B · Engine & Sequencing · §8
You will almost never lack units. The risk is drawing the wrong unit profile, which is what the mulligan is actually for.
The opening hand is drawn from the shuffled 39. Trophy Hunter is separately available from the Champion Zone and is not part of these calculations.
P(at least one hit) = 1 − C(N−H, 4) / C(N, 4), with N = 39
Any shuffled unit: 99.91% for at least one, 97.80% for at least two. A natural one or two-Energy unit, ten copies: 71.12% for at least one, 26.70% for at least two. A shuffled Ambush unit, or , five copies: 43.62%. A six-Energy unit, three copies: 28.76%, with 3.18% for two of them.◆src
The Legend is essentially never textless because of a unitless opener. The actual risk is the wrong unit profile: too many sixes, too many three-drops with no early presence, units whose effects have no targets, with no Fury for Accelerate, or Kinkou with nothing else on the board.
Roughly 71% for at least one natural one or two-Energy unit means almost three hands in ten do not have one before the mulligan. and Trophy Hunter improve the practical curve later, and neither repairs an opening that spends the first relevant cycle without a body on a battlefield.
At 31 shuffled units, 97.80% of openers hold at least two. At 30 it is 96.78%, at 29 it is 95.51%, at 28 it is 93.98%, and at 27 it is 92.18%. Those numbers stay superficially high, and the qualitative cost is larger than they suggest.
Removing units also reduces Legend trigger density, Ambush density, Kinkou support, Legion sequencing, and Twilight targets, Thrill targets, and your ability to threaten two battlefields at once.