The first combo is the easiest to get out as it only requires 2 cards in play:
Mindcrank: Lose life? Mill cards.
and
Duskmantle Guildmage's first activated ability: Card goes to GY? Lose Life.
Repeat until victorious.
The combo relies on having
available. The rest is a waiting game, as this now prohibits your opponent from:
1. Casting any
Instant or
Sorcery spells
2. Discarding cards
3. Sacrificing permanents
4. Paying any life or taking any damage: This includes but is not limited to: Fetch-lands, Shock-lands, Pain-lands,
Thoughtseize, etc.
The cards in this combo can be tutored several different ways. Both pieces can be
Transmuted, to your hand via
Muddle the Mixture.
Fabricate can retrieve
Mindcrank should you need your
Muddles for defensive casting.
Aether Vial can allow you to cast
Guildmage a turn early, to set up for a win with this combo as early as turn 3. Yep.. Turn 3.
Even if
Mindcrank is destroyed, it can be returned to your hand via the death of a
Myr Retriever.
Your opponent will more than likely have a harder time removing your
Artifact than the
Creature from the board. Thus, your 2/2
Guildmage will be the prime target for removal the instant it enters play. So, the
Guildmage should be cast
Mindcrank, and only if you have the required mana to trigger the combo the same turn.
Here's why: Say you have
Mindcrank already in play. You cast
Guildmage, with the mana still available to activate his first ability. You opponent lets
Guildmage resolve and ETB; but, decides to
Fatal Push your
Guildmage. In response, activate
Guildmage's ability. His effects last the rest of the turn; the opponent's
Push resolves (removing the
Guildmage);
Push goes into the graveyard, and begins the combo: lose a life, mill a card, lose a life, mill a card, lose a life, etc.
Altar of the Brood can help with this wincon as well. With
Altar and
Crank in play, simply cast the
Guildmage and activate his first ability in response to
Altar's trigger (on the stack). All opponent's who put a card in their GY will lose the game.