Endgame Percentages

To check out GM Muller's credentials AND to see the following statistics "normalized" to add up to 100% (this table percentages add up to 53%) AND to find out what "normalized" means and why this table only adds up to 53% see my blog  http://www.chess.com/blog/NimzoRoy/endgame-percentages  

SOURCE: Fundamental Chess Endings by GM Muller & Lamprecht 2001  

A tip o' the hat to Wafflemaster for contributing the following quote that directly precedes the table below in its original source Fundamental Chess Endings by GM Muller & IM Lamprecht © 2001 

"You don't trust statistics?  You are probably right, but these are based on a well-edited database that contains nearly 1.7 million games mainly from the last two decades.  Our aim here is to see how often we can expect to get a particular type of ending in our chess career.  There is no definite answer as we are talking about probabilities and the answer might also depend on your style and choice of openings.  However, some endings are certainly m ore likely to arise than others.

We searched for endings that were on the board for at least two half-moves (a very short time: just one move by each player).  If you search for longer-lasting endgames the numbers drop rapidly.  Let's take all ending from the database as an example: 

Half moves | Quantity
2   -------   142 488
10  -------  111 534
20  -------    80 990
40  -------    34 693

Stigmatisert, I think your first option is the correct one.

But what is Kt?

Kt is old notation for N, the knight.

The implications are clear. If you want to study endgames, study rook endgames.

Further thoughts: R+B v R+B (both same and opposite colours) is almost twice as frequent as R+N v R+N, and both constitute vast swathes of all endgames, so those endings are important. R v B and R v N have a similar ratio too, and a fair frequency. B v N endgames are another significant chunk of the lot, so it's important to learn when which piece is better. Q endgames are only about 9.4% (normalised version) of the time, and most of those cases can be handled by the concept "perpetual check".

Rook endings are more important than minor piece endings. And always learn the fundamental pure pawn endings, as those are the basis of everything else. (Percentages of pure pawn endings not given, but I'm guessing it's part of the missing 47%, and even then most of the other types would simplify to these cases were it not for resignations.)

Stigmatisert that's a good question - go look it up yourself! What do I look like it, Mr Know-it-All? JK!! Keep on reading...

I think I read somewhere or other that they went thru a BIG DB of several million games (the program and/or PC actually did all the work of course) and the percentages indicate how often the listed ending showed up in the DB. BUT all the figures in the table above only add up to 53%, and someone at chesstempo.com "improved" the data to add up to 99.9% but I dunno how - I'm trying to get a hold of him to find out. I'm also handicapped by not having the book the data comes from, so who knows how much info we're missing here? Still, I think their findings are probably accurate enough to draw important conclusions from ie endings with one or more rooks are very common with and without other pieces and/or pawns; B vs B endings are relatively uncommon etc etc. Go to my BLOG which has more info and is not yet finished (I hope)  http://www.chess.com/blog/NimzoRoy/endgame-percentages

Good point fyroegef Math isn't one of my strong pts (if anything is) and it might have taken me a month of Sundays to figure out your explanation on my own (or longer). Here's a direct quote from the person who did "normalize" the results (without describing how) It looks like what he's saying jives with your explanation on how to end up with results adding up to 100%  (or vice versa) without your explanation the quote below didn't really register with me when I read it previously:

The original data (Müller, Karsten; Lamprecht, Frank (2001), Fundamental Chess Endings, Gambit Publications, ISBN 1-901983-53-6) had percentages were games that went into those particular endings, rather then the percentage of endings. I've normalised them to 100% so that it now shows the percent occurance of a particular ending if the game gets to that stage. Some of those are drawn, so they could be removed and the data re-normalised.

Woa, B vs B happens much rarer than I would have thought.

And Q vs Q, a tad more often.

Other thing that looks weird to me : bishop vs pawns more often than knight vs pawns ?

What's at 0.81? It says R vs. 2?

If I understood this correctly it is wrong to say 47% ended before the endgame. The reason is that the same game can be counted for several types of endgames. For example a rook endgame that turns into a pawn endgame and then turns into a queen endgame (promotion) would be counted 3 times (I hope the middle of the rook trade does not count as R vs pawns). If this is the case it would be even harder to get to a conclusion.

"...had percentages were games that went into those particular endings, rather then the percentage of endings."

So I'm guessing fyroegef's assumption that the other 47% ended before the endgame is correct, based on this phrase. But Martin0 has a good point on double counting endgames that simplify to other types.

More info also was added above the table

It was based on that sentence I think it should be double counting games with several endgames and if that is the case it would not be 47% games that ended before the endgame (although the idea is correct why it isn't 100%). If we for example would assume there were 4 games where 1 game became both rook ending and pawn ending while the other 3 games ended before the endgame it would be

25% Rook endgame

25% Pawn endgame

And since that adds up to 50% it is wrong to assume 50% of the games ended before the endgame (75% ended before the endgame in this case)

Hm. I see what you mean with the double counting. And if the methodology quoted from FCE in the first post (NimzoRoy updated it with a quote thanks to wafflle) was used, we would get overlaps, double-counting, and even a handful of false cases (i.e. those where the material on the board was from the middle of a tactical simplification with zwischenzugs or whatnot, not representative.) How these cases were handled makes a difference (to use your example, would it be 25% each R and P endgames, 12.5% each R and P endgames, or 0% R endgames 25% P endgames? With the FCE method it's the first...)

It's also slightly fishy that R v R, R+1P v R and R+2P v R are all listed separately. Basically there are issues with this study?

I see the update, then the two half-moves at least removes simple trades to make less false endgames (although it does not take into account if it takes more moves to regain material in a trade, by for example a fork).

Having said this I think it's a good list for comparing how often endgames occur. These small details are not very important from a practical point of view (since they avoided to count a lot of false endgames in simple trades).

I don't think it's wrong the way this is presented. About every 5000th game end up with Bishop+Knight vs King, so now we really know how important it is to know how to win those endgames.

(answer : not at all)

But what if you set your live chess to "auto-knight" on promotion? :-P Learn the 3N+K v K too!

I don't see anything fishy with K+R+P vs R or K+R+2P vs R. As a matter of fact GM Nunn wrote an entire book on K+R+P vs K*. I've also wondered about the R vs R but ASSume it means with (multiple) pawns present, since K+R vs K+R =  K vs K. Maybe the Wafflemaster can help out here since he actually owns the Mueller book.

I wouldn't assume there are really simple issues with the study, GM Mueller is an endgame expert and also has a PhD in math - so I'm guessing he knows something about statistics and how to compile them correctly.

* http://www.amazon.com/Secrets-Rook-Endings-John-Nunn/dp/1901983188

The categories are arbitrary, but I don't fault him for that. What would be really informative was some info on how he pruned the data to eliminate the simple issues, but I don't see that happening short of asking GM Mueller himself. The little extract from FCE seems a very simplified version of the method.