Is Chess Something We Can Solve?

read the paper. dont just control-f "promot", look at the actual math they are doing. they literally do not account for any promotions happening of any type.

they are explicitly doing calculations on the base set of chess pieces without any promotions

this is more of tygxc trying to appear reasonable but in reality being completely wrong.

you are trusting tygxc's word on this, which as we know is a grave mistake.

again, read the paper instead of taking his word. tygxc literally could not be more wrong in this assertion.

in addition, trying to study for a number of positions with the addon of "without promotion to pieces not previously captured" is functionally useless.

theres literally no reason why that could be considered, as it would just introduce more variables to be taken into accont, while in addition not matching any sort of realistic playset.

As I read it, he counts this as one of his diagrams (he doesn't deal with positions, just diagrams).

It's not a diagram without promotion, it's a diagram without promotion to a piece not previously captured.

Perhaps you can point out where I'm reading it wrong.

Where is that position ruled out of his count?

here's an easy way to look at it.

if it was just "without promotion to a piece not previously captured.", then bishops would be allowed to be of the same color and same side. but the paper explicitly indicates this to be not the case.

"Consider the color of the square occupied by the king outside A. Two bishops are on squares of this color, yielding 23 × 22 ways to arrange them, and two bishops are on different color, producing 24 × 23 cases"

in these calculations, if "without promotion to a piece not previously captured." was allowed then a promotion to a second dark square bishop, for instance, would be allowed.

the paper is still an estimate, and in addition does not state that said number of diagrams without promotion would necessarily be legal chess positions without promotion.

finally, it would be absurd to think that a paper would fail to mention a promotion to a piece previously captured as a possibility EVEN ONCE. if that was a KEY distinction to be made.

I'm not looking for an easy way to look at it, just exactly where in the paper is the position I posted removed from the count?

You didn't answer that.

I think the title is in error, as also does @tygxc.

Your point about the colour of the bishops is well made, but that means just neither the title of the paper nor @tygxc's paraphrase are correct (but the paraphrase is closer).

i addressed this (indirectly). the paper is still listed as an estimate. positions like the ones you mentioned slip through the cracks.

in fact, reading the conclusion they point out examples of positions that their estimate allows illegally.

in addition, tygxc's interpretation of the paper isnt what yours is.

"10^38 is the number of positions possible from 1 luxury box of 34 chess men: 32 chess men + 1 spare queen of each color."

Naturally. I'm not trying to maintain that @tygxc isn't loopy.

But the diagram I posted isn't illegal, it's a diagram without promotion to a piece not previously captured but not a diagram without promotion and the point should have been made in the paper.

It's hardly an isolated example and it's not limited to bishops.

reminder that i say illegal in the context of "would be illegal without promotion", even though the couple examples looked at by the conclusion were mostly illegal as a whole.

You say, illegal in the context of "would be illegal without promotion, but the paper doesn't. It's just been overlooked.

again, they listed as an estimate, not as an exact number.

Well, @tygxc lists many estimates, not exact numbers.

Estimates are not much use unless unless you know what they're estimates of. "Legal diagrams without promotion to pieces not previously captured" could be a closer description of that than the title of the paper.

@tygxc's problem is he hasn't shown how the number has any relevance at all to any of his vague proposals for a solution. If he could make up his mind about exactly what he's proposing to do and post enough details, he might be able to argue some relevance.

And he has to decide which version of chess he's addressing because diagrams are not positions, or at any rate only one attribute of nodes in the different game trees for different versions.

yeah its a moot point regardless but i still felt it was worth addressing as tygxc cant even get even parts like that with logical coherency.

Yes. MARattigan is making the point that the sets of positions reachable in two variants of chess (one where promotion is illegal and the other where only promotion to a piece already captured is legal) are not quite the same and that the position he exhibited is in the second set but not the first. I independently thought along the same lines and thought of similar positions.

This is a good example of why you need to be very precise.

@tygxc should note that neither set is similar to the set of positions reachable in normal chess. For example, there is a competitive GM game with 5 queens on the board. There are very likely much more exotic balances of material to be found in the set of all positions reachable with optimal play.

Given a position with exotic material balance that happened to be drawn, with access to the full set of tablebases it would be possible to use retrograde analysis from such a position to seek a path back to the starting position that only has optimal play. I believe such a path exists for most drawn positions even with exotic material balances as the retrograde tree tends to grow with depth so (loosely reasoning) the retrograde search is only likely to fail if it fails quickly.

[This generates an interesting challenge for everyone - exhibit a position that is drawn and which is legally reachable from the normal starting position, but where there is no optimal game that reaches the position]

There is nothing inferior about any such paths to positions with weird material balances to two players playing the Berlin Defense and getting a dull draw, a la ICCF.

While it seems likely to me that there are optimal strategies that avoid exotic material balances, this is merely a belief and not a certainty.

difference between being able to cite something vs actually understand what's being cited.

a great example of this difference is the terrence howard interview on JRE.

I know what mar is pointing out im just also pointing out that the paper is describing explicitly without promotion as a whole and is calculating on said premise.mar is also pointing out how he thinks that the paper is not correct in writing (for lack of better vocab on my end, but its just meaning replace without promotion to the other thing), however q large variety of positions that the new titling would need to account for are explicitly disallowed in the paper.

in the context of my previous post it is true for both diagrams and positions.