Does anyone know what percentage of 7-piece endgames are draws?

I was recently thinking about the endgame tablebases. There's a really nice website which allows you to input an endgame with 7 or fewer pieces and see the theoretical state of the game.

I wasn't sure where to look, but I was wondering what kinds of statistics have been collected from this data. For example, what percentage of games are draws (with/without the 50 move rule). The best I could find was this blog post which only discusses the 5 piece table base, and also didn't include more general statistics.

My thought is that this could give some insight into the theoretical state of chess overall. If we imagine that theoretically perfect play leads to one of these endgames randomly, then we can asses the likelihood that chess is a theoretical draw.

I would download the tablebase and look for myself, but I do not have the resources to store and parse over 8 terabytes of data.

They have the 7 piece tablebase here too.

The raw data would require some processing. I think you'd want to weight it by factors such as number of permutations and frequency of occurring in practical play. For example in games that reach an ending, rook endgames probably account for something like 50%. I understand you're interested in the theoretical, but for example, it's sensible that rooks are saved for so long considering they (probably) gain more value than any other piece as the game progresses.

As for endgame knowledge giving some intuition about whether perfectly played chess is a draw, when you study endgames you discover that when everything else is equal, being a pawn ahead is typically not enough to win (the exceptions being knight endgames and pawn endgames in which being a pawn ahead is often an overwhelming advantage). The drawing margin of chess is fairly large.

I would guess that only a small percentage are draws.

The tablebase has to include all kinds of ridiculous unbalanced positions along with a relatively small number of balanced positions.

Yeah, Q+B+N+R vs lone king for example. When dealing with all possible positions, the majority won't be balanced. That's a good point to make.

We can't necessarily rule out the possibility that maybe, with perfect play, black would have to sacrifice a ton of material right before the endgame in order to delay mate as long as possible. Of course, no human would play like this because it is obviously easily winning for the opponent.

Besides, I don't know if the massively imbalanced endgames would outnumber more balanced endgames. It seems like there are more permutations of things like Q + N vs Q + B or R + N vs R + N + Pawn etc, than perumations of positions where one side has an overwhelming material advantage. Like if you randomly deal playing cards, it is generally more likely that everyone gets a roughly mediocre hand, than one person getting a full house. Although, we'd have to look at the tablebase to know for sure.

In any case, it would be interesting to see the data with positions where one side has an overwhelming material advantage excluded.

Using your cards example... its more likely people get very imbalanced hands (both high and low cards) and not 4 of a kind.

In chess it's the same way. Taking legal positions at random, it's very unlikely to get something balanced... it's just common sense.

You make a fair point, what I wrote was a bit naive. Of course, positions where material is exactly equal are unlikely in the same way that positions where one side has an enormous material advantage are unlikely. What I'm saying is that I expect most positions to have a relatively slight material advantage for one side. The question is whether this material advantage is more often winning than not.

Let's play a game where we draw chess pieces at random. I draw from a bag of white pieces, and you from a bag of black pieces. There will be a total of 6 pieces (leaving kings out).

Here are the 5 equally likely categories where e.g. 3, 3 means I get to draw 3 and you get to draw 3:

5, 1
4, 2
3, 3
2, 4
1, 5

So first of all, there is only a 1 in 5 chance we'll have the same number of pieces.

But now we draw. Ok, I get 4 and you get 2.

I draw 3 pawns and a rook for a total point count of 8.

With your two pieces, how many combinations add to 8? Well, only a rook and a minor piece. So the odds are 6/15 * 5/14 I think (about 14%) that you draw this.

And even then, RPPP vs RN? How many of those are draws? Not many. Too imbalanced.

Yeah, actually I think you're right llama51. Sorry I'm being a bit dense. Most random endgames games will probably be winning then. It would still be interesting to know if the proportion of draws is higher than we might expect or how things change when we remove majorly imbalanced positions.

Oops, I counted times where you draw two rooks or two knights. I think it's a bit over 7%

But yeah, most positions are silly.

Regarding the opening post -
first if 'endgames' are qualified as positions - well then its a big number.
If they're qualified as 'sequences of moves' or 'games' then its a much much higher number.  An unmanageable number?
Well supposedly the 7 piece Szygy and Lomonosov tablebases have 'solved' all 7 piece positions and 'games' too - (except for castling and en passant considerations) ....

Many of the positions would be materially very Lopsided -
and those are mostly Not going to be draws !
Plus - all positions could be subdivided into 'material situations'
Even with just seven pieces on board - there is going to be a big number of 'situations' - before even considering where the pieces are placed.
Legally placed that is.  Supposedly the tablebases have already taken care of that.
But materially unbalanced positions are going to outnumber materially balanced.
Most 7-piece would not be draws.
But that needs some qualification too.
So many of them would be 'silly'.  
Like 5 pieces against Lone King - where that King should have resigned a while back.
5 knights.  5 Queens.
Three queens against two defending pawns.  

Doing just a little of the math for 'critical' positions though ...
5 pieces besides Kings means somebody has at least one extra piece more.
And if material is otherwise balanced - then that extra piece - whatever it is - is still going to be enough to Make the Win in a lot of the cases.
If its a Queen or rook - its getting more obvious (the King that's up material will have to escape checks though - that'll often be the main issue)
If the extra piece is a pawn - its getting tougher.
Issue:  if the pawn can promote or threaten to - then the defender will have to give up a piece for it then.  So that's two pieces against one then left.  So then it mainly depends on what those two against one pieces Are.
If they're all minor pieces - you've got a draw.   Rook and bishop against rook - very tough - very 'pivotal'.   Queen and rook against Queen? 
Win.  Could the defender get a perpetual?  Sometimes.

If the extra piece is a bishop or knight - that's getting more drawish. 
But not necessarily.  If the other four pieces are two pawns each - you know where that's usually going.
Piece-up Won ending ! 

All tablebases don't take castling into account, but en passant is definitely considered. You can test this yourself on Syzygy or Nalimov (Lomonosov has been down for a while).

en passant is 'considered' ?  Does that mean they've 'totally taken care' of that in the tables?
When reading the Wiki article about the tablebases - they did not seem to explicitly say that castling and en passant were taken care of thoroughly.  In a messy way - they seemed to indicate the opposite.
But perhaps there's a newer more updated Wiki article or other article that addresses that.
It speaks to the immense difficulty of the task of solving that they had to skip castling possibilities onboard - to get the job done.
Castling would only figure in a small percentage of positions but they had to skip it.

In another forum - somebody has been talking for weeks about the computers doing many 'nodes per second' means chess could be 'weakly solved in five years'.  I'm not buying that though - and nobody else there seems to be.  

The main Wikipedia article on Tablebases seems very clear on the issues of castling and e.p.:

Tablebases assume that castling is not possible for two reasons. First, in practical endgames, this assumption is almost always correct. (However, castling is allowed by convention in composed problems and studies.) Second, if the king and rook are on their original squares, castling may or may not be allowed. Because of this ambiguity, it would be necessary to make separate evaluations for states in which castling is or is not possible.

The same ambiguity exists for the en passant capture, since the possibility of en passant depends on the opponent's previous move. However, practical applications of en passant occur frequently in pawn endgames, so tablebases account for the possibility of en passant for positions where both sides have at least one pawn.

But what about 'account for'?
And 'same ambiguity'.
To 'translate' that - would you agree it would have been better to say something like -
"They Totally solved for 7 pieces - with all possible en passant situations included in the Solving - but they had to skip castling possibilities.  It just wasn't feasible."
Then the question:  What about six-piece ?  They 'had to' skip castling there too?  Do I care?  No.  Point:  Something 'fishy'.

@Rocky64 - I appreciate you posting that.
While you were doing so - I was posting something else and our posts crossed - so I'll delete that - and post it under.  

@Rocky64 please note I edited and added to my post above.

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Some may say - 'hey we already covered that !'.
Maybe - but things can be put differently.  Everyone has their own way.
Like this:
Perhaps - in this particular forum - the idea of seven pieces on the board means somebody always has an extra piece and that will often be decisive and mean its a Win -  will be discussed more.
Most 7 piece would be even more lopsided than that. 

Am I certain of that?
When you start setting out the big series of 'material situations' terms each also expressing its number of possible legal positions that can be generated - that are all possible in 7-piece ...  there'll be one or two in the middle of the series that are least unbalanced ...  and is there a possibility that the number of positions arising from those one or two situations - outnumber all the other situations  ?
Frankly - I don't see how that would be possible.
It wouldn't be so.
Would such positions be more likely to arise?
Because whoever has already resigned - in the more unbalanced positions?
And because some of the more unbalanced positions are 'silly' ?  
That would be plausible.  Reasonable.
But not least unbalanced legal positions outnumbering the possible others. 
Unrealistic !   
Maybe whoever didn't claim that - didn't say it.  I'm saying that.

No worries! 

from the previous post:
"a much greater proportion of seven piece endgames that even amateur players might actually arrive at is going to be nearly balanced."

Its still three pieces versus two.  That's quite an imbalance when its averaged in.
Its a great topic though.
It promotes controversy !  

Why would people play on - if its 'a draw' ?
Usually - when simplified positions continue on in a game - one side is playing for the win and the other side is defending.
Most of the time - the side with only two pieces against three is going to be the one looking for the draw.
And if that side has only one piece against four - why is the game continuing?
Only because of some weird situations that can come up ...
maybe the side with four is short of time.
If one side has four isolated pawns that aren't too advanced and the other side has a rook - then it might be the side with the four pawns that's trying to draw.
Regarding the forum topic and does anybody know?
Well if its in the tablebases and was stated here - I missed it.  I'll look again.
If its not stated here and hard to find in the tablebases ... 

"Tablebases assume that castling is not possible for two reasons. First, in practical endgames, this assumption is almost always correct. (However, castling is allowed by convention in composed problems and studies.) Second, if the king and rook are on their original squares, castling may or may not be allowed. Because of this ambiguity, it would be necessary to make separate evaluations for states in which castling is or is not possible."

I think the glitch about castling is very suspect.
If only a low percentage of 7 piece positions would in theory have castling positionally possible - then why did they factor it out?
Gets even more suspect when its considered they allowed en passant in.

It would be like factoring out double check.  Doesn't come up very often - doesn't mean you would taint the tablebase projects by skipping it.