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Can one be compelled to use his king when there are alternative moves? Especially if that move will end up having the king killed. My opponent saud I was obligated to use the king.

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No. You are never obliged directly to use a specific piece to move.

The only exception is trivial: a game played under forced capture rules where there is exactly one piece able to make a capturing move.

Even then, if that piece has a choice of captures, the player may choose which capture to make.

It is likely your opponent has either confused this rule with another, has played in environments with this uncommon variant rule, or the king had a capture available and no other pieces did.

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    There's a second variation where you are required to make the best capturing move.
    – Andrew
    Commented Feb 12, 2018 at 22:03
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You are not obligated to use a king because it is a king. There are however rules variants for checkers/draughts that obligate you too make captures when possible. there are two versions of this:

  1. If you have a piece that can capture, you must use a piece to capture, and must continue to capture until that piece no longer has a legal capturing move.
  2. If you have a piece or pieces that can capture, you must take the most captures you can with one of those pieces.

The second rule is harder to enforce, and harder to work with, but it does exist as a variant. It means you need to evaluate the best possible move when you have two choices of where to take before doing anything. If that king was the only piece that could make a capture, your opponent may be correct, though it would depend on the rules variant.

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