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When I started playing chess, I learned many of the rules of chess on my own. I was playing chess online, and then I realised that pawns can capture in such a fashion. At first, it was weird to me. Like, wow! How can a pawn capture like this?!

Then I read the theory of en passant. I have come to know that such kinds of rules exist in chess. By the way, it's an interesting rule.

Now here comes the main question: How can we teach this rule to a beginner (in a plain language or simplified way or associating any story to it)?

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How can we teach this rule to a Beginner? (in a plain language or simplified way or associating any story to it)

The history gives the story.

At one time pawns could only move one square at a time even on the first move. But this made the game a bit slow. To speed it up the rule was changed to allow a pawn to move either one square, as before, or two squares on the first move.

But this changed the way one pawn could stop another pawn from moving because of the risk of capture. So, for instance, a black pawn on g4 stops a white pawn on h2 from moving. Before the rule change the only move the white pawn could make was from h2 to h3. Then the black pawn on g4 could capture it. After the rule change the black pawn could move straight from h2 to h4 thereby dodging the attack from the black pawn. This was unfair to the black pawn on g4 and changed the game in an unintended way. So, to even things up again the en passant rule was introduced which said that in that situation the g4 black pawn could take the h4 white pawn as if it had only moved one square.

The rule only applies on the move immediately after the double pawn move because with the old rule (only allowed to move one square on move one) if black didn't take immediately then white could move the pawn on his next move and the chance was gone.

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    The second para also answered the question of "why en-passant is a necessity?" – Creepy Creature Mar 2 at 17:22
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    @CreepyCreature Yes. If the h2 white pawn could escape the black g4 pawn by moving h2-h4 on the first move it would completely change the game. When the double first move for the pawn was introduced the new en passant rule was needed to retain the balance. – Brian Towers Mar 2 at 18:16
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    Of course, the two rules taken together still have a significant effect on the game's strategy (beyond "just speeding up the game"). One wonders if the original rationale is still applicable. – Kevin Mar 2 at 18:52
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    Mostly a great answer! In the last sentence, though, I recommend not assigning a gender to a hypothetical chess-player ("on their next move" is better, in my opinion). There is a lot of implicit bias against women playing chess in many cultures, and a pronoun that assumes that a hypothetical chess-player must be male perpetuates that bias. – Greg Martin Mar 3 at 9:24
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    @GregMartin Absolutely, it's so important! it's terribly off-putting to see this way of writing in chess literature all the time, and it's being adopted by anyone who gets into chess! "Player", "opponent", the color of the pieces or pronoun "they" should be exclusively used to remain gender-agnostic, unless of course the players at hand are known. – Phonon Mar 3 at 11:50
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In simple words: if a pawn jumps two squares and lands right next to an opponent's pawn, then the opponent can capture that pawn in the following turn as if it had moved only 1 square. That is, only right after you made your jump, your opponent has the option to take by en passant, past that turn it is no longer allowed.

So keywords to remember: two square move, right next to, and following turn.

Visually:

 [title "Visualised example"]
 [fen "r1bqkbnr/pppppppp/2n5/4P3/8/8/PPPP1PPP/RNBQKBNR b KQkq - 0 2"]

 1...d5 2.exd6 (1...d6 2.exd6)

Notice the end scenarios are the same after either d6 and d5, as in after the capture one cannot tell if it had been by en passant or a normal capture.

Intuitively, you can imagine the rule is there so that one cannot jump past another pawn and completely evade the option of a trade. Exactly similar to when you move your pawn only one square, and your opponent still has the option to capture your pawn if they so desire.

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As much as I hate to cite Wikipedia, they have a decent article regarding en passant:

https://en.wikipedia.org/wiki/En_passant

It is a special pawn capture that can only occur immediately after a pawn makes a double-step move from its starting square, and it could have been captured by an enemy pawn had it advanced only one square. The opponent captures the just-moved pawn "as it passes" through the first square. The result is the same as if the pawn had advanced only one square and the enemy pawn had captured it normally.

I hope that helps a little.

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    "As much as I hate to cite Wikipedia" Well, dare I say, you shouldn't. – Marc.2377 Mar 3 at 5:53

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