Just your typical very aggro burn mage deck with Barnes thrown into the mix for some extra value and high-roll potential. You are trying to get in a decent amount of damage early game with your minions before kinda of transitioning into a freeze mage and cycling your deck and burning your opponent out with your spells.

I like Barnes in this deck because he can pull a 1/1 copy of deathrattle minions or Sorcerer's Apprentice and your opponent might not immediately remove it because it is only a 1/1. Also the high-roll potential with[Hearthstone Card (Ragnaros, the Firelord) Not Found] of course.

Kobold Sandtrooper has replaced Mana Addict with Saviors of Uldum coming because Addict just really wasn't good outside of the early game and was a dead draw a lot of the time. Now with Sandtrooper you can get a decent body with the extra face damage on deathrattle. Cloud Prince also should probably be added to the deck somewhere as well but dilutes the Barnes summon pool.

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Cards that are good to summon with Barnes:

Loot Hoarder - Draws a card

Bloodmage Thalnos - Draws a card, +1 Spell dmg

Leper Gnome - 2 dmg to the enemy hero on deathrattle

Mad Scientist - Pulls a secret from your deck on deathrattle

Sorcerer's Apprentice - Makes your spells cost (1) less

Kobold Sandtrooper - The new addition with Saviors of Uldum and a pretty good one at that with the 3 dmg to the enemy hero on deathrattle

Ragnaros the Firelord - Throws an 8 dmg fireball the turn he gets summoned 

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This leaves the only bad card to summon with Barnes is Medivh's Valet and just one bad outcome doesn't always mean you shouldn't run Barnes.

Just try to get some damage in early with minions, stay alive with Ice Block, and then burn your opponent out with spells. Don't be afraid to use some burn as minion removal and make sure to save a Frostbolt to activate your Ice Lance.

If you want to remove Barnes because reasons... (or you don't have him).

If you want you can replace Barnes and Ragnaros the Firelord because they aren't exactly necessary for this archetype of deck or you don't have them because they are wild legendaries. I would recommend replacing them with 2x Cloud Prince. Other options are to put in cards like Primordial Glyph, Coldlight Oracle, another Loot Hoarder, or maybe Aluneth (if you have it) if you really feel like you don't have enough draw.

Possible budget replacements:

Bloodmage Thalnos ===> Another  Loot Hoarder (Although I really suggest crafting Thalnos as it fits it many decks and is in the classic set)

Cards to consider if you have them: Cloud Prince [Hearthstone Card (, Coldlight Oracle (although has less synergy with the deck than Research Project), Aluneth, Leeroy Jenkins (as a fireball #3 kind of), Argent Horserider (very good charge card and can also be used for board control)