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So, you can capture any piece in chess except for the king. But what happens if me and my opponent get all pieces captured (except for the king)?

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Since you can't move your king into check, you can't legally check the other king.

The Laws of Chess, section 5.2b, states that:

The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.

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When you only have Kings then you can take a tour of the entire board till the end of the World without any hesitation . :-) (Just Joking ) .

The Game at this point is a DRAW . Since neither Player can play without any objective and Game of Chess is all about Checkmating your King then without any material resistance it is DRAW . Infact a lone King with a Knight or Bishop and also against another King is also a DRAW material is not sufficient to Capture King .

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    I recall seeing two young boys playing with just their Kings, and remarking that it looked like a draw. Five minutes later I saw them putting the pieces away. ME So you found out out it was a draw! BOY No, he won, He got his King to the 8th rank and it became a Queen. Maybe FIDE could consider this as a possible solution to the preponderance of draws. – Philip Roe Sep 14 '17 at 14:30
  • @PhilipRoe - even if K promotes to Q, Q alone can't deliver mate - so quite an odd game – Laska Dec 22 '19 at 6:21

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