HAT, stands for Hand Artifact Traptrix. This deck was a wildly successful deck in the 2014 format and it dominated a lot of the top competition, so much so that the format would later come to be known as HAT Format. The deck, HAT, is broken down into 3 parts.
Hand, Fire Hand, and Ice Hand. Fire Hand is a 1600 ATK monster with an effect that allows you to destroy a face-up monster when its destroyed by your opponent's card, and then it lets you special summon an Ice Hand from the deck. Ice Hand's effect allows you to destroy a face-up Spell or Trap your opponent controls when it is destroyed by your opponent's card, and then it allows you to special summon a Fire Hand from the deck. The Hands in the deck allows the player to have a consistent way to break down the opponent's board, effectively punishing them for controlling a face-up monster on your turn. As neither of these effects have a once per turn restriction, you could use them over and over until you've wiped your opponent's field.
The next section is the Artifact lineup. The Artifacts are a series of monster cards that can be set in the Spell and Trap card zones, and they special summon themselves from the GraveYard when destroyed as well as apply an effect to give you additional advantage. In the case of HAT, the Artifacts that would be ran are Artifact Beagalltach, Artifact Moralltach, and the trap card, Artifact Sanctum. Artifact Beagalltach was used in the more combo oriented version of the deck, the control versions much like this one would just run the Moralltach and the Sanctums. Starting off with Artifact Moralltach, its effect allows you to summon it from your GraveYard when it is destroyed in your Spell and Trap card zone. If Moralltach was summoned on your opponent's turn, it allows you to destroy one face up card they control. Beagalltach's effect allows you to destroy a card in your Spell and Trap card zone when its summoned, this allows you to destroy your Moralltach and get it back as a monster to easily make the Rank 5 XYZ monster, Artifact Durendal. Artifact Sanctum's effect lets you summon an Artifact monster from your deck. Between the 3 copies of Artifact Sanctum, and the 3 copies of Artifact Moralltach, you are effectively playing 6 copies of Moralltach, which allowed the deck to maintain a lot of consistency.
Finally, the Traptrix. Traptrix are a series of cards that have different effects that revolve around the Hole trap cards, such as Trap Hole, Bottomless Trap Hole and so on. HAT would run 2 of the Traptrix, that being Traptrix Dionaea, and Traptrix Myrmeleo. Dionaea when normal summoned allows you to add a Hole trap card from your deck to your hand, but when it's special summoned, it allows you to destroy a Spell or Trap card your opponent controls. Myrmeleo when Normal Summoned allows you to Special Summon a Traptrix monster from the GraveYard in defense position, but when Myrmeleo is Special Summoned, it allows you to set a Hole trap card from your GraveYard, but it banishes it if it's still on the field during the end phase of your next turn. Traptrix monsters themselves are also unaffected by the effect of Hole trap cards, that makes them a pretty reliable Normal Summon, as they also have a decent amount of ATK points.
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