Gameplan
The general gameplan in this deck is to start dropping creatures as quickly as you can. Through Edgar's eminence ability you will rapidly generate a huge board of vampires and swarm out your opponents. With the large board state that you generate, you want to start pressuring your opponents and make them feel the wrath of your blood-sucking army (who will progressively get stronger with +1/+1 counters or tribal buffs). Additionally, casting Edgar as soon as you can is usually a good plan (granted you have some sort of a board presence). The sheer amount of power he adds to your board can be very overwhelming for opponents and the best part is you can swing with him the turn you play him.
While the overall strategy of this deck may sound simple to execute, it can be quite tough to accomplish because playing aggro in EDH isn't a trivial task. Aggro gets tough to play in EDH because you are generally playing against 3 other players, each of whom have 40 life. Doing 120 points of damage with tiny vampires can be quite a daunting task, however we have a bunch of cards that collectively drain our opponents to make this easier. These are some of the key cards that help us solidify our victory:
Purphoros, God of the Forge - Probably one of the best cards to run in EDH when you want to amass an army of creatures. This card is especially powerful in Edgar because each creature we play nets us another 1/1. This means that at minimum, each time you play a creature you're doing 4 damage to each of your opponents before even swinging for combat.
Impact Tremors - Similar to Purphoros, Impact Tremors allows us to ping each of our opponents, every time a creature ETB's on our side. It also only costs , so we can drop it earlier in the game.
Throne of the God-Pharaoh - Since our general strategy is to play tons of vampires and swing with them, most of the time we will have a board state with many tapped creatures. Throne lets us ping our opponents once again after combat. This card can get out of hand really quick when you start swinging with 5+ vampires every turn.
Malakir Bloodwitch - Malakir Bloodwitch is a great way to mass ping each of our opponents. Since our main goal is to play swarms of Vampires the life loss that Malakir Bloodwitch is always very significant; we also get to gain a crap ton of life off of her ETB. Additionally, this is something we can recur so we can trigger this over and over again.
Sanctum Seeker - This vampire from Ixalan really works well this the overall strategy of this deck. Our main goal is to turn our vampires sideways and Sanctum Seeker really starts to hurt once you have amassed a huge army. It also gains us a ton of life, which is a nice added bonus.
Twilight Prophet - This card does a great job of pinging all of our opponents, gains us life and draws us a card as well.
In addition to mass pinging our opponents we want to be able to protect our board state from wrath effects. Due to this, we run cards that make our board resilient or let us recur our creatures. I'll further expand on these cards below in the "Single Card Discussion" section under the "Interaction" section. In general, this deck doesn't run any traditional "combos" but uses synergistic cards to make an aggro strategy more approachable in a multiplayer environment.
Match Ups
Like any EDH deck, this deck has bad match ups and it's important to know which match ups will give you grief. Assessing who is a threat to you at the current point in the game is a very important skill that many EDH players lack. There are a couple of different archetypes that you will come across and this is generally how you want to play against them. Below are how you should usually prioritize your targets against some common EDH archetypes. (I bolded "usually" because in EDH there are always varying game states and your target priority can greatly change)
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Control/Stax/Pillowfort - These are the players who are normally playing a plethora of board wipes; the bane of our existence. The quicker you take out these targets, the less likely you are to be on the receiving end of a wrath effect, thus losing your entire board state. Save your interaction spells (especially your protection spells) for these players.
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Aggro - Having another aggro deck at the table can lead to some very interesting political situations when playing this deck. All of it really depends on who is the aggressor. If you start as the aggressor, try to close out the game quickly by taking out the other aggro player(s) and then finishing off the rest. GO HARD, OR GO HOME. (Haste outlets are very useful in these match ups) If you aren't the aggressor try to politically convince the other players that aggro player X is the problem and that they should direct their resources towards them. You run a decent amount of interaction in this deck, you can use those pieces politically to create temporary alliances. Once the other aggro player(s) have been eliminated, swarm out your vampires and go for the kill.
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Reanimator/Voltron - These decks generally aren't too much of an issue because they rely on a couple of BIG creatures rather than many little creatures. Because we are running many little creatures, most of them expendable. Additionally, the longer our creatures stay on the board, usually the larger they get through the various pump effects available to us in the deck. Because of this, sometimes we can easily contest the large creatures these types of deck throw at us. Additionally, we run a fair amount of single target removal, which can greatly hose these strategies.