Mage lacks just enough spell damage potential to build a deck around. You may have enough spells in the deck to kill your opponent, but they come out too slowly to form a consistent strategy around.
So this deck attempts to solve that issue three ways.
The first way is spell specific draw with Elemental Allies and Starscryer. By focusing the draw on spells you load up earlier with the spells you need to kill your opponent. The goal is to kill your opponent with face damage before they can get rolling. Never mulligan either of these cards, spell draw is very important. Use Bonfire Elemental to draw an extra card and trigger Elemental Allies as a bonus.
The other way is to do impactful damage to your opponent with early minions that pack a punch. Fire Hawk can achieve this and can be played as early as turn 1 with Elemental Evocation. Get this card out as early as you can because it is very vulnerable. But even one hit with this can be important and if not, he will draw a minion control card from your opponents hand.
An early 2x Animated Avalanche is probably the highest probability win condition. You can have them on the board as early as turn 2. But even a turn 4 or 5 pair of Avalanches are very hard to deal with. So never mulligan Elemental Evocation, Animated Avalanche or Fire Hawk, unless you have more than one.
The final method for this deck to do enough face damage early enough is with extra damage. Celestial Emissary, Cosmic Anomaly and Astromancer Solarian all have Spell Damage to extend your damage impact to your opponent and when needed for minion control.
Flamewalker also contributes to the amount of damage inflicted. I find it is better to wait to play him until you have a few spells to play the same turn. He attracts a lot of attention and will be taken out quickly. Plan for him to have an impact his first turn if you can.
I don't tend to keep any of these cards in my starting hand, choosing to mulligan them for something of higher early potential. The spell boost cards can all be played well mid and late game.
Every other card does damage. The cheap ones get very good value when boosted.
So the priority of strategy is:
1) Get Animated Avalanche in play early.
2) Draw spells
3) Do early minion damage to the face
4) Use boosted spells to the face when possible, but sometimes you must control the board a bit. This is a tricky area that takes some play to find the right path in each case.
Finish the job with boosted spells and minions as the situation allows. Never forget to be aware of your opponents health level and your ability to finish him off.
Turn 4 to 7 wins are not uncommon. The deck still has potential later than that but you will almost never run out of cards, someone will win before that.
A turn 2 or 3 2x Avalanche play will always stop your opponent cold and you will see your card light up as he tries to figure out wtf just happened.
Be warned, I have gotten people down under 5 health several times only for Reno to restore it all. You can still win but it's tough as you have extended yourself significantly at this point.