Building on the Svetlana decks in the post above, this is
my current tournament deck. I don't like it. It is a
top 10% deck, but it is not as overpowering as other Heracles decks. [I've tried edit as I wrote this, but I'm too tired to do a full proofread right now. Sorry: maybe later.]

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First, the tournament meta has changed: except for Heracles decks, most Structure-intensive decks have disappeared. Slow Righteous with two to four structures are much less common. Bacon and Eggs (Utopia Beacon and Earthquake Generator) is nearly dead. Wallstall has stalled. When I first got Heracles, my super-fast Siege was devastating to many different decks and I did very well with Cannon Walker and Heli-Duster.
Things have changed. I feel like there are only five types of decks:
- Heracles
- Strike that is primarily based on Assault cards (rather than Structure cards like Earthquake Generator)
- Sycophant (not Grim Specter)
- Noob decks
- "Other"
Some of the "other" decks are excellent, but that is often because the player who designed it and is playing it is an excellent player. Let's be honest: the first three deck archetypes do not require any deck-building skills and they only require minimal skill to choose which of three cards to play on any given turn. "Should I play Sycophant or Sycophant or Full Power?" Many of the decks in the "other" category are too sophisticated for most players, so they do not turn into mainstream decks; furthermore, nearly all of the good decks in the "other" category require serious War Bonds. My point: when you are designing your tournament deck, if you don't account for the "other" decks, you will not consistently break into the top 10%.
But this thread is about Heracles decks, so let's return to explicitly talking about the deck above, why I am using it, and why I don't like it.
Because of the dramatic shift away from Structures, I have less Siege. Against other Heracles decks, however, my fast Siege is often my advantage. Killing Mobile Base is often devastating to enemy Heracles, but because of Refresh, I must have two activated Siege cards that hit the base in the same turn. This can be difficult when multiple structures are in play. When fighting Heracles, I sometimes wish I had more Siege, but Cannon Walker and Heli-Duster are weak against almost every other common deck, so this is the balance I have settled for right now. Also, some games I like having two Heli-Duster and one Cannon Walker, and other games, I wish it were the other way around. It's frustrating.
Longshot is a bit of a strange card in this deck. In a significant number of games (more than half?), I hold Longshot and don't play it until the end of the game--when it is basically unnecessary because I have already won. I have built Heracles decks without Longshot and used a Raider Assault card or Structure instead, and those decks have been successful, too. On the other hand, in many games, Longshot makes it impossible for me to lose. When playing against Heracles, if I can keep the enemy Rally structures under control, then my opponent cannot kill Longshot, and I slowly win the game (Disease in the enemy deck can neutralize Longshot, though). Against Strike decks, an early Longshot can give me the edge and force my opponent to play Iron Maiden early in the game. But I might be biased towards Longshot: I was one of the first players to get it, I won a lot of games during that time, and I love the card. I might be overestimating Longshot's value, so especially if you are using Command Center (like I am!), you might want to look for a Raider Assault card (Night Ranger?).
This is a good time to mention a major reason my Heracles deck is so different than other Heracles decks: I don't own many of the typical Heracles cards. I have purchased a ton of Homeworld packs, but I don't have Mobile Base. I don't own Pantheon or Pantheon Shard. I don't have Adamantite Armor (which actually look like a good card for Heracles) or Night Ranger. So I have an approach to Heracles.
I have to admit that I irrationally hate Kilgore. I am always looking for something other than Kilgore, but it is just too versatile to ignore. Against Dracorex or Dalia, he can still attack (Dalia takes him to zero, but Svetlana Rally 1, then maybe add Burst 2); against Armored (Thunder Crag!) and Protect, he can Pierce; and against Refresh/Heal, Disease is great. Wait 2 is annoying, but Health 6 is good against Strike.
Teslatank is necessary to deal with Sycophant. Swipe and Enfeeble give me a chance to beat Sycophant. Wait 2 is annoying and Health 4 is a problem against Strike, but Armored 1 is good against Strike Decks. If Teslatank is in front of Ravenous Dredge and Teslatank has Protect 1, then Ravenous Dredge cannot damage and Poison Teslatank.

The primary reason for this card is Sycophant. Teslatank can wipe out a ton of Sycophants, but only if it is activated. An activated Command Center is strong against Sycophant, but it almost impossible for one to survive long enough to activate. So far, Obliterator has been very useful against Sycophant, and, even better, it has been useful in all types of situations. Strike decks usually have cards with Attack 1, so when their Attack 1 becomes Attack -1, Rally isn't very useful (e.g., Ravenous Dredge and Mortar Bunker). It doesn't have Intercept (like Longshot), but it has Health 9 and Evade, so at worst, it soaks up a lot of damage and gives me time to activate other cards. In the long run, I'm not sure that this card will stay in the deck, but for now, it is useful.
Because of Obliterator and Longshot, I am considering Acropolis. I don't like the longer wait or the lower health, but I do like the extra attack for Longshot and the extra counter damage against Sycophant.
This deck is relatively weak against Strike, which is a shame. The low Health and Attack of Heli-Duster and Cannon Walker can be a major problem. In tournaments with more strike, I might add Maximum Damage, Prism, and/or Mortar Bunker, but the Fast Siege aspect of the deck means it will always struggle against Strike more than other Heracles decks struggle against strike.
Against many other Heracles decks, I have the advantage, but some Heracles decks nearly always kill me. My main advantage against other Heracles is Siege, but if they use Impulse Walker, then I lose that advantage and I usually die. Switching to Cannon Walker is not great, however, because Heli-Duster has a chance of Flying over Swipe and damaging or killing Heracles. Cannon Walker will always get hit but can survive one non-Rally Kilgore Burst or one non-Rally Heracles Swipe.
If I want to dramatically change this deck without using War Bonds, I think my only two options are Mobile Base and Undertaker. Every other card I think might improve the deck requires War Bonds. Maybe that will change with the mystery 90-card set that will allegedly be released soon, but right now, I believe that Heracles needs multiple War Bond cards to regularly break the Top 5% barrier. (I do have Svetlana, which is a War Bond card--I won some War Bonds during the time when I had Longshot and no one else did; now you know why I am so attacked to Longshot!)