Lightning Bolt: This card is a staple in most formats that it's legal in and it being in burn is pretty self explanatory. Decks that are too cheap to have
Lightning Bolt probably aren't worth playing.
Shard Volley: A worse version of Lightning Bolt but a staple in this deck. I chose this over Shock and other one mana 2 damage cards because in this deck usually after you've emptied your hand you won't need more then one land to play stuff. I think it's worth sacrificing a land for an extra point of damage but this can always be replaced with Shock.
Searing Blaze: Removal for creatures and a way to deal damage for ? This card is slightly worse in this deck because you won't use it at instant speed because there are no fetch lands. You will usually want to save it for a turn that you play a land but 1 damage to a creature and 1 to your opponent isn't the worst. Right?
Searing Blood: This card is kinda just ripping off Searing Blaze. It also kills creatures and deals damage for two red mana. So yeah... Really the only difference is instead of having to have had a land enter the battlefield that turn your opponent has to have a X/2 or X/1 creature
Skullcrack: There are like a ton of modern decks playing cards that gain life. Soul sisters is a real deck right? Skullcrack prevents damage from being prevented from cards that prevent damage. And stops players from gaining life. It's currently priced around a dollar so it's not worth playing more than two copies. But it's always good to pack main deck hate against turbo frog.
Thunderous Wrath: The best burn spell in non blue decks! One mana 5 damage! It's not played in most burn decks because if you get it opening hand it's awful but otherwise it's great. One annoying thing about it is you have to draw your card carefully each turn to make sure you don't accidentally draw Thunderous Wrath without first revealing it to your opponent so you can cast it for it's miracle cost.
