Ideas:

Openings

• Opening Traps
• Identifying Opening Tactics

Middlegame

• Simplify to winning endgame?
  

Endgame

• Checkmates
• Rook Endings
• Opposition
• Triangulation
• Bishop vs. Knight
• Basic pawn endings
• Advances pawn endings

Tactics

• Forks/Double Attacks
  
• Pins
• Skewers
• Clearance Sacrifice
• Decoys/Deflection
• Discovered Attacks
• Removing the Guard
• Zwischenzug / In-between Moves / Desperado

Attacks

• Opposite Castling
• Attacking f7/f2
• Mating Nets
• Attacking h7/h2
• King Hunt
• Defending the Attack

remember, these have to be positions with concrete wins, draws, conclusions. they need best lines. i think it is hard to do that with something like  "initiative".

that is more pawn endgame than initiative in my mind :) simple counting. initiative is unquantifiable.

I'd suggest that if you insist on making categories, you should try defining the categories based on the skills needed to win or draw, rather than the aspects of the position. That way it's easier for the user to see which skills he needs to train. It's better to see that you're not good at finding a winning plan in a quiet position, than to see that you mostly make mistakes in the strategy and endgames sections. So instead of picking the type of position you want to train, I'd say one should choose the skill he wants to train.

So one quick suggestion for a categorization schema would be something like:

• Simple Patterns: Simple, not to deep calculations, including for example mates in 2, 3, or simple forks, pins, smothered mates, etc.
  
• Higher Tactical Abilities: Deep tactics, where there's still a forced win of material, but which require more calculation and for example good pattern recognition
• Intuition: Long-term sacrifices; not "castling into it" when defending; when it is ok to grab (poisoned) pawns etc.
• Position Assessment: After a possible (forced) sequence of moves, who's better? How much compensation does one side have for the sacrificed material?
• Piece Assessment: How to get a piece to a better square, or how to exchange a bad for a good piece, etc.. Could also involve exchange sacrifices or pawn sacrifices, to improve the strength of your own pieces and reduce the strength of your opponent's pieces. This generally involves closed positions with no big tactical tricks yet.
  
• General Opening Play: Not getting yourself in trouble in the opening; developing pieces fast enough, placing pieces on good squares, not playing too defensive etc.
• General Endgame Play: Seeing the strengths and weaknesses of your pieces and pawn structure, and anticipating it. Using the king as an active piece when needed, placing the pieces and pawns on the right squares etc.
• Endgame Tactics: This category would basically consist of all endgames that are "over"; no deep manoueuvres anymore, you just have to know or calculate how to win or draw (like K+B+B vs. K, K+B+N vs. K, K+Q vs. K+R, K+R+P vs. K+R, but also defending K+R vs. K+R+P, etc.)
• General Attacking Play: How and when to attack; controlling the attack; adding pieces to the attack, getting rid of the opponent's defending pieces (or pawns)
• General Defensive Play: How to defend from attacks; seeing how the opponent is going to attack, and anticipate it by taking out the sting of the attack (trading pieces, adding pieces to the defense, making space for your pieces and king etc.) and then win using the material advantage you had because your opponent sacrificed too much

Your category setup would suggest that 90% of the positions are finished off by (simple) tactics. Then why play the game out against a computer? What's the difference with the Tactics Trainer, or certain courses in Chess Mentor then?

not really. tactics trainer doesn't really do things like pawn storms or long endgames, etc. the point isn't to pick easy positions with checkmate in 4, the point is you have an winning position that might take 20-30 moves to convert - can you do it? :)

Backwards pawns? ... ie, exploiting d5 in many Sicilian lines?

I'm gonna have a hard time with all this :) ... positional play is just a means to an end in my books ... If you wanna see how to set up Bxh7+ tactics ... THEN i'm the guy for you :P.

Erik,

I think you indicated that the positions will already be categorized, which provides a hint to the user just by its name, correct?  Do you also intend to let the user, if stumped, get an additional hint if he/she asks?  The reason I'm asking is because sometimes you can give a 'hint' such as, "Is there a way to place two of Blacks pieces on the same diagonal?"  The user might then find a sacrifice that lines up the K and Q, for example.  The hint also provides instructional advice, i.e.  look for moves, even if it's a sacrifice, that force your opponent to place two pieces on the same line.

Incidentally, while I found the idea of a typology based on skills needed to be initially intriguing, I think it would be quite hard to categorize positions this way.

Erik... I'm getting a somewhat muddy picture of what's wanted -- in one post you talk about positions that need "best" lines but in a later post you speak about 20, or 30 move finishes... a 20 or 30 move best line is probably not realistic in most cases outside of some endgames.  

To be clear: You don't want "white to move and win" positions -- (where the task is to find an exclamation point move or two along forcing lines in order to solve) --

You want positions where accurate play (rather than necessarily brilliant) leads to a distinct result -- a win, or draw.

The positions sought can generally be seen as: "White to move and convert his advantage --"  So we aren't looking for the tactical brilliancy so much as the correct technique. The idea is to test the player's technique in a situation that should have a known outcome. (Perhaps 'Technique test' is a good name for these positions?)

(am I in the ballpark here?)

Upon reflection, I do think some simpler techniques have a right and wrong "best line is the only line" sort of outcome...

Basic mate-tests would be like this.  For example, you've got a classic smothered mate coming from a windmilling N and a Queen sac (there's a name for it, and it slips my mind) -- that would be a relatively short "one way is the right way" sort of position (do we even want these kind, I think we do)...

Whereas a pure Q v R ending on the other hand has multiple correct solutions (all insanely hard to find against a computer, too)

Ditto for say a position test called, Queenside majority ==  there might be a million ways to win it... that's fine...  the idea is to take a classic queenside majority and promote a pawn/or win material arising from the promotion threats -- which brings up another point...  ... it'd be cool in my opinion, if in certain postions, (queenside majority for example) you were awarded credit if you acheived a certain evaluation, for example >+5.00 ... the advantage has been converted... the test has been passed. No need to take it all the way to mate.

Moving to another point:  it would be nice, I think, if it were possible to have positions 'tagged' with multiple headings... for example a Lucena ending position could be tagged as 'Rook endings -- Pawn promotion -- Fundamental endings -- Intermediate. No need to stress about the perfect taxonmy of problems if things can be sorted and retrieved by a variety of different handles.

I guess that's enough for one post.

EXACTLY

great points. basically we want  positions that are winnable with solid play. that could be a tactic, or an attack, or converting with an extra piece, or queening a pawn, or a queenside pawn majority...

you are right - it isn't where there is ONE best line. it is where there is one ADVANTAGE and you have to convert it. the simplest is just a K+Q v K checkmate. there are lots of ways to win that (and one way to stalemate it!!).

you will get a position setup against a computer and then try to win it :)

But erik, if you get positions that are "already winning", aren't you excluding 99% of winnable positions? Like the greek gift mentioned in another topic; if white doesn't play Bxh7 on the first move against the computer, and black plays f6 or g6, there's no use continuing. Basically the only positions you can put into this program are endgames...

Of course that's not bad either, but let's make it clear (for me :P) then. The only positions you want are positions where the material is already won and you have to convert it to a win(?) or positions where you're a little down in material, but not enough to lose(?).

In that case, shouldn't you also exclude your ideas "Attacking f7/f2", "Defending the attack" etc.? Either the user is able to convert it to material gain or mate, or he doesn't and gets to play out a equal or worse position against the computer.

i don't agree. i believe we can come up with positions where it will be effective :)

yes. but again, more important than stuffing it with 1,000 positions is making sure they are singularly instructive. better to have 300 KEY positions than 1,000 random ones.