user3237: I am a 1750 Elo player with a very positional, quiet and strategic style of play.
I would like to know which variation I should play when, as White, I face the King's Indian Defence: 1...Nf6 2...g6
The variation must meet these two conditions:

On average it must tend to lead to positions which are as much solid, positional, slow, closed, quiet and strategic as possible (I want nothing sharp and tactical).
I should be able to play it both by beginning with 1. d4 Nf6 2. c4 and by beginning with 1. Nf3 Nf6 2. c4

Don't hesitate to suggest me more than one variation, so that if I don't like the first variation maybe I shall like the second one.

user7500: You can try the Exchange Variation:
[fen ""]
1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. Nf3 O-O 6. Be2 e5 7. dxe5 dxe5 8. Qxd8 Rxd8

GM Gregory Serper has an article covering the opening here.

user2173: King's Indian has many variations but I will try to be short. There are some variations which you should prefer and some to avoid. I can't provide you full information. It's better to look some books.  By Eduard Gufeld, for instance.
Let's start from fianchetto.
[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. g3 d6 6. Bg2

There are many variations there. If black play e5 or c5 it seems to suit your style. After Nc6, a6 and Rb8 position can be sharp or cannot. for example
[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. g3 d6 6. Bg2 Nc6 7. O-O a6 8. d5 Na5 9. Nd2 c5 10. Qc2

There if black plays Rb8, b5 and after that e6 they can sacrifice the rook (by taking your bishop b2) and the position will be rather sharp. If black plays e5, Ng4 and f5, the position will suit your style better.
[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. e4 d6 6. Be2 e5 7. O-O

In the classical line black can put knight on c6 and this position will be better for white if you know how to play. You can look how Vladimir Kramnik does it. If black takes on d4 and plays Nd7-c5 many pieces will be on the board. But this continuation is not popular nowadays. So, you need some theory in main lines.
There is another positional variant for you, but it works well only against inexperienced people who don't know how exactly to play with black. If black plays right, you will not even think about advantage, but otherwise your chances to lose will be very low. The pair of bishops is amazing.
[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. e4 d6 6. h3 e5 7. dxe5 dxe5 8. Qxd8 Rxd8 9. Bg5 Re8? 10. O-O-O c6? 11. Nxe5 Nxe4 12. Nxe4 Bxe5 13. Nf6+ Bxf6 14. Bxf6

I would recommend you start from the last option. I get the position above very often

user291: The Petrosian system ( 1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.e4 d6 5.Nf3 0-0 6.Be2 e5 7.d5) is relatively high in strategy and low in tactics (for a King's Indian).

user2042: According to Joe Gallagher-Starting Out The King's Indian Defense and David Vigorito-Attacking Chess-The King's Indian Volume 2 the most solid line for White in King's Indian is the Fianchetto variation. I tend to agree with it. 
Before explaining why, let me just show you the tabya so I can better explain my point of view :
[Title "KID, the Fianchetto variation"]
[fen ""]

1.d4 Nf6 2.c4 g6 3.Nf3 Bg7 4.g3 O-O 5.Bg2 d6 6.O-O Nc6

After briefly looking through the lines ( there is a vast amount of work to review ) I came to the same conclusion as the above writers based on the following :

Center remains fluid, so Black can not pursue standard ...f5 idea as in other lines;
Because of the first point, and the fact that fianchetto castling is very hard to crack, White king is ultra safe ;
White has more space;

It is not easy for Black to find counterplay, but he can reach equality if he knows how to play this line. Tactical shots are limited to the rook sacrifices along the b-file so Nf6 + Bg7 battery can profit from discovered attack, but otherwise things are positional and dynamic. 
There are several sub-variations here, but I would recommend you to play Panno line, since Yugoslav attack is quite sharp and theoretical.
[Title "KID, the Fianchetto variation-Panno line"]
[fen ""]

1.d4 Nf6 2.c4 g6 3.Nf3 Bg7 4.g3 O-O 5.Bg2 d6 6.O-O Nc6 7.Nc3 a6 8.h3 Rb8 9.e4 b5

White has 2 options here, cxb5 and e5 but I advise you cxb5 as it is safer one. Play will become dynamic, but you have dodged a lot of theory and sharp tactical mayhem from Classical line or Saemish attack... For detailed coverage of this line get Vigorito's book. It is printed in 2011 and is very well written, in my opinion.
Do not forget that KID is a sharp opening and that you can not "sterilize it", you can only reduce the level of sharpness and that is it.

3237: <p>I am a 1750 Elo player with a very positional, quiet and strategic style of play.</p>

<p>I would like to know which variation I should play when, as White, I face the King's Indian Defence: 1...Nf6 2...g6</p>

<p>The variation must meet these two conditions:</p>

<ul>
<li>On average it must tend to lead to positions which are as much solid, positional, slow, closed, quiet and strategic as possible (I want nothing sharp and tactical).</li>
<li>I should be able to play it both by beginning with 1. d4 Nf6 2. c4 and by beginning with 1. Nf3 Nf6 2. c4</li>
</ul>

<p>Don't hesitate to suggest me more than one variation, so that if I don't like the first variation maybe I shall like the second one.</p>
 7500: <p>You can try the Exchange Variation:</p>

<pre><code>[fen ""]
1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. Nf3 O-O 6. Be2 e5 7. dxe5 dxe5 8. Qxd8 Rxd8
</code></pre>

<p>GM Gregory Serper has an article covering the opening <a href="http://www.chess.com/article/view/find-your-own-quotmiraclequot-opening" rel="nofollow">here</a>.</p>
 2173: <p>King's Indian has many variations but I will try to be short. There are some variations which you should prefer and some to avoid. I can't provide you full information. It's better to look some books.  By Eduard Gufeld, for instance.</p>

<p>Let's start from fianchetto.</p>

<pre><code>[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. g3 d6 6. Bg2
</code></pre>

<p>There are many variations there. If black play <code>e5</code> or <code>c5</code> it seems to suit your style. After <code>Nc6</code>, <code>a6</code> and <code>Rb8</code> position can be sharp or cannot. for example</p>

<pre><code>[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. g3 d6 6. Bg2 Nc6 7. O-O a6 8. d5 Na5 9. Nd2 c5 10. Qc2
</code></pre>

<p>There if black plays Rb8, b5 and after that e6 they can sacrifice the rook (by taking your bishop b2) and the position will be rather sharp. If black plays e5, Ng4 and f5, the position will suit your style better.</p>

<pre><code>[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. e4 d6 6. Be2 e5 7. O-O
</code></pre>

<p>In the classical line black can put knight on c6 and this position will be better for white if you know how to play. You can look how Vladimir Kramnik does it. If black takes on d4 and plays Nd7-c5 many pieces will be on the board. But this continuation is not popular nowadays. So, you need some theory in main lines.</p>

<p>There is another positional variant for you, but it works well only against inexperienced people who don't know how exactly to play with black. If black plays right, you will not even think about advantage, but otherwise your chances to lose will be very low. The pair of bishops is amazing.</p>

<pre><code>[Title "White to move"]
[fen ""]

1.d4 Nf6 2.c4 g6 3. Nf3 Bg7 4. Nc3 O-O 5. e4 d6 6. h3 e5 7. dxe5 dxe5 8. Qxd8 Rxd8 9. Bg5 Re8? 10. O-O-O c6? 11. Nxe5 Nxe4 12. Nxe4 Bxe5 13. Nf6+ Bxf6 14. Bxf6
</code></pre>

<p>I would recommend you start from the last option. I get the position above very often</p>
 291: <p>The Petrosian system ( 1.d4 Nf6 2.c4 g6 3.Nc3 Bg7 4.e4 d6 5.Nf3 0-0 6.Be2 e5 7.d5) is relatively high in strategy and low in tactics (for a King's Indian).</p>
 2042: <p>According to <em>Joe Gallagher-Starting Out The King's Indian Defense</em> and <em>David Vigorito-Attacking Chess-The King's Indian Volume 2</em> the most solid line for White in King's Indian is the Fianchetto variation. I tend to agree with it. </p>

<p>Before explaining why, let me just show you the <em>tabya</em> so I can better explain my point of view :</p>

<pre><code>[Title "KID, the Fianchetto variation"]
[fen ""]

1.d4 Nf6 2.c4 g6 3.Nf3 Bg7 4.g3 O-O 5.Bg2 d6 6.O-O Nc6
</code></pre>

<p>After briefly looking through the lines ( there is a vast amount of work to review ) I came to the same conclusion as the above writers based on the following :</p>

<ol>
<li>Center remains fluid, so Black can not pursue standard <code>...f5</code> idea as in other lines;</li>
<li>Because of the first point, and the fact that fianchetto castling is very hard to crack, White king is ultra safe ;</li>
<li>White has more space;</li>
</ol>

<p>It is not easy for Black to find counterplay, but he can reach equality if he knows how to play this line. Tactical shots are limited to the rook sacrifices along the <code>b-file</code> so <code>Nf6 + Bg7</code> battery can profit from discovered attack, but otherwise things are positional and <strong>dynamic.</strong> </p>

<p>There are several sub-variations here, but I would recommend you to play <em>Panno line</em>, since <em>Yugoslav attack</em> is quite sharp and theoretical.</p>

<pre><code>[Title "KID, the Fianchetto variation-Panno line"]
[fen ""]

1.d4 Nf6 2.c4 g6 3.Nf3 Bg7 4.g3 O-O 5.Bg2 d6 6.O-O Nc6 7.Nc3 a6 8.h3 Rb8 9.e4 b5
</code></pre>

<p>White has 2 options here, <code>cxb5</code> and <code>e5</code> but I advise you <code>cxb5</code> as it is safer one. Play will become dynamic, but you have dodged a lot of theory and sharp tactical mayhem from <em>Classical line</em> or <em>Saemish attack</em>... For detailed coverage of this line get Vigorito's book. It is printed in 2011 and is very well written, in my opinion.</p>

<p>Do not forget that KID is a sharp opening and that you can not "sterilize it", you can only reduce the level of sharpness and that is it.</p>
