This is a modified version of RDW/UR Phoenix I came up with (I'm sure I'm not the first, but I couldn't find a comparable thread). A strictly worse (budget) version of this deck I've been running on Arena has pretty much lifted me to Gold 1 over the last couple weeks, the complete version is probably just as good as the established decks in the format.
Why should you play this deck instead of RDW or UR Pheonix?
Pros: BR Phoenix is a more consistent, is more resilient, and is has more card advantage than RDW and is faster and more explosive than UR Phoenix. Playing a fast deck on Arena is good because you get more games in, so it takes less time to rank up.
Cons: A little slower than RDW (a good match up if their initial draw isn't fantastic because you usually win if you can outlast them), and less card advantage than UR Phoenix.
The primary goal of the deck is to get an Arclight Phoenix or two in the grave, play 3 spells and swing until your opponent concedes or their life hits 0. Another way to win is to get Guttersnipe out, and start cycling through your deck with Crash Through and Warlord's Fury. If Guttersnipe stays on board, it almost guarantees victory for you because it acts like a powerful engine taking on 2 damage to all of your spells (which can add up to a lot with The Flame of Keld out, or when you can play 4-5 spells per turn, but it dies to almost all removal. It's a good idea to play Guttersnipe later in the game when your opponent's removal has already been used on your other creatures, maybe when you have 4-5 mana (and a couple cheap spells in hand to play in response to removal).
Most of the cards are pretty standard in RDW. Runaway Steam-Kin is better in this deck, because not only can it become a beefy creature, it can give you the extra mana you need to get to 3 pre-combat spells or to feed your Guttersnipe. With Steam-Kin and Guttersnipe in play, this deck feels more like a combo deck/engine when you play it given how quickly you can cycle through your deck.
Warlord's Fury and (less so) Crash Through have relevant abilities, but if your opponent isn't paying attention (and you play fast) often times they forget that your creatures have first strike since the spells are mainly used as cantrips for you. ~25% of the time, you can get a free creature because your opponent forgot that your creatures have first strike and made poor blocks.
Carnival // Carnage hits all the 1-toughness creatures in the format and turns on spectate. Against control, you can Blightning them.
The sideboard should have Duress or Drill Bit for control match ups and vs gates since Gates Ablaze is the only card that beats us, and the rest really depends on your meta-game and matchups.
Why should you play this deck instead of RDW or UR Pheonix?
Pros: BR Phoenix is a more consistent, is more resilient, and is has more card advantage than RDW and is faster and more explosive than UR Phoenix. Playing a fast deck on Arena is good because you get more games in, so it takes less time to rank up.
Cons: A little slower than RDW (a good match up if their initial draw isn't fantastic because you usually win if you can outlast them), and less card advantage than UR Phoenix.
Okay, enough yappin, to the deck!
BR Phoenix Main Deck
4 Crash Through
4 Warlord's Fury
4 Ghitu Lavarunner
4 Shock
2 Lava Coil
4 Runaway Steam-Kin
3 Rix Maadi Reveler
3 The Flame of Keld
4 Light Up the Stage
1 Skewer the Critics
2 Guttersnipe
2 Risk Factor
4 Arclight Phoenix
4 Dragonskull Summit
2 Blood Crypt
11 Mountain
The primary goal of the deck is to get an Arclight Phoenix or two in the grave, play 3 spells and swing until your opponent concedes or their life hits 0. Another way to win is to get Guttersnipe out, and start cycling through your deck with Crash Through and Warlord's Fury. If Guttersnipe stays on board, it almost guarantees victory for you because it acts like a powerful engine taking on 2 damage to all of your spells (which can add up to a lot with The Flame of Keld out, or when you can play 4-5 spells per turn, but it dies to almost all removal. It's a good idea to play Guttersnipe later in the game when your opponent's removal has already been used on your other creatures, maybe when you have 4-5 mana (and a couple cheap spells in hand to play in response to removal).
Most of the cards are pretty standard in RDW. Runaway Steam-Kin is better in this deck, because not only can it become a beefy creature, it can give you the extra mana you need to get to 3 pre-combat spells or to feed your Guttersnipe. With Steam-Kin and Guttersnipe in play, this deck feels more like a combo deck/engine when you play it given how quickly you can cycle through your deck.
Rix Maadi Reveler, Risk Factor and The Flame of Keld (Tormenting Voice works here too) all let you pitch extra lands, The Flame of Kelds and Arclight Phoenixs, along with refilling your hand with gas.
Warlord's Fury and (less so) Crash Through have relevant abilities, but if your opponent isn't paying attention (and you play fast) often times they forget that your creatures have first strike since the spells are mainly used as cantrips for you. ~25% of the time, you can get a free creature because your opponent forgot that your creatures have first strike and made poor blocks.
Carnival // Carnage hits all the 1-toughness creatures in the format and turns on spectate. Against control, you can Blightning them.
The sideboard should have Duress or Drill Bit for control match ups and vs gates since Gates Ablaze is the only card that beats us, and the rest really depends on your meta-game and matchups.