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

Question

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)?

Answer 1

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)

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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

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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.

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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...

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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

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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

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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

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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

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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

Answer 2

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.

Answer 3

Not on average, but in general, there are 1 to 6 pawns in the endgame (7 and 8 excluded because that is statistically impossible.