From the source rules

Who goes first in War (card game)?

Bicycle Cards rules, standard 52-card pack (English)

Nobody goes first: both players turn up a card at the same time. Anyone may deal.

Source & edition

All 16 Bicycle Cards (The United States Playing Card Company) starting rules

If your rules call for a random choice, use the player picker.

Rule details

If the turned-up cards match in rank, it is War: each player adds one card face down and one face up.

If there’s a tie

The rulebook doesn’t say. If you need a tie-break, pick a player at random.

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