that synergize well are: Newspaper zombie (once attack cranks to 5, you can bonus attack the next turn); (b) Abracadaver (the 3 bonus damage is really handy, and you can use bonus attacks to trigger it); (c) Kite Flyer -- you get a card, its a science zombie, and the stats aren't bad. I use one of each of these.
November 2016
Also, I use 3 Rocket Science not 2, and I'd probably use a 4th Beam Me Up if I had it. That said, it is fun to have some variety, and Newspaper Zombie and Abracadaver can both be very useful at times.
November 2016 - last edited November 2016
I've been using a Professor Brainstorm tricks deck for a couple of weeks now, and I love it. It really gives the Zombie Hero the advantage of going last. Here is the deck I use. Sorry, but I don't know all of the names of the cards, so all I have is the screenshot, which I took recently.
I use more tricks than you do, but looking at your deck, I see some changes I am going to make, including removing the "draw 2" cards and including some paparazzi zombie cards. I suggest considering the use of some space cadet zombies, as they can be really helpful in blocking some plant attacks and are also useful in filling empty lanes after the plants turn.
Since most of my zombies are science zombies, I also like to use the mad scientist zombie late in the game, when I hopefully have a couple science zombies in the field who would benefit from the free attack.
Lastly, I really like the gargantuas because they help to fill up the lanes that I would otherwise have to use other cards to fill.