A player at a -1 has a 33% chance of first turn on the roll-off, and, if they fail, a 17% chance of seizing. It actually works out to about a 55.6% chance of failure. Which is close enough to a coin-flip to make it stupid. GW needs a very well-paid statistician on staff. I volunteer myself.
P(A) or P(B) = P(A) + P(B) .
P(A) & P(B) = P(A) * P(B)
For someone at a disadvantage, we want the probability that they initially succeed (33.3%) or the probability that they initially fail (66.7%) and subsequently seize the initiative (16.7%).
33.3 + 66.7 * 16.7 = 44.4% chance of first turn.
Rather than a noteworthy advantage to the opponent done first, that's close enough to a coin-flip for horse-shoes, hand grenades, or statistics.