Opening advantages from a tablebase point of view?

[andytoh]

How do the advantages for White obtained from opening theory show up from a tablebase point of view? Let's say there is a position where opening theory strongly believes a certain move gives White a slight advantage. Let's suppose that chess is also fully solved. Does the position change from 1/2-1/2 to 1-0 (assuming a draw from the start)? If not, then how is it mathematically an advantage? Does it go to another drawn position where there are significantly more losing choices for Black than before? Since chess is not fully solved, then no one here will know the answer, but I was just wondering what people's guesses are.

[kronsteen]

The fact is, the notions of good looking position, promising start, having an advantage, etc… disappear completely in the world of fully solved games such as (currently) any chess position with 6 pieces or less.

As soon as perfect knowledge becomes available, every position gets a definitive assessment : win, loss, or draw. Wins and losses can be described more accurately with a “true” metric (Distance to mate for example). On the other hand, draws are something like a vast empty world where all positions are equal to each other (value = 0), the “advantage” a side may have being not relevant as an opponent with perfect knowledge will always be able to defeat any winning attempt. If one side has access to perfect knowledge and plays against an opponent who has not, he will rely on traditional evaluation to try to win a position he knows to be drawn.

Metrics for theoretically drawn positions would more or less necessarily refer to the probability of either side making a mistake (i.e a move changing the evaluation of the position from draw to loss), or inducing such a mistake from the opponent, both notions becoming meaningless as soon as perfect knowledge can be accessed.

Speaking of a “promising start for White”, if chess were fully solved, the resulting position would be either a win for White, or a draw. If it is a win, an if the initial position of the game is a draw (the majority opinion among players), it means that at least one black move leading to this position is defective as it changes the evaluation from draw to loss, and it is this move who has to be fixed. If it is a draw, it is possible that no mistakes from either side have been made so far, and as explained above, all winning attempts from White in a perfect knowledge world are destined to fail, and its practical chances necessarily refer to its capability to force lines of play requiring difficult-to-find Black defence, a notion related to human (or chess engines) behaviours and weaknesses, who are subjective, evolutive, and therefore not suitable for measure by a definitive & mathematically defined metric (who could be used as a metric for draws in EGTBs for instance).

[ernest]

if chess were fully solved, the resulting position would be either a win for White, or a draw.

That's what most people "think", but it cannot be proven today it isn't a win for Black (zugzwang, ...)

[Matt]

Sure would be fun to pair a 32 man tb with a chess engine giving it about half a second to analyze the position, then play the worst possible scoring move that does not change the position from the TB knowledge of winning to draw (Even by repetition / 50 move rule) or draw to loss ... To me at least, it would make for hilarious positions, crazy commentary and making some good natured fun of the game. Some of these mate in 300's I have looked at with the EGTB's don't make a bit of sense to my human mind (I really don't see what is being forced), can't imagine what a full blown game could look like against such a setup.

[andytoh]

Metrics for theoretically drawn positions would more or less necessarily refer to the probability of either side making a mistake (i.e a move changing the evaluation of the position from draw to loss), or inducing such a mistake from the opponent.

That's the closest I can think of for a metric for drawn positions as well. Clearly not all drawn positions are equal (assuming neither side has access to perfect knowledge). The problem with using probability is that, for example, a drawn position where one side has only one correct move choice for the next 10 moves to maintain the draw may seem like a position with a high value for the other player (the probability of maintaining the draw being low if moves were chosen at random), but may actually not be if the next ten correct moves are actually quite obvious to any decent player. So using probability trees cannot be a good choice of a metric for drawn positions, simply because moves are not chosen at random.

[andytoh]

After studying immense amout of opening theory, I have to conclude that not only is chess drawn from the beginning, but almost all moves in opening theory that are not given a ? by opening theorists result in tablebase draws. Moves that are given ? or even ?! by opening theorists may or may not lead to a forced checkmate (i.e. a win) for the other side, and these are the only positions we would need tablebases for. Moves that are given a !, but not preceded by a ? or a ?! for the other side (i.e. a good plan is found but the other side has hitherto made no strategic error), mostly still result in a tablebase draw. This is just my opinion.

[kronsteen]

About notations :

In EGTBs, a "?" is a move that changes (always downwards for the side making it) the evaluation of the position : win to draw, draw to loss, or win to loss. A “!” is a move that is not the unique legal move but is the only one who doesn’t change the evaluation of the position.

Without EGTBs, “?” is a bad move, “!” a good move, and there are some refinements (?? = blunder, ?! = dubious, !? = interesting, !! = brilliant). If human analyses were perfect (but they are not), ? and ?? would change the evaluation of the position and other moves would not. On the other hand “!” moves are not meant the same way in both cases (as a “!” move in EGTB sense can be absolutely evident).

Unfortunately for theorists (and fortunately for the game), 32 piece EGTBs will never exist, and we can only guess what the truth would look like should the game of chess be fully solved. By observing what previous human assumptions about theoretical results for chess endings were and how EGTB knowledge have altered them, my own guesses (but these are nothing more than guesses with absolutely no firm scientific arguments) about the theoretical result from beginning chess positions would be that :

- the initial position is drawn

- all 20 initial possible white moves still lead to a draw, even 1. f3

- on the other hand, I would bet that when a side gets an advantage, the transition from a theoretical draw to a theoretical forced win would come faster than expected. I would not be surprised that beginnings such like 1. e4 a6 2. d4 would be already won for white, and maybe even dubious-but-not-so-silly black starts such like 1. e4 b6 2. d4 Bb7. Being one pawn ahead in no inferior position results almost certainly in a win, the theoretical limit would be probably somewhere between 0.3-0.6 pawn in standard evaluation

- when a position becomes a win, the distance to mate (DTM) would most often be “reasonable”, in the 30-100 move range. The fact that the longest DTM in EGTBs roughly doubles with every additional man (127 moves with 5 men, 262 moves with 6, 545 moves with 7) doesn’t mean that huge numbers will be commonly reached with many more men, and I would bet that DTM for “won but very close to draw” positions could sometimes exceed 100 moves, but this would be uncommon, and cases with DTM>150 would exist but would be extremely few.

- If both sides play an optimal DTM strategy from a won beginning position, the almost universal scenario would be that an equilibrium (at eval =-0,4 for the losing side for instance) would settle for some time, then the position of the losing side would start to visibly deteriorate after what he would be quickly finished off. From a “randomly chosen” initial winning position, he time needed for the losing side’s position to start to crumble would be a decreasing exponential (in probability), explaining the above statement that very long wins would be very exceptional.

[guyhaw]

Draws do not have a depth in the DTM (depth to mate) metric.

However they _might_ have a depth in the DTZ (depth to move-count zeroing move) or even DTC (depth to conversion and/or mate) metrics.

Back as far as 2002, I certainly wanted to distinguish between draws which had DTx-depths and those that did not in my investigation of the Reference Fallible Endgame Player.

Endgames played out by engines (either constrained not to lose a half-point, or not) indicate how good an engine is at attacking or defending in a specific endgame.

g

[kronsteen]

Draws do not have a depth in the DTM (depth to mate) metric.

However they _might_ have a depth in the DTZ (depth to move-count zeroing move) or even DTC (depth to conversion and/or mate) metrics.

Yes, and many other metrics for draws could also be built under the following rules :

- both sides are always constrained to playing drawing moves

- the goal of the game, instead of mate, is some kind of event “E”. For example, E could be : pushing a pawn up to xth rank (or queening it – if x=8), converting to another endgame, delivering stalemate… . There are, in fact, two possibilities :

1) One side tries to make “E” happen (as fast as possible if he can) and the other side tries to prevent “E” from happening (or delay it as much as possible if he can’t)
2) Both sides try to make “E” happen for them before the opponent does the same for him, and if they can’t try to prevent the other side from doing so. This implies that “E” is not a board-related symmetrical event (for example a conversion move by either side), but a side-related event (for example delivering stalemate)

DTC / DTZ for draws can in fact fit in either possibility. In the first version, White tries to make a conversion / zeroing move happen (even if it is a black move) and Black tries to avoid this. In the second version, both sides try to make themselves the conversion / zeroing move and before the opponent does.

Many interesting problems in chess endings could be investigated by using such metrics with different setups for E. Here are some :

Up to which rank is White able to push his pawn in endings such as kqpkq, krpkr… even if the initial position is drawn ? : set E to “White pawn reaches xth rank without being captured immediately”.

On which positions in various endings (krbkr, krnkr, kqnkq, krpkb, krppkr…) is the defender forced to rely on a stalemate trick in order to save the game ? : set E to “deliver stalemate”

[Kirill Kryukov]

Yes, and many other metrics for draws could also be built under the following rules :

- both sides are always constrained to playing drawing moves

- the goal of the game, instead of mate, is some kind of event “E”. For example, E could be : pushing a pawn up to xth rank (or queening it – if x=8), converting to another endgame, delivering stalemate… . There are, in fact, two possibilities :

1) One side tries to make “E” happen (as fast as possible if he can) and the other side tries to prevent “E” from happening (or delay it as much as possible if he can’t)
2) Both sides try to make “E” happen for them before the opponent does the same for him, and if they can’t try to prevent the other side from doing so. This implies that “E” is not a board-related symmetrical event (for example a conversion move by either side), but a side-related event (for example delivering stalemate)

I did exactly this for 3x3 chess: When in a drawn position, both side's goal becomes to stalemate as soon as possible (or to delay being stalemated). This allows to create "Stalemate in N" problems, which can be quite fun. It also allows to define the "longest stalemate" position. Stalemate in 14 moves is the longes in 3x3 chess. (Example)

I did not do this for 3x4 chess, but it should be doable, because I guess that the combined stalemate + checkmate metrics will still fit within one byte.

Best,
Kirill