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Question: On average, how many pawns are there at the start of the endgame?

To answer:

  1. You can choose your definition of the endgame as long as you can show a credible reference that supports your choice of definition. What I have in mind is the same as lichess which I understand to be 6 or fewer non-pawn and non-king pieces.

  2. You may answer for both sides total (e.g., 10 pawns total on average) or for just 1 side (e.g., 5 pawns per side on average).

  3. As to the sample...maybe the same/similar sample from which 38 moves average was obtained.

  • 3.1. You can pick your own sample like, say, all standard world championships except 2021. Or 21st century standard world championships except 2021

What I tried:

  • Checking out some of my recent games on lichess (that reached the endgame), I see a lot of my games have at least 10 pawns. A few of my games have 6 or lower though. I estimate the average is at least 10 pawns.

Little context:

  • I think choker has too few pawns, relative to start of the endgame of regular chess/9LX. I want to verify/disprove this conjecture by seeing the average in actual games. In particular, choker seems to have, on average, 5 pawns total for both players. This is about half what I think the average for start of endgame in regular chess/9LX is.

  • Alternative question: Is the average number of pawns probably significantly greater than 5 (total, not per player)?

BCLC
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    I find this question interesting. It's best put to people interested in standard chess statistics, not variants. – Mobeus Zoom Nov 20 '21 at 17:09
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    you do not do yourself any favours by undoing edits, that people make (often with considerable effort) to make your questions presentable, in order to restore unreadably casual language and large volumes of irrelevant extraneous details. – Mobeus Zoom Nov 20 '21 at 17:49
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    I find it interesting too (figures/types can be easily googled) and strongly suggest replacing "however" by "officers at most 9 P~=1Q~=2RR~=3NNN, any pawns, for both sides". Whereas this can be questioned, it's quite realistic aaaaand, it can be easily queried on a megabase. – Hauke Reddmann Nov 21 '21 at 18:35
  • @HaukeReddmann like how please? – BCLC Nov 21 '21 at 20:07
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    @BCLC: If it's OK for you (see above ;-) I try to edit the first paragraph. Or do you mean "how to query"? I never work with online stuff, including megabases, but if this can't be done with "internal" features of them, it can be done with Costeff's CQL system. – Hauke Reddmann Nov 22 '21 at 08:11
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    @HaukeReddmann what do you mean by 'officers at most 9 P~=1Q~=2RR~=3NNN, any pawns, for both sides'? gonna edit post to say people can choose their own definitions (as long as there is some reference to support their definition) – BCLC Dec 01 '21 at 00:37
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    OK, longdefinition is looooong: "A king doesn't have to fear mate any longer if the officer material of the opponent is not larger than 9 pawn units, which corresponds approximately to a queen or two rooks or three minor officers (or a rook and a lminor), and thus indicates the beginning of the endgame. The indicated material also approximately coincides with the standard endgame classifications - YMMV. (The material shown in Karsten Müller's "Fundamental Chess Endings" exactly coincides with my suggestion, except for Q+minor vs Q+minor.) – Hauke Reddmann Dec 01 '21 at 09:11
  • @HaukeReddmann i mean it's up to you. if you want that definition to answer that question then go ahead, but i don't really wanna make a post for each definition or to limit the post to just 1 definition. btw the definition of course has to be well-defined enough to explain to a computer. eg at most 6 pieces (except kings and pawns) total is well-defined. – BCLC Dec 01 '21 at 15:16
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    @BCLC: I haven't the software to chase after the question, so my definition is rather moot. I just wanted to suggest a sensible definition for you to adapt which is also computer applicable (I'm certain Chessbase or whatnot allows a search for this material, maybe split by type), such that you question doesn't get closed on "too nebulous". – Hauke Reddmann Dec 03 '21 at 12:21

3 Answers3

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for all games in magnus carlsen world standard and world fischer random chess championship matches (basically all world championship matches except world rapid and world blitz)

Average throughout all championships:

for all: (13+10+11+12+10+12+8+14+11+14+14+13+12+12+14+10+12+12+9+9+10+14+12+12+14+11+12+13+12+11+6+16+15+14+12+14+8+10+9+12+11+10+10+10+14+7+5+12+14+14+14+12+9+6+12+5+11+10+8+6+11+9)/(4+2+4+11+11+12+10+8)=11.1129032258... ~ 11.11

for all classical (and thus excluding 9LX huhu): (13+10+11+12+10+12+8+14+11+14+14+13+12+12+14+10+12+12+9+9+10+14+12+12+14+11+12+13+12+11+6+16+15+14+12+14+8+10+9+12+11+10+10+10+14+7+5+12+14+14+14+12)/(11+11+12+10+8)=11.5769230769... ~ 11.58

for all rapid including 9LX: (9+6+12+5+11+10+8+6+11+9)/(4+2+4)=8.7

for all rapid excluding 9LX: (11+10+8+6+11+9)/6 = 9.1666666666... ~ 9.17

Average by championship, rounded to 2 decimal places:

Championship Average
2021 vs nepo 11.73
2019 vs wesley (which was all rapid) 08.00
2018 vs fabi (classical only) 11.55
2018 vs fabi (classical and rapid) 11.38
2018 vs fabi (rapid only) 10.50
2016 vs sergey (classical only) 12.33
2016 vs sergey (classical and rapid) 11.38
2016 vs sergey (rapid only) 08.50
2014 vs vishy 10.60
2013 vs vishy 11.50

Remarks:

  1. the lowest average in all these (8 pawns) is the 1 that magnus lost namely to wesley so in 2019 fischer random world championship. of course all those games were rapid.

  2. Lowest in classical only is 10.60 in 2014 vs vishy. the 3 rapid only entries are all below 10.60: they are 08.00, 10.50 and 08.50. I guess pawns have a higher mortality rate in rapid compared to classical.

2021 vs nepo

https://lichess.org/study/1NIB7sSp

1 - 13

2 - 10

3 - 11

4 - 12

5 - 10

6 - 12

7 - 8

8 - 14

9 - 11

10 - 14

11 - 14

average: (13+10+11+12+10+12+8+14+11+14+14)/11=11.727272...

2019 vs wesley

https://lichess.org/broadcast/fischer-random-championship-finals-game-1/-/DM0hC3u1

1 - 9

2 - 6

3 - 12

4 - 5

5 - N/A

6 - N/A

average (all rapid): (9+6+12+5)/4=8

2018 vs fabi

https://lichess.org/study/fCum15PU

1 - 13

2 - 12

3 - 12

4 - 14

5 - 10

6 - 12

7 - 12

8 - 9

9 - 9

10 - 10

11 - 14

12 - N/A

T1 - 11

T2 - N/A

T3 - 10

average (classical only): (13+12+12+14+10+12+12+9+9+10+14)/11=11.545454...

average (classical and rapid): (13+12+12+14+10+12+12+9+9+10+14+11+10)/13=11.3846153846...

average (rapid only): (11+10)/2=10.5

2016 vs sergey

https://lichess.org/study/vENPCM25

1 - 12

2 - 12

3 - 14

4 - 11

5 - 12

6 - 13

7 - 12

8 - 11

9 - 6

10 - 16

11 - 15

12 - 14

T1 - 8

T2 - 6

T3 - 11

T4 - 9

average (classical only): (12+12+14+11+12+13+12+11+6+16+15+14)/12=12.3333333333

average (classical and rapid): (12+12+14+11+12+13+12+11+6+16+15+14+8+6+11+9)/16=11.375

average (rapid only): (8+6+11+9)/4=8.5

2014 vs vishy

https://lichess.org/study/nurfx2OL

1 - 12

2 - 14

3 - 8

4 - 10

5 - 9

6 - 12

7 - 11

8 - 10

9 - N/A

10 - 10

11 - 10

average: (12+14+8+10+9+12+11+10+10+10)/10=10.6

2013 vs vishy

https://lichess.org/study/9xUbdEqD

1 - N/A

2 - 14

3 - 7

4 - 5

5 - 12

6 - 14

7 - 14

8 - 14

9 - N/A

10 - 12

average: (14+7+5+12+14+14+14+12)/8=11.5

BCLC
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0

It is impossible to predict the number because there are more possible outcomes in chess than in any other game I can think of. When you play in the first 15 moves "most" games will lose 2-4 pawns and at the end of a game with Grandmasters or Masters, the number can range from 4-2 pawns on the board because they tend to sacrifice the pawns for an advantage. But for 1 advanced player and one beginner player you could end up having 6 pawns on both sides because the beginner player will most likely lose in fewer moves than 2 advanced players. If 2 beginner players are playing it could go from 5-8 because they tend to play quicker and not spend time analyzing the board.

Some people define the endgame as the last 5 pieces while come define it as the last 10-20 moves or when one player has a major advantage. When you say average you have to count all if not most of the possible outcomes so you should the number depends on the type of player (defensive or attacking), Strength of player (Rating), Time control (5 min, 30 min, 1 hr). Many GMs play defensively, and many beginner players prefer attacking their opponent's pieces. So there is no real definite answer but it depends on what kind of player you play.

SecretAgentMan
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Varun W.
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  • 1 - 'Some people define it as the last 5 pieces ' --> ok let's do 6 like lichess assuming 'it' is start of endgame ? 2 - why can't we apply what you're saying to average number of moves per game? 3 - in my own games i found the average is at least 10. was what i did somehow invalid? – BCLC Dec 03 '21 at 01:58
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    3 - Of course not. I mean number of pawns per side (Dark and light). – Varun W. Dec 03 '21 at 03:20
  • Varun W. - rephrase: in my own games i found the average is at least 5 per side. was what i did somehow invalid? (FYI i didn't downvote) – BCLC Dec 03 '21 at 11:54
  • what happened to your comments? btw i said before i didn't downvote but i newly downvoted because you didn't answer my other questions eg about the number moves of per game. (weird how downvote explanations get removed it's like how can answers improve otherwise?) – BCLC Dec 04 '21 at 20:17
  • I did not delete my comments but where are there – Varun W. Dec 04 '21 at 21:10
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    I really don't think the answer is impossible to find. Just get a set of games and look! Yes, it will vary by player, but there's still going to be an average. – D M Dec 05 '21 at 14:19
  • Yes but this question is asking for ALL games not by player – Varun W. Dec 05 '21 at 15:28
  • Varun W. not every single game in history. hmmm....what do you suggest? a specific sample size like say world chess championships? – BCLC Dec 05 '21 at 20:32
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    Oh could you please update the question to just world championships. – Varun W. Dec 06 '21 at 00:03
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    Also, could you please define your definition of endgame like as a recordable way not opinion based. – Varun W. Dec 06 '21 at 00:12
  • Varun W. ok edited post. you can choose your own sample eg world championship games except 2021. definition of endgames you can choose for example 6 pieces (except kings and pawns) or less. and ok fine i'll remove my downvote – BCLC Dec 07 '21 at 00:34
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Not on average, but in general, there are 1 to 6 pawns in the endgame (7 and 8 excluded because that is statistically impossible.

user30492
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    I don't think 7 and 8 pawns are statistically impossible at all. Players can just exchange all their minor and major pieces if they wanted to. Also, you have now included all possibilities of pawns... e.g. 1-6 and not 7 or 8, which doesn't really answer the question! – odinchess.com Dec 07 '21 at 23:01
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    any references? statistics? and is it 1 to 6 per player? or total? no offense downvoting until this is clarified – BCLC Dec 08 '21 at 00:48
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    What is the basis for your answer? – SecretAgentMan Dec 20 '21 at 21:17