The mulligan bug referenced in my earlier post exists across multiple formats, as seen in 40 games of Base–Fossil. Again, a deck with 1 Basic Pokémon will never take a mulligan unless the opponent also takes a mulligan.
To test this, I played a deck with 1 Mewtwo and 59 Psychic Energy. The Mewtwo deck only took 1 or more mulligans in 8 games, and all 8 of these games saw the opponent mulligan as well.
Full Mulligan Results:
Game 1: 0 mulligans
Game 2: 0 mulligans
Game 3: 1 each, Mewtwo deck takes additional 1
Game 4: 0 mulligans
Game 5: 0 mulligans
Game 6: 0 mulligans
Game 7: 1 each, Mewtwo deck takes additional 6
Game 8: 0 mulligans
Game 9: 0 mulligans
Game 10: 0 mulligans
Game 11: 0 mulligans
Game 12: 0 mulligans
Game 13: 0 mulligans
Game 14: 0 mulligans
Game 15: 1 each, Mewtwo deck takes additional 4
Game 16: 0 mulligans
Game 17: 1 each, Mewtwo deck takes additional 2
Game 18: 0 mulligans
Game 19: 0 mulligans
Game 20: 0 mulligans
Game 21: 0 mulligans
Game 22: 1 each, Mewtwo deck takes additional 14
Game 23: 0 mulligans
Game 24: 0 mulligans
Game 25: 0 mulligans
Game 26: 0 mulligans
Game 27: 0 mulligans
Game 28: 0 mulligans
Game 29: 0 mulligans
Game 30: 1 each
Game 31: 1 each, Mewtwo deck takes additional 31
Game 32: 0 mulligans
Game 33: 0 mulligans
Game 34: 0 mulligans
Game 35: 0 mulligans
Game 36: 2 each, Mewtwo deck takes additional 15
Game 37: 0 mulligans
Game 38: 0 mulligans
Game 39: 0 mulligans
Game 40: 0 mulligans
Game starting
Game type: QUICKPLAY
Game format: Base-Fossil (1999)
Battle started between JasonKlaczynski and seenag!
TheAquaPiplup is now a spectator of the game from neutral POV
Coin flip result: HEADS
JasonKlaczynski will start
Game setup complete
Between turns
Turn 1 begins
JasonKlaczynski drew 1 card
seenag wins the game! Opponent has surrendered
TheAquaPiplup has exited spectation.
seenag has closed game view.