I decided to try to get the digital game's achievement of winning w/out a hero card ever entering play.
Managed to get GloomWeaver down to 8, but an Exploding Wagon took out my remaining heroes at that point. Team was Legacy, Fanatic, Tempest, Ra, and Haka.
I therefore got to see a screen I'd not seen before: GloomWeaver winning! It was a pretty cool scene.
You could keep re-rolling until you get an insta-win versus Wager Master, but that wouldn’t be as much fun. 
I think I did it with a team of Legacy, DW Fixer, Ra, Fanatic, and Haka, and just beat on Baron Blade until dead, in Insula Primalis.
But yes, the Insta-Wager works as well.
My method was Dark Visonary, Omnitron-X, SS Tachyon and Greatest Legacy vs. Gloomweaver.
Use Dark Visonary to make sure any Relics are either on top or bottom, Omni to discard the top card of Gloomy's deck, Tachyon the bottom two, and Legacy to make sure a relic isn't on top for the villain turn.
I can just see Gloomy playing two Relics at once from SS Tachyon… But that does sound like an awesome strategy.
Is that the fastest theoretically possible cardless victory?
That would be Wager Master’s zero turn victory.
That Wager Master zero turn victory would also unlock Mobbed by Paparazzi
I did this achievement using SS Tachyon, Dark Visionary, and Garndpa Legacy against Gloomweaver.
I did this a little while ago, so my memory is a little fuzzy
I think I had Ra, Youngest Legacy, DW Mr Fixer and Haka vs Baron Blade
The key was playing in final wasteland. Unforgiving wasteland was out, so a monster knocked BB down to zero on his front side and he was removed from the game. Game over early.
It is, and kind of risky – when I won that way, I also got the last-hero-standing-with-1-HP achievement.
I didn't think of Gloomweaver when I got the acheivement.
I played Legacy, Ra, Tempest, and F6 Zero versus Ennead in the Final Wasteland. Tempest whittled everyone down while Ra and Zero focused on the primary target and the Wasteland pitched in.
I must really hate myself.
I used YL, DW Fixer, Haka, Ra, Fanatic vs. Dreamer. "Oh, a villain I don't have to DPS down," I said. "Perfect!" I said.
Six tries before I got it.
Then I played Wager Master the next day and got a 0 turn victory for /just/ Mobbed by Paparazzi. I kid you not.
Who is this Bowie guy?
And where is his knife?
I thought he was trying to be The Sovereign
I thought he was the King of the Goblins.
With the setup right that's only possible if Dark Visionary reveals 2 relics and the third is on the bottom of the deck on the first turn.
Can anyone inform me what the Wager Master 0 card win condition is?
You need a Wageling and Losing to the Odds to come out (in that order) and all heroes to start on odd HP.
There are other methods that could damage the heroes too. Impossible Quandary+Losing to the Odds is also a possibility.
One other thing to note is that Wagelings needs to be played before Losing to the Odds and The New Deal can't be between them unless there is a second Wageling after it.
Probably your best chance of getting the insta-win is to use 4-Heroes with odd starting HP, as that makes Impossible Quandary safe, and then you are just waiting for the correct line-up of Wageling and Losing to the Odds.
I did this one way before Wager Master by using Legacy, Fanatic, Ra, Tempest, and Chrono-Ranger against Ambuscade in Insula Primalis. To be honest, the volcano helped almost as much as our base powers.
If I had to do it over again now, I'd swap Tempest out for F6 Absolute Zero.