No I did not know that I wasn't able to use them both. What is the reason behind it because I have never heard that. Thank you for taking a look at the deck and offering some advice.
Sycamore and Juniper share the same card text, but have different names. Normally, we are allowed 4 copies of any one card in a deck with exceptions to basic energy and ACE SPEC. cards (like Master Ball, you can only have 1 ACE SPEC. trainer card in a deck). The problem with that is with Sycamore and Juniper having different names, we would technically be allowed to have 8 copies of the same card text. For that reason they ruled that you can have only 4 copies of either card in your deck, but not both at the same time (e.g. 3 Sycamore & 1 Juniper, 4 Sycamore 4 Juniper, etc.).
I have a very successful build of Alakazam. It's fast, employs prize denial, and is very low energy . Based on the deck idea you have, here's what I would recommend testing with changes in bold (although because the build is different than mine, you'll need to tweak it further to suit your deck/play style):
Pokemon: 15
4 Alakazam-EX (FC)
4 M Alakazam-EX (FC)
2 Eevee (SM)
2 Espeon-GX (SM)
2 Shaymin-EX (RS)
1 Hoopa-EX (AO)
Trainers: 38
4 Alakazam Spirit Link (FC)
4 Ultra Ball
4 VS Seeker (RS)
4 Trainers Mail (RS)
4 Super Scoop Up
2 Devolution Spray (FC)
2 Mega Turbo
1 ACE SPEC. Scoop Up Cyclone
4 Dimension Valley (PF)
3 Lillie (SM)
1 Professor Sycamore or Professor Juniper
2 N (FC)
1 Brock's Grit (EV)
/Super Rod
2 Lysandre (AO)
Energy: 9
3 Mystery Energy
6 Psychic Energy
Pokemon:
4 Mega Alakazam EX
Having 4 Megas increases the likelihood of hitting one Turn 2. Evolving ASAP is important in this deck to start spreading damage counters. It also gives you more flexibility in using Devolution Spray and Super Scoop Up, allowing for more optimal play. With more evolutions, there are more opportunities to evolve to spread damage. Alakazam is also squishier than most EX's. In almost all of my games, I utilize all 4 copies of both the Mega and basic EX.
2 Shaymin EX
With Super Scoop Up, I have never needed more than 2 physical copies to prevent one from being prized in the early game. That and you are going to want all the room on the bench that you can get, between Hoopa, Alakazams (I recommend having 3 on the field when possible for using Devo Spray), and an Espeon GX.
2 Eevee
IMO the best starting pokemon is Alakazam. You can evolve Turn 2 and start hitting with the Mega to take 2HKOs in most cases. I would set up Espeon on the bench, Super Scoop Up the initial damaged Alakazam, and move up Espeon to really spread the damage after Alakazam started the initial spread(s). You will probably not need to set up 3 Espeon GX in a game, so it's safe to cut the numbers down to 2 Eevee and 2 Espeon GX.
Trainers:
4 Trainer's Mail
Having 4 copies helps get those crucial Spirit Links, Super Scoop Ups, Supporters, VS Seekers, etc., although early game, I typically prioritize getting 1 Spirit Link on the field. Alakazam, at least in my build, is about maneuverability and having an answer to your opponent every turn. 4 Trainer's Mail is crucial to this deck. I've tested with 3 and I always miss having a 4th.
4 VS Seeker
Like Trainer's Mail, a maximum count of this card increases the answers you have. It essentially gives you extra copies of your supporters, which is important in every deck (except for item lock decks where 3 is often an acceptable count).
4 Ultra Ball
Being able to get a turn 1 Hoopa/Shaymin/needed evolotions is really important for this deck to function successfully. Discarding can hurt, but it's worth it in the long-game.
4 Super Scoop Up
Alakazam is squishy, and picking up a heavily damaged mega, moving a benched Alakazam to active, only to put the spirit link down on the new active Alakazam and evolve it immediately back into a healthy one, spreading damage, and putting down an energy to attack (with Dimension Valley, or with Mega Turbo to hit 2 energy in one turn), is amazing. Denying your opponent a prize, punishing them with more damage, and then hitting even harder than you already were? It is definitely part of why I love the deck so much. That and you can pick up Hoopa and Shaymins (bench liability, or for reuse as needed).
2 Devolution Spray
Less than two isn't enough and sometimes 3 would be nice, but when I have 3 in the deck, I often run into them too early in the game and get stuck with harder-to-play hands because of it. 2 seems to be a sweet spot.
1 ACE SPEC. Scoop Up Cyclone OR Computer Search
I agree with you on your reasoning for using Master Ball - discarding cards can be painful for this deck. It's another reason why I maximize critical cards, so that if I do have to discard them, I know I have at least 1-3 more copies in my deck. However, having a guaranteed "Super Scoop Up" effect has won me games on its own. Likewise, I have tested with Computer Search. Each have their merits, and in some games I wish it was one or the other. Personally I really like Scoop Up Cyclone because it's a guaranteed prize denial and grants me an extra evolution damage spread.
0 Max Elixir, 2 Mega Turbo
With evolution being your primary means of damage spread, things can get a little volatile. Max Elixir isn't guaranteed to work, but Mega Turbo is. Also, if you Ultra Ball/Sycamore away some energy or if an Alakazam goes down, you have some already in the discard pile to fuel the card.
4 Dimension Valley
A lot of decks run stadium disruption, so this gives you another counter stadium as well as ensuring you don't miss a turn of attacking because you missed an energy. Having 4 helps cut down on the total energy needed in the deck.
1 Brock's Grit OR 1 Super Rod
I personally prefer Super Rod, because it doesn't use my supporter for the turn. I can see the merits of both, so it's up to your playstyle. Oh, and with Super Scoop Up, you shouldn't be having a ton a pokemon in the discard pile, but like I said, this is player preference.
3 Lillie, 1 Sycamore, 2 N (6 Draw Supporters)
I haven't gotten to playtest with Lillie yet, so I don't know what proper counts would be. In my own deck, I run
4 N, 2 Colress, 1 Sycamore (6 Draw Supporters). Just food for thought.
2 Lysandre
If I had the room, I'd run 3. With only 20 damage going to the active and 30 damage going to a benched pokemon, using Lysandre to pull up a more damaged pokemon equals easier, faster knockouts. Also spreading damage along the entire bench, instead of focusing on one pokemon when you evolve means that every pokemon on the field has a target on its back. This alone can make opponents misplay. It's harder to detect your strategy when you spread mostly evenly, instead of focusing on a target.
Energy: 9
3 Mystery Energy
This could be dependent on your meta and how many Enhanced Hammers are running around, but this meets the D-Valley 1 energy requirement AND takes CC off of the retreat cost. That's free retreat for Hoopa and Alakazams (I haven't checked Espeon's, but it will affect that card too for the better). It's part of the mobility of the deck, being able to hit and run to spread the damage out on your side, and assists in making sure everything runs smoothly.
6 Psychic Energy
This should be sufficient, but if you feel you need more, I wouldn't bump this up to more than 8.
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Obviously, this puts us 2 cards over. Since we added 2-2 Espeon GX, cuts will have to be made. The above build was built for speed in mind.
-1 Trainers Mail
-1 Sycamore/Devo Spray OR Mega Turbo/Dimension Valley
Trainer's Mail can function well enough with 3, and the above are what I would first consider cutting for the other slot, in that order.
Please note: I haven't had a chance to play with Sun & Moon trainer cards yet and have very little idea about the impact they will have on the deck. The edited decklist I gave you is based on my knowledge of how it plays from before SM came out. Cards like Lillie, Nest Ball, etc. will cause the deck to run differently, so keep that in mind if you test out the above deck list with further additions/substitutions.
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I really adore my Alakazam deck and have been playing it since Fates Collide released. It's a really cool, complex, and fun deck to play. The more you play it, the more strategies you find - it is so versatile. I hope my comments and suggestions help. Let me know if they work for you. I have yet to find a good partner for Alakazam, but Espeon GX has a good shot at being worth the 4 spots it takes up. Best of luck!