user224: (Originally I hoped a lengthy prologue would not be needed here, but some of the answers and comments have led me to write one so that the purpose of the question is clear, thus this is now much longer.)
When my child was around six or seven years old, I taught them the rules of the game and basic principles of opening play. At the time, chess didn't seem to hold a lot of interest. However, move forward a few years, and playing with school mates after classes were over led to an interest in the game. Quickly the kid rose above the novices at school and could even beat the teacher. Games between the two of us became competitive, even though I usually - but not always - win. The kid played a few tournaments: in the first 8 the kid had positive records in all but one, which was an open where all opponents were adults with ratings 300 to 500 points better with one exception - an unrated player. There are three trophies on a shelf from these tournaments, including first place from the beginners section of our state scholastic championship. Along the way, we signed up for a year of chess instruction from professional instructors. Also, the kid watches videos online about all aspects of the game and has worked through at least one well respected chess book. It is clear that the kid has a decent understanding of opening principles for someone at this level.
At tournament nine the kid had a bad day. One game in particular stands out: The opposing player opened with 1) a4 ... 2) h4 (or something similar, I don't have the scoresheet). Ultimately, the other kid won the game because my kid didn't know how to respond and got rattled. In some ways this isn't surprising, as any time any person encounters an unusual situation they can get confused and make poor choices. 
Don't get me wrong, I certainly want my youngster to learn good chess principles. I don't want to play first moves like a4, h4, a5 or h5, in serious games, nor do I want the kid to do so (at all).  However, I've seen other games opened this way by players just learning the game (or using strange openings to confuse their opponents). In order to boost my kid's confidence and provide experience against games like this, I want to (occasionally) play openings at home that may be seen in games at this level. I don't expect to win these games, but that isn't the point: The point is to provide an experience that will benefit the psychological aspects of my kid's game if another player tries a similar opening in the future. Thus, I'm seeking some guidance on strange openings like 1) a4 or 1) h4, that I could at home play against my kid to help prepare for future tournaments.

user3495: I'd like to give a more complex answer. I will give an opening that was played frequently [at least by the standards of off beat openings] at the highest level by people of Grandmaster Strength. That is the "Julian Hodgson" Trompowsky. 
1. d4 Nf6
2. Bg5 Ne4 
3. h4 
At GM level against GM opponents that is the only opening that I can think of where a rook pawn move is for practical purposes playable. From an absolute theoretical point of view it will get the 3. h4?! symbol for dubious. But it is not clear over the board how to meet it as black and get any advantage. Hodgson, a strong GM, was also a specialist in the Trompowsky and he used 3.h4 a lot here in the 1990's. I haven't got the statistics offhand of his record with 3.h4.  Apologies for not giving a diagram; not my strong point but could use one. 
Obviously at the elite professional level of chess players are not usually going to open on the first move with a rook pawn. But a few moves later as here is possible. Of course if someone wants to be a smart alec and say well there's the fourth move of the main line Spanish then you can go ahead lol. Sorry that is a chess joke.  

user19174: Actually, it doesn't matter how your opponent play the opening. You should teach your students to main aspects of the chess. In the opening, the goals are very clear. There are (mainly) 2 important things: 

Importance of the center: Try to take control and dominate the center 
Development: Try to develop your pieces as fast and as effective as possible - generally in order to their values. (pawns first, knights and bishops after, rooks and queen followed)

If you or your student basically apply the opening rules especially to an opponent who don't, then it can be an easy win with hight possibility. You would enter the mid-game with a big advantage and turning it into a clear win is up to you.

user12523: How can 1.a4 be bad, when some guy named Magnus played it against a grandmaster and won? :-) See Carlsen-Radjabov (2012), from the World Blitz Championship.
Now, I don't think it counts as much preparation, but my rule of thumb against kids who open with 1.a4 is ...e5 and against h4, ...d5. I think ...e5 and ...d5 are both legitimately good moves, but the reason I pick the one opposite to the rook pawn is that I've seen those kids love their rooks, and their plan is often an early rook lift to a3 or h3, and they often to forget to look out for ...Bxa3 or ...Bxh3. Admittedly, this "trap" only works at the extreme beginner level, but that's the level where I've seen this opening (I haven't played against Magnus Carlsen), and if they don't blunder I didn't lose anything. Anyway, two things you could try if you want to simulate this kind of game against your kid are the rook lifts already mentioned, and early pawn storms.
Back to the original question, what's an "effective" rook opening? It seems to me that non-beginners who play such an opening basically treat it as a waiting move and then play a normal opening (the Carlsen example is basically a Four Knights Game after the 1.a4), perhaps trying to transpose to something where the move is useful. With 1.a4, you are roughly giving up a tempo, which means losing the first-move advantage, but at low levels of play this is not very important. Moving the h pawn may be worse because it has a bigger effect on king safety.

user8063: I made a terribly long book study of well-known and lesser-known unusual openings to contend with my grandpa's massive advantage in opening theory. He could match me in general openings, but I specialized. I would get the upper hand in the opening because he had no idea how to play against what I would produce. Of course he was still better than me and the game would turn around in the mid game ...
I can say categorically as follows from my book search:

There are no known remotely good openings starting with a2-a4.
The best response to a2-a4 is to advance the c, d, or e pawn two squares. I favor the c pawn because I favor the Sicilian defense, not because it's actually any better.
The best way to play if you start with a2-a4 is to play a center-pawn opening with a wasted move. That is, you're now playing the matched center-pawn opening as black. It's possible that pushed pawn will be useful later, but probably not.
If a rook is brought out early, it is likely to be chased around by minor pieces and can't meaningfully participate in the center battle.
Don't deploy anything to b6.
If a4-a5 is played, play a7-a6 in response.

If you really want to give your youngster some practice on this, play it and bring the rook out until he learns to chase it around. This play is unsound, but that's the point. Defending unsound gambits is something that needs to be practiced later on, so why not this now given your youngster is already facing it.

user18809: Your kid did not lose the game because he did not know how to respond to that opening. He lost the game because he played worse! (by the way you're telling the story, probably because of a tactical blunder) I don't really think there is any human being on the planet who has prepared a line against 1.a4
I wouldn't really have a clear preference for any "rook pawn" opening. 1.a3 is sometimes played at "high" levels, as it could transpose to other openings where the a3-push is useful. h4 is a common attacking move, but only after Black has castled or, at least, moved the "g" pawn

user18998: I'm seeing a lot of great answers being met with, "This doesn't answer my question" - so I'm going to go ahead and answer your literal question (even though the answer won't help you out at all.)
a4 is the strongest opening rook-pawn move. In tournament games, it still leaves white with a slight edge to winning (28.9% to 25.8%) which is much smaller than good moves and nearly concedes the entire advantage of going first.
a3 is the next strongest of the four, and leaves black with a slight edge.
h3 and h4 both leave black with a considerable lead.
Now, that that's over with, will you finally listen to why this doesn't matter?  If you're concerned with training purposes, you don't want to train against a4 specifically.  What you want to do is occasionally pick some purposely strange opening decisions that your kid has never played against.  Did he reply to your e4 with the sicilian?  Then try playing 2. b4 against him and see if he keeps his head.
That's why everyone is saying "Teach him opening fundamentals."  Because you're not going to be able to train him on how to react to every strange/atypical opening move.  There's simply too many of them.  What you can train him on is how to react when your opponent starts doing stuff you don't expect.

user18421: Learning good chess principles and playing against clearly dubious openings like 1. a4 or 1. h4 are not mutually exclusive.  In fact, following solid opening principles is the best way to counter weak openings like this.
The moves 1. a4 and 1. h4 are both poor because they do not follow any of the opening principles.  Namely, they do not help control the center, they do not develop or prepare to develop any pieces and they actually reduce the king's options as to which side to castle on by weakening the pawn cover on one side of the board.  
To counter such a move, you should simply play normal opening moves.  1... e5 or d5 is a good start.  If white allows it, you can take over the center by advancing the other central pawn two squares as well.  Then simply continue by developing the minor pieces and castling the king to safety.  At this point you will have a large lead in development if white has continued making many foolish pawn moves (which is likely against the type of players who open with 1. a4 or 1. h4) and should be able to make life miserable for the opponent.

user4418: 
Are there any openings with rook pawns that are more effective than
  others?

There are few recognized openings which start with a rook pawn move on move one, except in circumstances where the opponent starts with a double knight pawn move, because those are generally inferior moves on move one. 
One example where it is good is if white plays the Sokolski Opening (1. b4). Then 1 ... a5 is a good response.
However they are more common later on in any opening where your opponent fianchettos a bishop because challenging the fianchetto with a rook pawn rush is worth considering if it does not weaken your own position too much.

224: <p>(Originally I hoped a lengthy prologue would not be needed here, but some of the answers and comments have led me to write one so that the purpose of the question is clear, thus this is now much longer.)</p>

<p>When my child was around six or seven years old, I taught them the rules of the game and basic principles of opening play. At the time, chess didn't seem to hold a lot of interest. However, move forward a few years, and playing with school mates after classes were over led to an interest in the game. Quickly the kid rose above the novices at school and could even beat the teacher. Games between the two of us became competitive, even though I usually - but not always - win. The kid played a few tournaments: in the first 8 the kid had positive records in all but one, which was an open where all opponents were adults with ratings 300 to 500 points better with one exception - an unrated player. There are three trophies on a shelf from these tournaments, including first place from the beginners section of our state scholastic championship. Along the way, we signed up for a year of chess instruction from professional instructors. Also, the kid watches videos online about all aspects of the game and has worked through at least one well respected chess book. It is clear that the kid has a decent understanding of opening principles for someone at this level.</p>

<p>At tournament nine the kid had a bad day. One game in particular stands out: The opposing player opened with 1) a4 ... 2) h4 (or something similar, I don't have the scoresheet). Ultimately, the other kid won the game because my kid didn't know how to respond and got rattled. In some ways this isn't surprising, as any time any person encounters an unusual situation they can get confused and make poor choices. </p>

<p>Don't get me wrong, I certainly want my youngster to learn good chess principles. I don't want to play first moves like a4, h4, a5 or h5, in serious games, nor do I want the kid to do so (at all).  However, I've seen other games opened this way by players just learning the game (or using strange openings to confuse their opponents). In order to boost my kid's confidence and provide experience against games like this, I want to (occasionally) play openings at home that may be seen in games at this level. I don't expect to win these games, but that isn't the point: The point is to provide an experience that will benefit the psychological aspects of my kid's game if another player tries a similar opening in the future. Thus, I'm seeking some guidance on strange openings like 1) a4 or 1) h4, that I could at home play against my kid to help prepare for future tournaments.</p>
 3495: <p>I'd like to give a more complex answer. I will give an opening that was played frequently [at least by the standards of off beat openings] at the highest level by people of Grandmaster Strength. That is the "Julian Hodgson" Trompowsky. 
1. d4 Nf6
2. Bg5 Ne4 
3. h4 </p>

<p>At GM level against GM opponents that is the only opening that I can think of where a rook pawn move is for practical purposes playable. From an absolute theoretical point of view it will get the 3. h4?! symbol for dubious. But it is not clear over the board how to meet it as black and get any advantage. Hodgson, a strong GM, was also a specialist in the Trompowsky and he used 3.h4 a lot here in the 1990's. I haven't got the statistics offhand of his record with 3.h4.  Apologies for not giving a diagram; not my strong point but could use one. </p>

<p>Obviously at the elite professional level of chess players are not usually going to open on the first move with a rook pawn. But a few moves later as here is possible. Of course if someone wants to be a smart alec and say well there's the fourth move of the main line Spanish then you can go ahead lol. Sorry that is a chess joke.  </p>
 19174: <p>Actually, it doesn't matter how your opponent play the opening. You should teach your students to main aspects of the chess. In the opening, the goals are very clear. There are (mainly) 2 important things: </p>

<ol>
<li>Importance of the center: Try to take control and dominate the center </li>
<li>Development: Try to develop your pieces as fast and as effective as possible - generally in order to their values. (pawns first, knights and bishops after, rooks and queen followed)</li>
</ol>

<p>If you or your student basically apply the opening rules especially to an opponent who don't, then it can be an easy win with hight possibility. You would enter the mid-game with a big advantage and turning it into a clear win is up to you.</p>
 12523: <p>How can 1.a4 be bad, when some guy named Magnus played it against a grandmaster and won? :-) See <a href="http://www.chessgames.com/perl/chessgame?gid=1671724" rel="nofollow noreferrer">Carlsen-Radjabov (2012)</a>, from the World Blitz Championship.</p>

<p>Now, I don't think it counts as much preparation, but my rule of thumb against kids who open with 1.a4 is ...e5 and against h4, ...d5. I think ...e5 and ...d5 are both legitimately good moves, but the reason I pick the one opposite to the rook pawn is that I've seen those kids love their rooks, and their plan is often an early rook lift to a3 or h3, and they often to forget to look out for ...Bxa3 or ...Bxh3. Admittedly, this "trap" only works at the extreme beginner level, but that's the level where I've seen this opening (I haven't played against Magnus Carlsen), and if they don't blunder I didn't lose anything. Anyway, two things you could try if you want to simulate this kind of game against your kid are the rook lifts already mentioned, and early pawn storms.</p>

<p>Back to the original question, what's an "effective" rook opening? It seems to me that non-beginners who play such an opening basically treat it as a waiting move and then play a normal opening (the Carlsen example is basically a Four Knights Game after the 1.a4), perhaps trying to transpose to something where the move is useful. With 1.a4, you are roughly giving up a tempo, which means losing the first-move advantage, but at low levels of play this is not very important. Moving the h pawn may be worse because it has a bigger effect on king safety.</p>
 8063: <p>I made a terribly long book study of well-known and lesser-known unusual openings to contend with my grandpa's massive advantage in opening theory. He could match me in general openings, but I specialized. I would get the upper hand in the opening because he had no idea how to play against what I would produce. Of course he was still better than me and the game would turn around in the mid game ...</p>

<p>I can say categorically as follows from my book search:</p>

<ul>
<li>There are no known remotely good openings starting with a2-a4.</li>
<li>The best response to a2-a4 is to advance the c, d, or e pawn two squares. I favor the c pawn because I favor the Sicilian defense, not because it's actually any better.</li>
<li>The best way to play if you start with a2-a4 is to play a center-pawn opening with a wasted move. That is, you're now playing the matched center-pawn opening as black. It's possible that pushed pawn will be useful later, but probably not.</li>
<li>If a rook is brought out early, it is likely to be chased around by minor pieces and can't meaningfully participate in the center battle.</li>
<li>Don't deploy anything to b6.</li>
<li>If a4-a5 is played, play a7-a6 in response.</li>
</ul>

<p>If you really want to give your youngster some practice on this, play it and bring the rook out until he learns to chase it around. This play is unsound, but that's the point. Defending unsound gambits is something that needs to be practiced later on, so why not this now given your youngster is already facing it.</p>
 18809: <p>Your kid did not lose the game because he did not know how to respond to that opening. He lost the game because he played worse! (by the way you're telling the story, probably because of a tactical blunder) I don't really think there is any human being on the planet who has prepared a line against 1.a4</p>

<p>I wouldn't really have a clear preference for any "rook pawn" opening. 1.a3 is sometimes played at "high" levels, as it could transpose to other openings where the a3-push is useful. h4 is a common attacking move, but only after Black has castled or, at least, moved the "g" pawn</p>
 18998: <p>I'm seeing a lot of great answers being met with, "This doesn't answer my question" - so I'm going to go ahead and answer your literal question (even though the answer won't help you out at all.)</p>

<p><strong>a4 is the strongest opening rook-pawn move.</strong>  <a href="https://www.365chess.com/opening.php" rel="noreferrer">In tournament games</a>, it still leaves white with a slight edge to winning (28.9% to 25.8%) which is much smaller than good moves and nearly concedes the entire advantage of going first.</p>

<p><strong>a3 is the next strongest of the four</strong>, and leaves <em>black</em> with a slight edge.</p>

<p><strong>h3 and h4 both leave black with a considerable lead.</strong></p>

<p>Now, that that's over with, will you finally listen to why <em>this doesn't matter</em>?  If you're concerned with training purposes, you <em>don't want to train against a4</em> specifically.  What you <em>want</em> to do is occasionally pick some purposely strange opening decisions that your kid has never played against.  Did he reply to your e4 with the sicilian?  Then try playing 2. b4 against him and see if he keeps his head.</p>

<p><em>That's</em> why everyone is saying "Teach him opening fundamentals."  Because you're <em>not</em> going to be able to train him on how to react to every strange/atypical opening move.  There's simply too many of them.  What you <em>can</em> train him on is how to react when your opponent starts doing stuff you don't expect.</p>
 18421: <p>Learning good chess principles and playing against clearly dubious openings like 1. a4 or 1. h4 are not mutually exclusive.  In fact, following solid opening principles is the best way to counter weak openings like this.</p>

<p>The moves 1. a4 and 1. h4 are both poor because they do not follow any of the opening principles.  Namely, they do not help control the center, they do not develop or prepare to develop any pieces and they actually reduce the king's options as to which side to castle on by weakening the pawn cover on one side of the board.  </p>

<p>To counter such a move, you should simply play normal opening moves.  1... e5 or d5 is a good start.  If white allows it, you can take over the center by advancing the other central pawn two squares as well.  Then simply continue by developing the minor pieces and castling the king to safety.  At this point you will have a large lead in development if white has continued making many foolish pawn moves (which is likely against the type of players who open with 1. a4 or 1. h4) and should be able to make life miserable for the opponent.</p>
 4418: <blockquote>
  <p>Are there any openings with rook pawns that are more effective than
  others?</p>
</blockquote>

<p>There are few recognized openings which start with a rook pawn move on move one, except in circumstances where the opponent starts with a double knight pawn move, because those are generally inferior moves on move one. </p>

<p>One example where it <em>is</em> good is if white plays the Sokolski Opening (1. b4). Then 1 ... a5 is a good response.</p>

<p>However they are more common later on in any opening where your opponent fianchettos a bishop because challenging the fianchetto with a rook pawn rush is worth considering if it does not weaken your own position too much.</p>
