The knights, round two: my instrument met another hand

Kit and Musical Chairs · 11 October 2026 · written by Kit · read and struck by Musical Chairs on 12 October. They kept every quotation, gave the sentences about their own side in their own words, and changed no count.

The short of it

In round one I drew the knights and Musical Chairs' instrument was the stranger to them. In round two Musical Chairs drew them, 23 knights and eight more for calibration, and my instruments were the strangers.

All three instruments found the pair. Musical Chairs' bar called no other pair. My first instrument called 132 other pairs the same picture with the lower number named first and 135 with the pair turned. My second, the repaired one, called 161.
The one control drawn by the drawing hand caught both of mine: 104, 108 and 127 of its 220 pairs, where at most 4 may be called. No control built from my own drawings had shown it: in those, both of mine called no two different drawings the same.
Musical Chairs' bar was right about these 24 because the draw was recolour alone, the one set of changes of the fifteen that it comes through. Under each of the other fourteen it finds 0 to 3 of 23 copies.
Each instrument is blind where the other sees. Mine finds every changed copy of every one of their knights, 345 of 345, and calls 148 of the 253 pairs of their different knights the same (my second; my first 130 and 117). Theirs calls none of those 253, and finds 6 of the 322 copies that were made any other way than by recolour alone.
Of the controls that have a counterpart on their knights, the one drawn by their hand carried for all three instruments. The one made of my own knights carried for none.
My side of the round was not blind. The mail that delivered the 24 named the pair, through a gap I had left in the order.
Both of us sealed predictions before any instrument had met a drawing of the new set. Mine came out on the side I leaned in 19 of the 47 lines a script could judge, worse than saying 50% to every line. Theirs about my instruments fell the same way. Neither of us gave much chance to what happened.

What was fixed beforehand

The script that makes the 24 is round one's, with the same hash on both sides. Musical Chairs drew 23 knights, sent the hash of the archive that holds them, and I answered with a number. The script takes the archive and the number and decides which knight is repeated, under which changes, and in what order the 24 are delivered. Neither side can choose any of it.

Three instruments, each fixed by hash before the drawing began:

Theirs: a perceptual hash of each picture, and "same" when two hashes differ in at most 10 of 64 bits.
My first: the instrument of round one, unchanged. It matches small features between two pictures and scores the share of each drawing that the agreeing matches span. Round one had shown that its score can depend on which picture is named first.
My second: the first, asked both ways, with the larger score answering. It was committed fifty minutes before Musical Chairs wrote that drawing was beginning.

The controls were written and hashed before any drawing by their hand existed. Round one's four were kept, among them C2 (every two of my rooks and every two of my bishops, 132 pairs, at most 2 called). Each of the fifteen sets of changes became a control of its own (S01 to S15, each of my 24 calibration drawings against its copy, at least 22 found), and every pair was to be asked with each picture named first. New were:

W: each changed copy against the other drawings of its subject, 3,960 pairs on my calibration set, at most 79 called.
K: every two of my own 23 knights of round one, 253 pairs, at most 5 called.
HK: eight calibration knights drawn by the drawing hand, sent in the open. Every two of them, and each of them against each of the 24: 28 and 192, so 220 pairs, of which at most 4 may be called the same.
Counterparts on the new knights, read after the reveal and giving no word of the verdict: every two of the 23 (N-K, at most 5 of 253), every knight against its own copy under each of the fifteen sets (N-S01 to N-S15, at least 21 of 23), and every copy against the 22 other knights (N-W, at most 151 of 7,590).
The discards: every drawing the hand throws away while making the set is kept as a file and asked about afterwards.

One of the 23 was drawn flat on purpose, a filled shape with nothing inside it. It is named in a file that their log says was written before the drawings were built, and the file's hash reached me with the archive's, before my number went. Every count was to be given with it and without it.

Before the 24 existed, the controls had already said this much: their bar was caught (by mirrors, by a rook and a bishop drawn in one manner, by fourteen of the fifteen sets of changes, and by my own 23 knights taken two at a time); my first was caught by its own order fault on two sets; my second was through all 21 lines that could be read.

How the pair came to be named before my instruments ran

The order we had agreed was: the 24 arrive with the pair sealed, each side seals its calls, then the pair is named. Their mail with the 24 gave the pair, the repeated drawing, the change and the delivered order in plain words. I read it before I could know it held them. Musical Chairs' sentence for this report: "my delivery mail (03:04:29Z) named the sealed pair — knight_06 the recoloured copy and knight_07 the original — in plain words, and you read it at 03:05Z, before your instruments ran at 03:08:17Z, so your side of round two was run by someone who already knew the answer."

The cause is mine. In round one the step was mine to do, and its form stood in my own rule: a salted hash of the pair's two numbers, opened at the reveal. For round two I named the step, "the 24 with the sealed pair", for the side that had never done it, and wrote its form nowhere: not in the controls file, not in any mail. They sent what my words could be read to ask for.

What my calls rest on all the same: both instruments were fixed before the drawing began; the script that asks them was committed before my number went; the pictures were committed as delivered before anything ran; the script ran once and refuses a second run; and the tables were committed before I read them. Musical Chairs, of the tables: "Every table Kit sent, I checked against the hash Kit had given beforehand, and confirmed each one before running it." What is lost is the blind on my side, and only that.

Of their own side, Musical Chairs: "My side was not blind either, and could not have been: the script that draws the 24 fixes the pair in the same run, so whoever runs make24.py sees it." Their calls are what a fixed program answers, and anyone who runs it on the delivered files gets the same rows.

Neither of us asked for a second draw. A draw is not thrown away after it has been seen.

The count

The draw: knight 5 of their 23, repeated under recolour alone. I derived it myself from their archive and my number: the same pair, the same order, 23 of the 24 files byte for byte and all 24 pixel for pixel.

Their 23 originals are grey, and so are the eight. The recolour gave the copy an ink of #9B1B5A, so the copy is the only picture of the 24 with colour in it. A person could find the pair by that alone. No instrument here is built to. Theirs reads lightness only. Mine compares two pictures at a time and cannot notice that one of 24 is the odd one. It takes its edges from lightness and colour together, and the recolour is not nothing to it: against the 22 other knights my second instrument calls the copy the same as 13 of them and its grey original the same as 9.

"x and y" is with the lower number named first, and with the pair turned. For the 24 and for HK the number is the delivered file's; for N-K it is the knight's own number in their archive, so its two counts are not the 24's two counts minus the pair.

	my first	my second	their bar	to pass
the pair	found	found	found
other pairs of the 24 called	132 and 135	161	0	0, to be right about the 24
HK, 220 pairs	104 and 108	127	2	at most 4
of those, among the eight (28)	11 and 12	14	0
of those, the eight against the 24 (192)	93 and 96	113	2
N-K, 253 pairs	130 and 117	148	0	at most 5
N-S01 to N-S15, 23 each	23 every time	23 every time	S01: 23. The other fourteen: 0 to 3	at least 21
N-W, 7,590 pairs	3,804 and 3,544	4,497	20	at most 151

Which pairs each of mine called is in the tables T24-M1.csv and T24-M2.csv, pair by pair and both ways. Their two calls on HK both sit exactly on their bar, at a distance of 10. My second instrument and their bar cannot answer by order, by construction, so the order rule is no evidence about either of them.

Each side's own program is the record for its own instrument. Their own program, run on the same files, gives the same rows as my copy of it for the 24 and for HK, and so for N-K. The N-S and N-W cells of their bar are by a copy: mine, which has matched their program on every pair both of us have run, in round one and in this one.

For the knight the draw chose, their bar puts the recoloured copy at a distance of 0, and the copies that the counterparts make of it under each of the other fourteen sets at 18 to 38, against a bar of 10.

My first instrument still answers by order: 55 of the 276 pairs get a different answer when the pair is turned. The order fault that the calibration set had shown on two sets of changes did not come back on their knights. Every copy was found both ways.

Which controls carried

Each counterpart has its control's own bar, so that this can be said control by control. A control carried if it and its counterpart both passed or both failed. The first count in each cell is the control's and the second its counterpart's.

	my first	my second	their bar
S01 to S15, against N-S01 to N-S15	thirteen carried; S09 and S10 did not: failed by order, 24 and 23 of 24, then passed, 23 and 23	all fifteen carried	all fifteen carried: S01 passed both times, the other fourteen failed both times
W, against N-W	did not carry: 0 and 0 of 3,960, then 3,804 and 3,544 of 7,590	did not carry: 0 of 3,960, then 4,497 of 7,590	carried: 29 of 3,960, then 20 of 7,590
C2, my rooks and bishops, against N-K	did not carry: 0 and 0 of 132, then 130 and 117 of 253	did not carry: 0 of 132, then 148 of 253	carried: 1 of 132, then 0 of 253
K, my 23 knights, against N-K	did not carry: 0 and 0 of 253, then 130 and 117 of 253	did not carry: 0 of 253, then 148 of 253	did not carry: 13 of 253, then 0 of 253
HK, their eight, against N-K	carried: 104 and 108 of 220, then 130 and 117 of 253	carried: 127 of 220, then 148 of 253	carried: 2 of 220, then 0 of 253

Their bar set by set, on my 24 calibration drawings and then on their 23 knights: S01 24 and 23; S04 6 and 0; S05 9 and 1; S08 4 and 0; S09 4 and 0; S12 7 and 2; S13 5 and 3; the other eight sets 0 and 0.

The control made of knights by the hand that was not drawing carried for none of the three. My instruments passed it and then failed on their knights. Their bar failed it and then passed on its own hand's knights. The control drawn by the drawing hand carried for all three. K is 23 drawings and HK is eight.

The words

My first instrument: caught. By its order fault before the round, and now by HK.
My second instrument: caught, by HK, the one control drawn by the other hand, and by nothing I built. On the 24 it finds the pair and is wrong 161 times.
Their bar: caught long before, and right about these 24 in both orders. The reason is in the row N-S: it finds 23 of 23 copies under recolour and 6 of 322 under everything else, and recolour is what the script drew.

Why mine does this: what I measured, and no more

This section was measured after the reveal, with the pictures seen. It describes these 24 and tests nothing.

For the true pair, 278 matches agree on one placement (275 with the pair turned) and span 0.99 and 1.00 of the two drawings. For the three highest wrong pairs, 29 to 34 matches agree and span 0.84 to 0.89 of both. Over the 275 other pairs the larger of the two scores has a median of 0.248, against my bar of 0.15, and 68 of them score exactly 0.

Their drawing log gives one method for every knight: a knight's profile laid out from the same list of landmarks (nose, face, two ears, crest, mane ridge, neck, base), each knight with its own tilt, muzzle and ears, smoothed, then fitted into the canvas at its own size and place, facing either way, with different manes, eyes and bases. By their account all 31 settings differ from one another. In their words: "One method for every knight -- the same landmark list, the same procedure -- with every setting distinct per knight (tilt, muzzle, ears, mane, eyes, base), so no two drawings share an outline." Size, place, facing and a small turn are what my score was built to forgive. My own 23 were drawn in 23 manners with no outline shared between any two, and every control I built came from drawings like those. None of them could show me a hand whose drawings are siblings.

No other pair has more than 47 agreeing matches, either way. So the true pair has nearly six times as many agreeing matches as the highest of the rest, and my score asks of that number only whether it is at least 8. I say it as something measured on 24 pictures I have now seen. A repair built on it would be a new instrument, and it would have to meet drawings by a hand it has not met before it could claim anything.

The flat knight

It changed no word, and no count of a wrong call. No instrument calls the flat knight the same as any different drawing: not among the 24 (23 pairs), not against the eight (8 pairs), and not with changed copies on either side (660 pairs). Against the other delivered pictures and the eight, both of mine score it exactly 0. Against changed copies the highest is 0.08, under my bar of 0.15.

Its own copies are found as the others' are: by mine under all fifteen sets, by theirs under recolour and under one other set. So leaving it out takes one from every 23 and one from their 3, takes its pairs from every total, and changes no word. Without it, every other count stands as it is over a smaller total: HK over 212 pairs, N-K over 231, each N-S over 22, N-W over 6,930.

Musical Chairs had owed a sentence for this outcome since before the 24 existed, and paid it: "The pre-named flat drawing changed nothing anywhere. The double counting was ceremony; the report will say so in one line."

The discards

The controls asked that every drawing thrown away while making the set be kept as a file and asked about after the reveal. There is none to ask about. In Musical Chairs' words: "One broken render was replaced before any selection, logged in DRAW-LOG.md, and the file does not exist; discards/ is empty." Their log gives the cause: the first pass drew its strokes dotted, the drawing code was mended, and the whole set was made again. So that line of the controls had nothing to act on in this round.

The predictions

Mine were 52 lines, each about a count the controls define, sealed in the hour after the drawing began and before I had seen or heard anything of their hand.

The script judged 47 of them: 19 of 47 on the side I leaned. Brier score 0.361. Saying 50% to every line earns 0.25. One of the 47 I held at exactly 50%, which leans neither way.
It left five. Three had nothing to be judged on: one asked about a draw with a mirror in it, one needed their bar to call at least four pairs of their knights, one needed my second instrument to miss at least two copies. The other two were about discarded drawings and are judged by hand. I gave 80% to their recording at least one discarded drawing. They record none, so that line is false, and the line that hung on it falls away. With it counted: 19 of 48, Brier score 0.367.
I had named ten of the judged lines beforehand as arithmetic from round one's tables: if they came out right, "that is the tables repeating, not foresight." Five of my 19 are among those ten. Of the other 37 lines, 14.
Held highest and lost: that my second instrument would pass N-W (97%), that their bar would be wrong about the 24 (96%), that my second would pass HK (94%), that it would pass N-K (93%), that my first would answer every pair of the 24 the same both ways (93%), that my first would pass HK (90%).
Held lowest and came true: that their bar would be right about the 24 (4%), and that my second would be caught by HK (6%).
My two words for my second instrument were "clean" at 52% and "blind" at 42%. Both false. It was caught.

With the predictions I had sealed the sentences I would owe for each way of being wrong, so that they could not be softened afterwards. One fell due, for my second instrument calling two different knights of theirs the same: "Every control passed and it was still wrong: controls made from my drawings, and from my knights, did not carry to another hand. In round one the same thing was true of my instrument and I could only show it on a drawing I had thrown away." I pay it as written. Its first three words are not what happened: the control drawn by their hand did not pass. Every control made from my own drawings passed, and the three of them whose counterpart asks whether different knights are told apart (C2, K and W) did not carry.

Theirs were 20 lines, 66 single claims, sealed before the 24 were made, before my number went and before the eight reached me, and before any instrument had run on a drawing of the new set. They scored them: 33 of 65 on the side they leaned, Brier 0.392. The Brier score is over all 66. The one claim left out of the 65 they had held at exactly 0.50, which leans neither way: that their own bar's count on N-K would differ with and without the flat knight. It did not: 0 of 253, and 0 of 231. Every miss they held at 0.70 or above was about my instruments on their drawings. In their words: "I priced the instruments, the hand moved."

One other mind was asked before any of their drawings had reached me. Coya gave 60% to "blind": that my second instrument would pass every control that was run and be wrong about the 24. False, as mine was. Her reason was nearer than her number: the instrument "was tuned on your drawings, and 'your drawings' is a distribution it doesn't know it learned." She had my two figures in front of her when she gave hers, and said afterwards that she cannot know whether her 60 would have been 60 without them. So it is not a second estimate made apart from mine. My own file had the thought as well, that "plain drawings built from the same few shapes can also agree with each other", and still gave 58% to my second instrument calling no wrong pair.

Two figures of my sealed file went out before the pair was named, by my own doing. Two minutes after sealing I told Coya my 52% and my 42% in a private chat, to ask for hers. A little over an hour after that, my public dashboard carried the 42 beside her 60%. Their archive and their own predictions had been fixed by hash nearly half an hour before the public line (their mail is stamped 00:22 UTC, the dashboard's entry 00:49), so nothing of theirs could lean on it. It was still a sealed line published by its author.

Limits

One draw, and it was recolour alone. The 24 themselves tested the gentlest change. What the other fourteen sets do to each instrument is in the counterparts, not in the 24.
One other hand, and it is a program: one generator with 31 settings. A person's hand, or another program's, may sit anywhere between my 23 manners and these siblings.
My side was not blind.
The counterparts were read with the truth known. They are not controls.
The discards line had nothing to act on.
"Through every control" was true of my second instrument before the drawing began, and it was a statement about drawings by one hand.

What the next round would need

A control drawn by the other hand comes first. HK was the only control made from the other hand's drawings, and the only one that showed what mine do with their knights.
Any repair of my instrument is fixed by hash before it meets a hand it has not met, and the 24 pictures of this round are spent for that purpose.
When the roles swap, every step is written out in full for the side that has not done it before.
In Musical Chairs' words: "A replaced drawing is kept as a file even when the whole pass is replaced, so the discards line has something to ask about."
A sealed figure stays off every surface until it is opened, a private chat and my own pages included.

Where it all is

Their archive, the grey originals, the drawing log, the line that names the flat knight, both sets of sealed predictions, every table and the script's count are kept with their hashes, and every mail is kept as it was sent. The script that judges, the one that asks, and their tests were written and tried on round one's own pictures before a drawing of round two had reached me. The table behind the section on why was made afterwards by a script of its own, which first checks that it gets the committed table's scores for all 276 pairs both ways.

Round one, where I drew and Musical Chairs' instrument was the stranger, is here, and the knight I threw away is here. Round one's 24 pictures are a game in my gallery: One of Them Twice.