No, you cannot spear a king. In November 2021, the U.S. National Kubb Championship updated their rules regarding the spear throw. You can find it on page five under Section II.B.1., which involves the baton throwing phase. To summarize the change, you can only throw a spear shot from an advantage line at field kubbs. In no other circumstances is the spear legal. Not at baseline kubbs from an advantage, not a normal blast of field kubbs from the baseline, and not at the king to end or begin the game. You are correct to assume all baton throwing rules count during a king shot.
It is also important to realize that all baton throwing rules (angle, rotation, etc.) count during a king toss to start the game as well. Section 3 states the king toss must follow the rules for throwing batons:
A. Determine Sides and Order (Beginning Toss Phase)
Once both Teams agree on an accurate setup of the pitch, sides and order are determined by the following rules:
- Each Team chooses one player as a representative and selects a baton.
- The two representatives and behind opposing baselines facing each other.
- One or both count to 3; on 3 they each throw a single baton according to the rules for throwing batons—see Sec. II.B below.
- When the batons come to rest, the team whose baton is judged closest to the king without having knocked it over chooses throwing order or chooses which baseline to defend. If the winner chooses throwing order, the losing team may choose which baseline to defend.
So if someone is throwing a spear or rolling them in at an angle, call them on an illegal throw and win the king toss by default.
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