Additional damage inherits all of the properties of the base damage.
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Pounce
Strike: hand strike at +2 damage, and the opposing minion cannot strike for the remainder of the round (this doesn't affect the current strike resolution). If this strike is dodged, this striking minion takes 1 damage during strike resolution and the opposing minion gets an optional press.
Rulings
Damage done to the striking minion is environmental.
Minions can (uselessly) gain additional strikes even if they cannot strike.
If used with First Strike (e.g. Shadow Feint) it prevents the opponents normal non-dodge non-combat ends strike from resolving
The optional press can only be used during the current round.