Dark Link

Mulligan if:
* You have 2 or less power
* You don't have 2 primal influence
* You don't have any answers to early threats (Permafrost, Hailstorm, Polymorph, a castable Equivocate, even Unstable Form). Teacher of Humility will ruin your day.

I'll keep a hand that violates one of these rules if I draw both Mind Link and Rain of Frogs and there's a path to extra power/influence (Strategize, Vara's Favor).

Game Plan:
You win because you wreck your opponent's game plan and out-value them in the end game. You can confidently run 4x Rain of Frogs because you're dropping blockers and drawing cards each time (remember that cards in the void also transform and draw you a destiny frog). Most games you'll have a good idea of what your opponent has in their hand at any given time, and you'll have had a chance to transform their Channel or their Sword of the Sky King or their Temporal Distortion.

With all the transform copies you'll draw, you have plenty of fodder for Strategize or the Market, plenty of chump blockers to drop, and the occasional lucky draw.

Dealing with Aggro:
Survive the early game. You can win a fair number of games against aggro by just surviving. In these situations it's better to ditch Mind Link to a Strategize or Market in favor of more sweeps and removal. You'll win most of these games if you can hold on until you drop BSH.

Dealing with Control:
Mind Link + Rain of Frogs will win here. Save your Vara's Favor and your BSH for popping face aegis. It's a rare deck that can outlast you in the long game, provided that you save your Unseal/Disjunction for their game winners.

Dealing with Tempo:
This is a tough matchup. Any deck that can consistently drop bigger and bigger threats on curve is going to be a problem for you. You have removal, but no board wipes, and losing a turn to play Mind Link (or worse, draw it from the market and then play it) can lose you the game. Make solid Unstable Form plays, hope to hit a few targets with a Rain of Frogs and try to make it to the end game.

Some Notes on Unstable Form:
Unstable Form is so versatile. Pop aegis, trade it to the market, ruin their Makto. And you get two for the price of one! 9 times out of 10 it's an offensive weapon, even without a Mind Link up. Did you know that the average stats for a 3-cost unit is 2/2.5? That's probably going to be better than letting the turn 2 Teacher of Humility hit you. A few gotchas:
* If you're going to Unstable Form an enemy, know the average stats of what you're hitting, but also pay attention to the variance. You might turn Teacher into a 0/3 Warrant Officer, or you might get a 6/4 Refracted Sentinel.
* Ideally, keep some removal available to follow up if your Unstable Form backfires. Permafrost is good, just watch out for endurance units (and beware of Unstable Forming a frozen unit).
* Is your opponent playing some unit-less deck? Your BSH + 4 Unstable Forms has a 33% chance of turning into Scourge of Frosthome.

Update 10/5/18: Added Shimmerpack to market in place of Celestial Omen. Shimmerpack has won so many games for me.

Update 10/26/19: Made some changes over the past few releases, most notably adding in Royal Decree (good early insight into opponent's hand) and Yorja, The Tale Keeper (fantastic as a second payoff for all of the transformation effects in this deck).