Easy game, right?
In this case, sure. And while some games will undoubtedly be decided this easily by your Azure Mage, there are going to be plenty of games where it has only a marginal impact on the game. Maybe it dies at the hands of a mediocre removal spell like Wring Flesh before it has the opportunity to do anything special, or trades with your opponent's Phantasmal Bear because you know that you won't have the mana to really abuse your freshly cast Human Wizard.
It's very important to cast your game-breaking creatures at the right time. If you cast your best creatures at inopportune times, then they will do little for you. You might have to trade a bunch of them in combat for creatures, or walk them into removal spells that you probably could have realized that your opponent was holding if you had only taken a minute to think about the way the game had played out.
For example, if you cast your Flameblast Dragon only to see it get immediately answered by a removal spell, then you will have gained nothing. But if you cast your Flameblast Dragon onto a stalemated board against an opponent who has no cards in hand, then you will win the game in short order (unless your opponent happens to draw something fantastic).
Sometimes your deck is nice enough to take these decisions out of your hands, giving you an Azure Mage when you have a ton of mana, and next to no action left. But what happens when you draw Azure Mage in your opening hand? Do you cast it on turn two, knowing that it could easily die at the hands of a Sorin's Thirst or a Shock? Or do you wait until you have six lands to ensure that you'll at least draw an extra card from your Azure Mage?
If you wait to cast your Azure Mage until you're at six mana, then you get the added bonus that your opponent might have ran him or herself out of removal spells by that point, allowing you to draw extra cards to your heart's content. But your opponent isn't just going to dump his or her removal spells for no reason...
Why People Play Removal Spells (Abridged Version)
Unless one player is off to a tremendous lead or is in some way threatening to deal a ton of damage very quickly, you and your opponent are going to use removal spells to deal with each other's best, or otherwise peskiest, creatures.
If one player does develop a lead on the board and is looking to press that advantage to finish off his or her opponent quickly, then that player very well might use removal spells on mediocre creatures (that are serving a key defensive role) in order to keep the pressure on. With those would-be blockers out of the way, the aggressive player will be able to continue punching through damage in the hopes that he or she will win the game before his or her opponent is able to draw, cast, and ultimately take over the game with his or her best creatures. If the aggressive player is able to win before the game goes long, then the fact that he or she doesn't have any removal spells for that Furyborn Hellkite that's stuck in the other player's hand won't matter at all, because, well, the game will already be over.
If you allow yourself to fall too far behind, then the ability to spend four mana to draw an extra card probably isn't going to be that relevant, as you are going to need to spend your mana on things that will get you back into the game.
(Yes, there are of course exceptions to this: situations where you've completely run out of gas and you need to draw into some action, or when you desperately need to dig for your Fireball to burn out your opponent who has developed an overwhelming edge on the board, or when you know that you need to draw your Mind Control to take your opponent's best creature to have any shot of getting back into the game. But in general, if you're getting hit for a bunch of damage a turn, you aren't going to have the time to draw many extra cards at four mana a pop.)
So what does all of this mean for you?
Well, for starters, it means that unless you're actually putting a lot of pressure on your opponent, or unless your opponent is off to an extremely aggressive start that you are trying very hard to contain, then he or she probably won't have used all of his or her removal spells by the time that you cast your Azure Mage. So while it will be able to replace itself, you shouldn't expect it to live much longer than it would if you had cast it on turn two.
When to Wait
If you already have another creature that you could cast instead of Azure Mage, then you should probably go with that early on. While Azure Mage can attack and turn on bloodthirst for you, or block opposing two- and three-cost creatures, its biggest impact will generally be outside of combat.
So while you would undoubtedly prefer to have Azure Mage rather than Coral Merfolk in your deck, it is almost always better to play the vanilla 2/1 Coral Merfolk on turn two. (There are, of course, some exceptions to this, such as when you have a strong defensive three-drop in your hand, and you know that you are going to want to draw a card with your Azure Mage on turn four.)
If, after a few turns have gone by, you realize that the board is about to get pretty bogged down, and that you are not going to want to/need to use Azure Mage in combat, then it will be in your best interest to wait to cast your card-drawing 2/1, as you will get little to no benefit for exposing it to removal spells early.
When to Go for It
While you will want to draw a bunch of cards with your Azure Mage, there are going to be plenty of times where you simply need it to function as a warm body. If your opponent opens on Phantasmal Bear into Runeclaw Bear, then you are going to need to trade with one of them in combat or else fall extremely far behind. So if Azure Mage is your only two drop in this spot, you're going to have to play it and block with it.
Even though it might seem unfortunate/stupid/bad to trade your Azure Mage for a vanilla Runeclaw Bear, it's much better to trade with it immediately, rather than take a half dozen damage from the green 2/2 (before ultimately trading your Azure Mage for it when you realize that you aren't going to have the breathing space necessary to draw any extra cards).
If you don't think your opponent has any/many removal spells, or if you are trying to use Azure Mage as a lightning rod for your opponent's removal spells (clearing the path for the card(s) that you actually intend to win the game with), then you should just go ahead and play it when you have the extra mana.
If you have an aggressive draw and you think that you can get in a few hits with Azure Mage, then you should definitely cast it on turn two (assuming you think that you can actually kill your opponent quickly).
The Difference Between Gideon's Lawkeeper and Azure Mage
It can be mighty tempting to wait until late in the game to cast your Gideon's Lawkeeper in much the same way that you would wait to cast an Azure Mage. After all, you'd rather use it to tap down an opposing Primordial Hydra than simply see it die to a Wring Flesh.
But you can get a lot of mileage out of a Gideon's Lawkeeper early in the game that you (usually) can't get out of an Azure Mage. If you cast Gideon's Lawkeeper on turn one, then you will probably be able to get in an attack or two with it before your opponent casts any creatures, and whenever you have a single extra mana, you'll be able to tap down a key attacker orblocker, to net you at least a couple of points damage in the process.
So while Azure Mage will just sit around and watch combats go by, Gideon's Lawkeeper will be hard at work keeping your life total high and/or enabling some pretty nice attacks.
It's Almost Prerelease Time!
The M12 Prerelease is this weekend, so get ready!
If you’re playing in a Sealed deck flight at the Prerelease (and you don’t have a hyper aggressive deck/draw), be careful not to use your removal too early. Sure it might be tempting to get your opponent’s Zombie Goliath off the board, but if you do that, you’re going to be awfully sorry when your opponent takes over the game with Pentavus, Azure Mage, or Serra Angel.
If you hold onto your removal spells until your opponent plays something that you absolutely need to kill, then you shouldn’t be surprised if you end up walking away from the tournament with a bunch of M12 booster packs as a reward for your patience. Have fun!