Monday, December 26, 2011

Statistical relevance

I don't know how exactly CT has extracted their tactical problemset from a database of real games. Hence I don't know if their problems represent the statistical occurence in real OTB games.
But let us assume that it is true, for the sake of reasoning.

Rating distribution of tactical problems

Why is this actually a bell curve? Wouldn't it be logical that the simplest combinations occur the most? This looks like it is the result of filtering by CT.

There are only about 25 different tactical elements (pin, skewer, etc.) which combine to combinations. There are 25 x 25 = 625 combinations of 2 tactical elements. 15,625 of 3 tactical elements and 390,625 of 4 elements, 9,765,625 combinations of 5 elements .

There are two strategies to handle this increasing amount of possibilities:
  • Learn those 9,765,625 positions by heart.
  • Learn to reason logically with only the 25 elements.
In the beginning the easiest progress is made by the first method. I assume when both Munich and I had our haydays with improving 200 points in under 3 months, we were working according this method. But if you have more than 100K problems under the belt, like me, you start to fall victim of the law of diminishing returns. Hence I am trying to apply the second method now.

For the second method it is best to focus on high rated problems. Just to minimize the effect of learning new patterns. Since if I learn pattern 317,516 on top of the 317,515 I already have, how will that improve my rating? By 1741/317,515 ratingpoint? I must learn to reason instead!


  1. A tactic is usuall used only once at CT. Otherwise a 4 move tactics would come with an more easy 3 move tactics and a even easyer 2 move tactic and of couse the 1 move tactic. Then easy tactics would be more often.
    The tactics are generated by real games, so the tactic is result of a blunder.The Games of databases are from "better" players and not (that much) from beginners, their blunders are usually of "higher" quality.
    I am not that shure that its all about learned pattern, i think creating chunks by learning tactics is of importance too.
    The quantity of learned chunks can be measured in "ability to remember ( tactical ) chess possitions fast and complete.
    I did start at CT with standard tactics training = "focus on high rated problems. Just to minimize the effect of learning new patterns.". My standard rating did get up higher and higher... but my Fide estimate based on standard did go down and my Blitz rating did not change. The CT-Blitz-Rating is better correlated to the OTB-Elo then CT-Standard-Rating. My problem was: I was just getting slower and slower.
    If you realy benefit from your training then your fide estimate based on Blitz and based on Standard have to raise. If not ... April fool... :-(

  2. @Aox,
    the logical order is:
    First do it correct.
    Second do it fast.

    Now you have given up the first, what on earth are you speeding up?

  3. After plateauing for a long time in tactics, i found my way to improve again. Its slow, but i hope to improve the speed too.
    I think the most important thing is, to find a method to see the results of the training as quick as possible. If you are doing several different trainings between your checks of your progress then you never know what realy is responsible for the progress. My experience at the moment is, that there is seemingly a delay between training and response=improvment ( or opposit! ). That makes it even more complicated.
    It did take me more than 1 year to see that intense Standard dont help me. ( but its fun ;-).

  4. You keep talking about these elements why don't you expound on them a little bit more? I'm sure we all use elements (I call them indicators) that point us to the type of solution to the problem. Solving based on indicators is usually super easy when you are doing a really low rated puzzle but as the problems get harder I think it becomes more difficult to un-earth the solution. They help give you direction but you really need to be able to knuckle down and calculate, calculate, calculate. Anyways, can you post a recent game of yours (non-blitz)? Maybe tactics isn't even where you need to improve upon to gain strength? Just a thought...

  5. The tactics come from real blunders.
    In the CT database are only blunders that really have happened (if they were really punished is a different story. If not, at least it was a missed opportunity).

    The database contains approx. 2 mio games.
    The database contains almost only expert players. If you put the filter "2200+ vs 2200+" than approximately 1 mio games (= half of all games) are still there.

    It is amazing, that the average blunder is not 2200 FIDE elo rated (= approx. 2200 CT Blitzrating), but rather 1400-1500 (measured in CT Blitzrating).
    Of course such expert players are not very often so stupid to do a blunder such as a CT Blitz rated puzzle of 600, hence it makes sense that the ultra easy puzzles are getting smaller in numbers (= bell curve).

    But even ultra easy blunders obviously happened.
    These blunders could have happened under severe time pressure, or the games in the database can be rapid games or blitz games (then again, I doubt it contains blitz games of A-Class players. If Blitz, then certainly only GM-Blitz-games.)

    The CT database contain proportionally more check mates in the distribution of tactics. The reason lies in the (former) search approach. Richard assumed most deceisive tactics at the end of the game, just before a side resigned.
    Meanwhile he changed this search approach. Still, mates are a bit overrepresented. Also: Richard did not include many possible tactics because they are not forcing enough (too many alts, with too similar evaluation. Richard prefers the best move to be way better than the next alt-move. And a tactic must achieve at least 1.75 pawn-units in evaluation.)

    Aox and I have the impression, that higher rated puzzles often consist of more patterns than very easy puzzles. Reason: there are more side variations, and the nature of one pattern is not so stricly basic clear but a bit more mixed. (example: the solutional move is a fork and a pin (exploiting a pin) at the same time.
    But it is not like you think, that the difficult puzzles have many many tags within them. There is just the tendency of more tags to be applied, but there are still very difficult rated puzzles that are simply to considered as "fork". No other tag.

    So, I dont think, the arithmetics of 25x25 = 625 combination of tags are not so much present as tempo suggests. There is only a slight tendency of more patterns mixed in higher rated puzzles - but it is just a little tendency.

    What to conclude from all this? I dont know myself.
    But I think we are on the safe side, if we dont do too uncommon patterns with your guidance training. Too uncommon are puzzles, that contain very seldom patterns (or seldom guidance contexts), so even masters will often not be able to solve them.

    Each discovered that typical pattern have their typical own rating.
    There is the typical rating range of CT Blitz rating between 1300-1400 for a typical check mate smother with Q+N (check mate by suffocation).
    Hardly not before this rating range, and hardly not after.

    I have not much experience with high rated puzzles, though.