A nice casual deck using both of the Izzet Guildmage infinite combos.
First one, and probably the best well known, requires 5 mana. You have Izzet Guildmage already on the battlefield. Cast Lava Spike, then splice Desperate Ritual onto it. Now the Lava Spike that's on the stack reads "Deal 3 damage to target player. Add RRR to your mana pool." Cast the Desperate Ritual from your hand. You should know have RRR in your mana pool and a supped up Lava Spike still on the stack. Use Izzet Guildmage to copy said supped up lave spike. The copy will resolve dealing 3 damage to the opponent and adding another RRR to your mana pool. Rinse and repeat until the enemy is dead. This combo will only require 4 mana if Training Grounds is already on the battlefield since you won't have to cast the Desperate Ritual from your hand.
The other infinite combo is much simpler. Use Izzet Guildmage's ability to copy Manamorphose while Training Grounds is on the battlefield. The guildmage's ability will only cost you U to use, and Manamorphose will keep adding 2 of any color to your mana pool. Then cast Banefire for the win.
Other than that, basic protection is granted through Lightning Bolt and Mana Leak. Use
Clout of the Dominus
to protect what few creatures you have (all of which are multicolored). Gitaxian Probe and Manamorphose offer card cycling for cheap/free.
After playtesting, I realized another infinite combo. Nivix Guildmage with Training Grounds on the battlefield. Cast Manamorphose for infinite card draw. While it doesn't net you infinite mana, it can still be a really powerful play, promising that you'll draw into what you need to go off next turn.
More playtesting reveals yet another infinite combo. While Training Grounds is on the battlefield with Izzet Guildmage, you can play just a Desperate Ritual for infinite mana. Only helps if Banefire is already in your hand (which is rare seeing as how the deck only has one), but it's still a possible, viable combo.
Yeah, not a bad deck at all. Can be slow, only for casual. Yes, I know the lands can be upped to Sulfur Falls, Steam Vents, and Scalding Tarn, but that requires a lot more money, and boosts this relatively cheap decks price out of the water.
