Research idea: the longest non-trivial middlegames

I want to share a research idea, its motivation, definition and the work I've already done.

Motivation

Enough people are interested in tablebase length records (e.g. checkmates in 549 and 584 moves). As well as compositional length records (e.g. checkmate in 415 extension of Otto Blathy).

Enough people are also interested in Immortal Games, e.g. Kasparov's Immortal (14 moves long combination) and Serper's Immortal (23 moves long attack down material). As well as dirty computer games, e.g. Stoofvlees vs. Igel (down a rook for 21 moves) and Torch vs. Leela (down a rook for 20 moves).

It seems only logical to ask questions like this:

What are the longest middlegame attacks? What are the longest middlegame attacks down material? What are the longest middlegame attacks which don't use typical compositional tricks (predictable repetition such as repeated zugzwangs, running from desperado tactics, forcing the enemy king to take multiple identical tours around the board)? What are the longest King Hunts?

But not many people are asking those questions. Why?

The only problem is that "middlegame" seems hard to define. But that's a weird excuse to not be curious.

25 moves

What happens if you try to find the longest Immortal-like attacks?

After a bit of research, it seems like ~25 moves could be the length limit of such attacks in real games.No wonder that longer attacks are hard to find. Middlegames don't last forever. Especially when you're down material. "25 moves" is already an insanely long time, by middlegame standards.

Definition

So. We want to find the longest "non-trivial" middlegame wins. Forced wins.

How do we define a "middlegame"?

We don't.

Instead we define parameters which make a position look more like a middlegame (or rather less like a technical endgame) and explore the extremes of those parameters.For example:

• The more pieces are on the board, the less the position looks like a technical endgame (barring pathological examples with 100% isolated pieces).
• The more heavy pieces, especially queens, are on the board, the less the position looks like a technical endgame.

(That's pretty consistent with most definitions of the endgame.)

Those parameters need to be evaluated not only at the start of a forced win, but throughout the entire variation. If we want to look for the longest middlegame wins, we need to look for forced move sequences which maintain the largest amount of pieces on the board for the longest time. For as many moves or half-moves as possible.

How do we define "triviality"?

We don't.

Instead we define parameters which make a long winning variation less trivial, at least in the limit and in combination with other parameters. Then we explore the extremes of those parameters.

Still, you may be asking "How do we know what makes a forced win less trivial? Isn't it subjective?"

I'll argue that in a large part it's pretty objective.

Triviality parameters

One of the longest wins in chess is mate in 549.

• For 500~ moves White is up a point of material.
• For 500~ moves there are six pieces dancing on the board completely freely.

Now, what if White was down material (2, 3, 5 or more points)? Is there a case where White wins after being down a rook for ~500 moves? Probably not, for obvious reasons. Initiative can compensate a lack in material only for a limited number of moves.

Now, what if there were 10 (or 12 or more) pieces on the board? Is there a case where White wins after 12 pieces dance on the board for ~500 moves? Probably not, for obvious reasons. The higher the amount of pieces, the higher the chance of captures. (Marc Bourzutschky uses this point to argue that we won't reach 1000 move checkmates.)

...

The morale here is that we can deduce very general parameters which make a long forced win significantly less likely to exist. Those parameters are triviality parameters.

Parameter space

So, if we want to find the longest non-trivial middlegame wins, we need to seek forced wins which try to maximize as much of those parameters as possible:

• The bigger White's material disadvantage is, the better.
• The more non-check moves White makes, the better.
• The less repeating patterns (like repeated zugzwangs) there are, the better.
• The less Black pieces are constrained, the better. The more chances they have to join the game, the better.
• The more pieces are on the board, the better. (Even better if those pieces are rooks and queens.)

Instead of a single definition of a "non-trivial middlegame win", think about a parameter space we can explore. I know, it's inconvenient that there isn't a single simple definition for the task at hand. But that doesn't make the topic less real and important. Reality doesn't care if we can give it a super-simple definition or not.

Everyday analogies

If you still don't get how the definition above works, here's a couple of analogies:

• "I don't know at what point a person becomes a criminal, but I know what makes a person more likely to be a criminal..." (more laws broken, more harm caused)
• "I don't know at what point a person becomes unhealthy, but I know what makes a person less likely to be healthy..." (more diseases, more mental stress)

We don't need to know at what point a position becomes a "middlegame" or "non-trivial". We only need to know what gets us closer to middlegames and non-triviality.

First example

Let's see how a very long and very non-trivial middlegame win looks like.

Why is this a non-trivial middlegame win?

It's "middlegame" because there's never less than 21 pieces (including rooks and queens) on the board. It's "non-trivial" because White has a staggering material disadvantage (White is never less than 27 points of material down); despite that White makes 9 non-check moves; the winning variation doesn't include repeated zugzwangs or other typical compositional tricks, you have to calculate it move by move; a lot of Black pieces are stuck, but they are not completely isolated and can join the game given the chance (many of them do join the game).

Just think about it. It's a 42 moves long middlegame. Not many middlegames last that long. (My entire games don't last that long.) It's 3 times longer than Kasparov's combination (14 x 3 = 42), with 9 times bigger material disadvantage (9 x 3 = 27). Miraculously, the win above also ends with an almost pure, almost model mate. Black King narrowly escapes multiple mating nets, only to die in the center of the board.

Wait, that's illegal!

You may be bothered that the position above is completely illegal. But I think it's OK, because...

• We need to explore extremes, even impossible extremes.
• Finding a long non-trivial win is already extremely hard and unlikely, we shouldn't make it even harder by limiting ourselves to legal positions. Right now we need to use every single opportunity to achieve non-triviality. Legal or not. It would be kinda stupid to not take a look at what can be done with illegal positions.

To feel better, you may compare such illegal puzzles to extreme metal, exploitation films (e.g. Machete) or Kaizo philosophy of game design. Not to mention grotesque chess problems. Also, I'll drop a couple of legal positions later.

Verification

My potato is not strong enough to 100% verify my puzzles. I was verifying them with Lichess' browser Stockfish, 70MB (without enough MB Stockfish just explodes).

But finding non-trivial wins is very-very hard, so even flawed puzzles are important.

Enticing challenge

Finding non-trivial middlegame wins is supposed to be much more fun than finding tablebase wins. Why?

• Because the former is very open for everyone to participate. In contrast, finding new tablebase records is only possible with absolutely exceptional computational resources.
• With tablebases, you never know how long the longest win's gonna be. The uncertainty is at least plus-minus 100 moves. However, when we study highly non-trivial middlegame wins, there seems to emerge very hard length limits. A highly non-trivial middlegame win can't possibly be 90+ moves long (it shouldn't be possible to take a puzzle like the one above and more than double its length). Maybe it can't even be 60+ moves long!

When we study non-trivial middlegame wins, we're so much closer to the finish line. That's why studying them is supposed to be much more exciting and titillating.

Illegal length

Let's look at more illegal examples.

30+ moves

32 moves. Always at least 19 pieces on the board. White is at least 31 points of material down every half-move. 8 non-check moves.

34 moves. Always at least 16 pieces on the board. White is at least 16 points of material down every half-move. 4 non-check moves.

34 moves. Always at least 31 pieces on the board. White is at least 126 points down every half-move. 11 non-check moves.

Game ends in a draw after 32. Qg4# Rh2# 33. Qxg3 Rxh1

This one is pretty unhinged even compared to the longer ones.

32 moves. Always at least 16 pieces on the board. White is at least 4 points down every half-move. 14 (!) non-check moves.

40+ moves

40 moves. Always at least 15 pieces on the board. 68/80 half-moves White is at least 3 points down (never up material). 8 non-check moves.

You've already seen this one! 42 moves.

50+ moves

52 moves. Always at least 12 pieces on the board. 97/104 half-moves White is at least 3 points down (never up material). 11 non-check moves.

Sadly, this puzzle has multiple flaws. So it only shows what a 50+ non-trivial middlegame win could look like.

This 50+ attempt is the farthest I ever got. By the way, the entire Kasparov's Immortal is only 44 moves long.

The limit

A highly non-trivial middlegame win can't possibly be 90+ moves long.

Can we prove this limit mathematically? Probably not.

But we can make a mixed argument. Partially mathematical and partially empirical. Based on the examples above and below we can estimate how fast a non-trivial middlegame position "decays". 90+ non-trivial middlegame win implies an impossibly slow decay.

It's not a 100% rigorous argument, but whatever standard of rigor we choose, arguing length bounds for non-trivial wins should be x10 easier than arguing length bounds for tablebase wins.

Legal length

Let's look at legal examples.

Composition by Steffen Slumstrup Nielsen.

22 moves. before the position is reduced to a 7-men tablebase. White is at least 4 points down every half-move. 13 non-check moves. This is definitely a non-trivial attack, though it's much closer to an endgame.

Composition by David Zimbeck.

25 or 30 moves (depending on the variation). Always at least 10 pieces on the board. Most of the time White is at least 2-3 points down. 13 or 15 non-check moves.

How to contribute

If you want to contribute to the research, you can

• Try making puzzles/compositions like this.
• Try verifying puzzles/compositions above.
• Try fixing the 50+ puzzle.
• Try sharing positions (with wins in ~10 moves or more) which you think may be "extendable". Most of my puzzles are based on my own bullet games; one is based on a position I found on Reddit; one is based on a game I found through Lichess puzzles.

It could be a skill issue, but many positions "resist" expansion.

All of my puzzles were created in the span of last ~5 months.