user8527: A quote from Wikipedia:

The objective is to 'checkmate' the opponent's king by placing it under an inescapable threat of capture.

Suppose two players (A and B) play the game using the old fashioned way (no computer involved). If player A has player B's king checked from two positions.  Player B only knows how to block one of those two attacked positions. But there is a way for Player B to make a single move and block both attackers. What would be the proceeding of the game next? Should player A show player B how to do it? Or does the game end with player A winning even through this is not a checkmate?

user70: Once the players agree that the game is over and agree who has won, it's over. If later the player who lost realizes they had a saving resource, it is too late. The game is over.

user4362: I guess the question is what to do if one player doesn't find a legal move, but it is not checkmate. 
In a tournament game he would lose on time, lose because of repeated illegal moves or possibly resign. 
In a friendly game between amateurs you can handle the situation any way you like. It depends on whether you value the competitive or the social side of playing chess more. I would say if you allow takebacks, you might as well show player B the defence, otherwise a loss is the sensible result.

user6885: Each tournament has its rules, but what I was taught as a child when I played was that the agreement of the players was the end of the game; if you weren't checkmated, it was treated as though you resigned because you thought the position was a lost position.  Shake on it, and the game is decided.
As the winning player, it was considered unsportsmanlike to not point out the available move, but not obligatory.  The winner may not notice the move itself!  I remember one game where castling was the difference between being mated and winning the game, but it never occurred to either player that, that late in the game, someone might not have moved either their king or rook.  I also heard of one game which would have been won by an en-passent (but I never did confirm that it occurred).
In the end, it really depends on the situation.  If there's more important things than winning (like having fun and learning), not pointing it out is bad form.  If winning is all there is (which might happen in some master level play for large money), then... well... hopefully you don't make a mistake like this.  Usually the mistake at the masters level is resigning from a winning position, and they usually don't need their opponent to tell them about the mistake later -- all of their friends and their chess computers will make sure they know afterwards.

user3884: If player B is checked in two different ways, then there is by definition no way for player B to block both attackers with a single move. The only way to get out of double check is to move the king.
If there's a square for player B's king to move to that is safe, then he can get out of the check. If player B simply doesn't see it, then in a friendly game player A can certainly show player B where to move his king. In a competitive game player A should probably just let player B lose on time or forfeit by making an illegal move.
If there's no square for player B's king to move to that is safe, then it is in fact checkmate. Player A wins.

8527: <p>A quote from Wikipedia:</p>

<blockquote>
  <p>The objective is to 'checkmate' the opponent's king by placing it under an inescapable threat of capture.</p>
</blockquote>

<p>Suppose two players (A and B) play the game using the old fashioned way (no computer involved). If player A has player B's king checked from two positions.  Player B only knows how to block one of those two attacked positions. But there is a way for Player B to make a single move and block both attackers. What would be the proceeding of the game next? Should player A show player B how to do it? Or does the game end with player A winning even through this is not a checkmate?</p>
 70: <p>Once the players agree that the game is over and agree who has won, it's over. If later the player who lost realizes they had a saving resource, it is too late. The game is over.</p>
 4362: <p>I guess the question is what to do if one player doesn't find a legal move, but it is not checkmate. </p>

<p>In a tournament game he would lose on time, lose because of repeated illegal moves or possibly resign. </p>

<p>In a friendly game between amateurs you can handle the situation any way you like. It depends on whether you value the competitive or the social side of playing chess more. I would say if you allow takebacks, you might as well show player B the defence, otherwise a loss is the sensible result.</p>
 6885: <p>Each tournament has its rules, but what I was taught as a child when I played was that the agreement of the players was the end of the game; if you weren't checkmated, it was treated as though you resigned because you thought the position was a lost position.  Shake on it, and the game is decided.</p>

<p>As the winning player, it was considered unsportsmanlike to not point out the available move, but not obligatory.  The winner may not notice the move itself!  I remember one game where castling was the difference between being mated and winning the game, but it never occurred to either player that, that late in the game, someone might not have moved either their king or rook.  I also heard of one game which would have been won by an en-passent (but I never did confirm that it occurred).</p>

<p>In the end, it really depends on the situation.  <strong>If there's more important things than winning (like having fun and learning), not pointing it out is bad form.</strong>  If winning is all there is (which might happen in some master level play for large money), then... well... hopefully you don't make a mistake like this.  Usually the mistake at the masters level is resigning from a winning position, and they usually don't need their opponent to tell them about the mistake later -- all of their friends and their chess computers will make sure they know afterwards.</p>
 3884: <p>If player B is checked in two different ways, then there is by definition no way for player B to block both attackers <em>with a single move</em>. The only way to get out of double check is to move the king.</p>

<p>If there's a square for player B's king to move to that is safe, then he can get out of the check. If player B simply doesn't see it, then in a friendly game player A can certainly show player B where to move his king. In a competitive game player A should probably just let player B lose on time or forfeit by making an illegal move.</p>

<p>If there's no square for player B's king to move to that is safe, then it is in fact checkmate. Player A wins.</p>
