How much do players lose in the endgame versus perfect play?

[RobertJasiek]

The word "endgame" is not defined precisely so opinions on its start can vary.

Endgame / boundary play can occur from the start of the game. The endgame phase only consists of such moves. However, during a stage first appearing as the endgame phase, play can become hotter again and middle game fighting or killing might be resumed. Otherwise, we might consider the phase between middle game and game end when life statuses are settled. Even so, non-essential stones can be sacrificed, or offered as a sacrifice, also during the endgame phase.

I consider the start of the endgame phase when first endgame considerations become dominating. The stronger one is at them, the sooner one might perceive its start.

[jlt]

Some people say that the endgame starts when the life-and-death status of each group is determined. Even more confusing is that there are differences between endgame and yose, ask John Fairbairn about that.

Moreover, the question in this thread is a bit ambiguous. Let me rephrase it in two different ways.

1) Let X be the sum of points that I lose during the endgame (thus, if I am black and if endgame starts at move 150, then X is the number of points lost at move 151 + number of points lost at move 153 +...). Estimate A=the median value of X.

2) Determine the smallest integer B such that in a game where I lead by B points at the start of the endgame, the probability that I finish the game with a victory against a perfect player exceeds 50%.

I understand that Robert Jasiek gave an estimate of A, while Uberdude's experiment gives some hints on the value of B.

However, A and B are a priori different, my guess is that A>B.

[RobertJasiek]

Does anyone have some numbers that only count each local situation once?

Local situations change and exchanges can occur. Maybe you better ask for "counting each intersection only once for both players (or for each player), even if different mistakes affect same intersections several times"?

However, how would you want to do that? Not playing in one local endgame but playing in a different local endgame elsewhere must be considered together to assess sizes of mistakes. At different moves, different combinations of local endgames are involved.

[Bill Spight]

4d:

Antti Törmänen guesses that 100+ points are often lost.

I think maybe I don't know when the endgame starts...

As has been pointed out, the boundary between different phases of the game can be fuzzy. In the endgame the board breaks up into local regions of play. OC, ko fights can cover the whole board, because of the possibility of ignoring ko threats. Ko fights aside, the endgame typically starts when large scale fights end.

[Bill Spight]

Some people say that the endgame starts when the life-and-death status of each group is determined. Even more confusing is that there are differences between endgame and yose, ask John Fairbairn about that.

Moreover, the question in this thread is a bit ambiguous. Let me rephrase it in two different ways.

1) Let X be the sum of points that I lose during the endgame (thus, if I am black and if endgame starts at move 150, then X is the number of points lost at move 151 + number of points lost at move 153 +...). Estimate A=the median value of X.

2) Determine the smallest integer B such that in a game where I lead by B points at the start of the endgame, the probability that I finish the game with a victory against a perfect player exceeds 50%.

I understand that Robert Jasiek gave an estimate of A, while Uberdude's experiment gives some hints on the value of B.

However, A and B are a priori different, my guess is that A>B.

Suppose, as an example, that there are 6 endgame plays left, that gain 6, 5, 4, 3, 2, and 1 point. I play first. With perfect play I gain 3 points: 6 - 5 + 4 - 3 + 2 - 1 = 3. Now let me make the worst move choices I can; then I lose 9 points: 1 - 6 + 2 - 5 + 3 - 4 = -9. (I could make better choices with the same result: 3 - 6 + 2 - 5 + 1 - 4 = -9. )

Versus perfect play by me, I lose 12 points. I could have played 12 points better. I think that this is the number that Antti, Robert, and I are talking about.

Versus perfect play by the opponent, I lose 9 points. Had I been leading by 9 points I would have got jigo.

-----

Earier I said that the largest endgame plays typically gain about 5 points. 6 points is close enough for illustrative purposes. Now let's multiply the number of plays of each size by 11, so that there are 66 plays. Then my loss versus perfect play by me would be 102 points, and my loss on the board would be 99 points. This example is close enough to real life that you can see how someone could lose 100 points in the endgame, just by poor choice of moves.

Edited for correctness.

You can also see how, with a lot of plays, there is little difference between the two measures of loss.

[marvin]

Thank you for your responses, I have a better feeling now.

@jlt: I was thinking about this distinction, but it seemed hard to estimate the difference and I was happy by a rough estimate.

We still have quite a big difference in the estimates...
I don't have time now, but maybe later I will search for some handicape games and try to play the endgame for both sides and compare with the end result. In this way, we should get an estimation for the change of the sum of mistakes per rank (at some rank).
I also don't know what variance per game or per player to expect, so we might get mislead by a small sample.

Or if somebody has time and will or some already reviewed handicap games, he can post it here.

[Uberdude]

Now that we have KataGo, you could use it to approximate this question. Go through the endgame moves of some player you want to test (for a top pro Katago being weaker than perfect play has more impact than for a kyu) and add up the points loss estimates per move from KataGo.

[mhlepore]

Now that we have KataGo, you could use it to approximate this question. Go through the endgame moves of some player you want to test (for a top pro Katago being weaker than perfect play has more impact than for a kyu) and add up the points loss estimates per move from KataGo.

I was thinking about something similar with Katago, in a slightly different context. In a discussion on L19 a few months back, we got on the subject of how many points would you give up to have more time than your opponent. I think it would be interesting to find high dan games online (say on KGS, where time remaining is tracked) where Katago says:
1) the game is approximately even heading into the endgame, and
2) one player has considerably more thinking time than their opponent.

Then play the game out and see how the time crunch translates into a point gap throughout the course of the endgame. You'd need to have a lot of games to get some meaningful association, and there are some problems to worry about, but it seems like a fruitful research project.

[Shenoute]

Not about perfect play but it gives a rough idea of how many points mid-dan amateurs lose compared to professional play. Go World 6 to 10 (March-April to November-December 1978) ran a series called "Professional Endgame vs. Amateur Endgame" in which the same position was played twice, pro vs. ama and pro vs. pro, with the same pro being white both times. The results were:

GW#6
pro X vs. ama (3d): W+8
pro X vs. pro Y: B+4

GW#7
pro X vs. ama (2d): W+16
pro X vs. pro Y: W+4

GW#8
pro X vs. ama (4d): B+1
pro X vs. pro Y: W+7

GW#9
pro X vs. ama (3d): B+1
pro X vs. pro Y: B+7

GW#10
pro X vs. ama (3d): W+1
pro X vs. pro Y: B+7

[RobertJasiek]

How many moves were played?

[Bill Spight]

Japanese amateur ranks were rather stronger 40 years ago than they are today. And there was still a range of 2+ stones in pro strength, so it matters how strong the pro was. And, as Robert indicates, it matters how far the game was from the end, how much each play gained at the start.

Anyway, my guess is that pro Y was 7 - 9 dan. And the numbers seem reasonable.

[Shenoute]

How many moves were played?

I don't have access to my Go World collection right now but I will update when I do. If I remember correctly , it is something like 50-60 moves.

Japanese amateur ranks were rather stronger 40 years ago than they are today.

Indeed, that's why I made sure to include the publication date

so it matters how strong the pro was. And, as Robert indicates, it matters how far the game was from the end, how much each play gained at the start.

I don't remember all the names, I will update when I get back to my GW collection. Not all pros were top pros though. One name I remember is Hotta 3p (Hotta Yozo?). Also, the players in each issue were not the same, my constantly labeling them X and Y may have been misleading in this respect.

[Ferran]

Japanese amateur ranks were rather stronger 40 years ago than they are today.

Oh?

Care to expand? What happened? Less interest?

Take care.

[Bill Spight]

Japanese amateur ranks were rather stronger 40 years ago than they are today.

Oh?

Care to expand? What happened? Less interest?

Take care.

Unless you prevent it, rank inflation is a thing. As for rank inflation in Japan, I was not there for that inflation, so I can't say why it happened.

[Kirby]

Japanese amateur ranks were rather stronger 40 years ago than they are today.

Oh?

Care to expand? What happened? Less interest?

Take care.

Unless you prevent it, rank inflation is a thing. As for rank inflation in Japan, I was not there for that inflation, so I can't say why it happened.

in my opinion, rank inflation happens much more frequently in casual environments where there isn't a strict system in place. take a typical go club in some rural area with just a few players. maybe one guy's a 3d. a visitor comes and plays a game and beats him. since he beat the 3d, he must be 4d. he goes back to his club, and when his 3d rival beats him, that rival is 5d now. something like that...

with internet go, the system is more objective, and you typically have several data points from a variety of different types of players. i think it's harder to inflate in that case.