user109: [FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Nc3 Bb4 4. a3 Bxc3 5. bxc3 (5. dxc3)

I usually see bxc3 in this position and the main reason given is to capture toward the center, but doesn't bxc3 weaken the queen side and take the option of castling queen side away from white.  What is wrong with dxc3?  Doesn't this open up the file for the Queen and the Bishop's diagonal?

user791: Capturing toward the center with pawns is a general guideline that should be followed when appropriately, however, just like all the other positional guidelines. It should also be ignored when appropriate. In the specific case of the Ruy Lopez: Exchange Variation (the opening you mention) it is more popular to capture with the d pawn because it gives your queen an open file, and keeps your pawn structure a little better (two pawn islands instead of three).

user342: In my opinion, always capture towards the center when possible in the opening with your pawns. There are caveats to this of course, such as making sure to immediately capitalize on your advances by ensuring no pawns remain doubled. Also if there are attacks or tempos gained from not taking towards the center then by all means go the other way.
However, I would like to know why you would play 4. a3. To me, it seems like a blunder. I think that you should probably play Nd5 there.

[fen ""]

1. e4 e5 2. Nf3 Nc6 3. Nc3 Bb4 4. Nd5

I like this because it attacks the dark bishop for Black and gives White a nice tempo and some increased control over the center. More than likely Black will play Nf6 here, although Be7 would be possible to see as well. Either way it is beneficial to remove the bishop from the game.

user672: bxc3 gives you a majority of pawns in the center, and support for the pawn break d4!, possibly pushing c4 and still having d4 pawn-supported. Big advantages in the long-term.
With dxc3, you're right, the bishop is free, but with fewer pieces on the board, and Black to play, it's not much of an advantage. The file for the Queen, “attacking” the ♟d7, which belongs on d6 where it is well defended, is worth nothing, and the possibility of castling queenside is not very relevant either (e.g. Black traded his f2- and h2-threatening bishop)
Also keep in mind that the c pawns are doubled for the time being, and you don't want this situation to last until the endgame. It will be a lot easier to trade the ♙c3 on the d file than trying to support the b pawn, or merely blocking the d file for Black.

user72: Either is fine. bxc3 gives you a strong chance to push in the center successfully. It leaves a dangling pawn on a2, but by playing bxc3 you should already have resigned this pawn's fate to some sacrifice for a tempo later in the game. Note you can not play 6. d4 right away since black's response will most likely be 5. ... d5 or 5. ... Nf6 putting pressure on the e4 pawn which is awkward to defend for you at this point. You should most likely respond 6. d3 which dashes any hopes you had for a pawn charge to d4. Also, black can exert pressure on the doubled pawn at c3 which is also a bit awkward for you to defend. 
I personally would play dxc3. It is less committing. You no longer have to hope to pry open the middle with your pawn majority, and you have no dangling pawn you have to sacrifice eventually. You've opened up strong lines for all three of your white bishop, your dark bishop and your queen. Note this may seem not that important, but keep in mind your opponent just traded one of his bishops for your knight. If you can open up this game, you will have a strong edge on your opponent. Any attack on your e4 pawn can now be refuted, such as 5. ... Nf6 comes in with a strong pin 6. bg5. Also, it no longer looks silly for your white bishop to travel to d3 to defend e4.

109: <pre><code>[FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Nc3 Bb4 4. a3 Bxc3 5. bxc3 (5. dxc3)
</code></pre>

<p>I usually see <code>bxc3</code> in this position and the main reason given is to capture toward the center, but doesn't <code>bxc3</code> weaken the queen side and take the option of castling queen side away from white.  What is wrong with <code>dxc3</code>?  Doesn't this open up the file for the <code>Queen</code> and the <code>Bishop's</code> diagonal?</p>
 791: <p>Capturing toward the center with pawns is a general guideline that should be followed when appropriately, however, just like all the other positional guidelines. It should also be <em>ignored</em> when appropriate. In the specific case of the Ruy Lopez: Exchange Variation (the opening you mention) it is <a href="http://www.chessgames.com/perl/explorer?node=1112446&amp;move=4.5&amp;moves=e4.e5.Nf3.Nc6.Bb5.a6.Bxc6&amp;nodes=21720.21721.21722.21723.21724.21725.1112446" rel="nofollow noreferrer">more popular</a> to capture with the d pawn because it gives your queen an open file, and keeps your pawn structure a little better (two pawn islands instead of three).</p>
 342: <p>In my opinion, always capture towards the center when possible in the opening with your pawns. There are caveats to this of course, such as making sure to immediately capitalize on your advances by ensuring no pawns remain doubled. Also if there are attacks or tempos gained from not taking towards the center then by all means go the other way.</p>

<p>However, I would like to know why you would play <code>4. a3</code>. To me, it seems like a blunder. I think that you should probably play Nd5 there.</p>

<pre><code>
[fen ""]

1. e4 e5 2. Nf3 Nc6 3. Nc3 Bb4 4. Nd5
</code></pre>

<p>I like this because it attacks the dark bishop for Black and gives White a nice tempo and some increased control over the center. More than likely Black will play Nf6 here, although Be7 would be possible to see as well. Either way it is beneficial to remove the bishop from the game.</p>
 672: <p><strong><code>bxc3</code></strong> gives you a <strong>majority of pawns in the center</strong>, and support for the pawn break <code>d4!</code>, possibly pushing <code>c4</code> and <em>still</em> having d4 pawn-supported. Big advantages in the long-term.</p>

<p>With <code>dxc3</code>, you're right, the bishop is free, but with fewer pieces on the board, and Black to play, it's <strong>not much of an advantage</strong>. The file for the Queen, “attacking” the <code>♟d7</code>, which belongs on <code>d6</code> where it is well defended, is worth nothing, and the possibility of castling queenside is not very relevant either (e.g. Black traded his f2- and h2-threatening bishop)</p>

<p>Also keep in mind that the <em>c</em> pawns are doubled for the time being, and you don't want this situation to last until the endgame. It will be a lot easier to <strong>trade the <code>♙c3</code> on the <em>d</em> file</strong> than trying to support the <em>b</em> pawn, or merely blocking the <em>d</em> file for Black.</p>
 72: <p>Either is fine. <code>bxc3</code> gives you a strong chance to push in the center successfully. It leaves a dangling pawn on <code>a2</code>, but by playing <code>bxc3</code> you should already have resigned this pawn's fate to some sacrifice for a tempo later in the game. Note you can not play <code>6. d4</code> right away since black's response will most likely be <code>5. ... d5</code> or <code>5. ... Nf6</code> putting pressure on the <code>e4</code> pawn which is awkward to defend for you at this point. You should most likely respond <code>6. d3</code> which dashes any hopes you had for a pawn charge to <code>d4</code>. Also, black can exert pressure on the doubled pawn at <code>c3</code> which is also a bit awkward for you to defend. </p>

<p>I personally would play <code>dxc3</code>. It is less committing. You no longer have to hope to pry open the middle with your pawn majority, and you have no dangling pawn you have to sacrifice eventually. You've opened up strong lines for all three of your white bishop, your dark bishop and your queen. Note this may seem not that important, but keep in mind your opponent just traded one of his bishops for your knight. If you can open up this game, you will have a strong edge on your opponent. Any attack on your <code>e4</code> pawn can now be refuted, such as <code>5. ... Nf6</code> comes in with a strong pin <code>6. bg5</code>. Also, it no longer looks silly for your white bishop to travel to <code>d3</code> to defend <code>e4</code>.</p>
