adverb
scrambling; falling over each other; striving to be first
Describes a situation where many people compete eagerly to do something first, often in a disorderly rush. Similar to 我先に, but 我勝ちに emphasizes the selfish 'me first' attitude.
See also: 我先に
開店と同時に、客が我勝ちに店内に駆け込んだ。
As soon as the store opened, customers scrambled inside, each trying to be first.
子
The children all reached for the presents, falling over each other in their eagerness.
Both mean 'scrambling to be first,' but 我先に is more neutral, while 我勝ちに carries a stronger nuance of selfish competition ('I will win').
From 我 (われ, 'I, oneself') + 勝ち (がち, from 勝つ 'to win') + に (adverbial particle). Literally 'in a self-winning manner,' i.e., trying to beat others.